Derousseau's Generalization of the Malfatti circles

Equilateral Triangle

\(a:b:c=1:1:1\), \(A=60\degree\), \(B=60\degree\), \(C=60\degree\).


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Reference Triangle

reference triangle

Triangle Centers and their Extraversions

Approximately,
\[ \begin{alignedat}{4} I&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ I_{\mathbf{a}}&{}\approx{}&-1.000000000000&{}:{}&1.000000000000&{}:{}&1.000000000000&,\\ I_{\mathbf{b}}&{}\approx{}&1.000000000000&{}:{}&-1.000000000000&{}:{}&1.000000000000&,\\ I_{\mathbf{c}}&{}\approx{}&1.000000000000&{}:{}&1.000000000000&{}:{}&-1.000000000000&. \end{alignedat} \] \[ \begin{alignedat}{4} P&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ P_{\mathbf{1}}&{}\approx{}&0.005102175003&{}:{}&0.005102175003&{}:{}&0.989795649994&,\\ P_{\mathbf{2}}&{}\approx{}&0.005102175003&{}:{}&0.989795649994&{}:{}&0.005102175003&,\\ P_{\mathbf{3}}&{}\approx{}&0.002570762220&{}:{}&0.498714618890&{}:{}&0.498714618890&,\\ P_{\mathbf{4}}&{}\approx{}&0.989795649994&{}:{}&0.005102175003&{}:{}&0.005102175003&,\\ P_{\mathbf{5}}&{}\approx{}&0.498714618890&{}:{}&0.002570762220&{}:{}&0.498714618890&,\\ P_{\mathbf{6}}&{}\approx{}&0.498714618890&{}:{}&0.498714618890&{}:{}&0.002570762220&,\\ P_{\mathbf{7}}&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ P_{\mathbf{a}}&{}\approx{}&-0.477291366137&{}:{}&0.738645683069&{}:{}&0.738645683069&,\\ P_{\mathbf{1a}}&{}\approx{}&-0.069080899652&{}:{}&0.962172809687&{}:{}&0.106908089965&,\\ P_{\mathbf{2a}}&{}\approx{}&-0.069080899652&{}:{}&0.106908089965&{}:{}&0.962172809687&,\\ P_{\mathbf{3a}}&{}\approx{}&-0.037235063502&{}:{}&0.518617531751&{}:{}&0.518617531751&,\\ P_{\mathbf{4a}}&{}\approx{}&1.167669846111&{}:{}&-0.083834923055&{}:{}&-0.083834923055&,\\ P_{\mathbf{5a}}&{}\approx{}&1.086689796779&{}:{}&-0.008668979678&{}:{}&-0.078020817101&,\\ P_{\mathbf{6a}}&{}\approx{}&1.086689796779&{}:{}&-0.078020817101&{}:{}&-0.008668979678&,\\ P_{\mathbf{7a}}&{}\approx{}&1.016213521826&{}:{}&-0.008106760913&{}:{}&-0.008106760913&,\\ P_{\mathbf{b}}&{}\approx{}&0.738645683069&{}:{}&-0.477291366137&{}:{}&0.738645683069&,\\ P_{\mathbf{1b}}&{}\approx{}&0.962172809687&{}:{}&-0.069080899652&{}:{}&0.106908089965&,\\ P_{\mathbf{2b}}&{}\approx{}&-0.083834923055&{}:{}&1.167669846111&{}:{}&-0.083834923055&,\\ P_{\mathbf{3b}}&{}\approx{}&-0.008668979678&{}:{}&1.086689796779&{}:{}&-0.078020817101&,\\ P_{\mathbf{4b}}&{}\approx{}&0.106908089965&{}:{}&-0.069080899652&{}:{}&0.962172809687&,\\ P_{\mathbf{5b}}&{}\approx{}&0.518617531751&{}:{}&-0.037235063502&{}:{}&0.518617531751&,\\ P_{\mathbf{6b}}&{}\approx{}&-0.078020817101&{}:{}&1.086689796779&{}:{}&-0.008668979678&,\\ P_{\mathbf{7b}}&{}\approx{}&-0.008106760913&{}:{}&1.016213521826&{}:{}&-0.008106760913&,\\ P_{\mathbf{c}}&{}\approx{}&0.738645683069&{}:{}&0.738645683069&{}:{}&-0.477291366137&,\\ P_{\mathbf{1c}}&{}\approx{}&-0.083834923055&{}:{}&-0.083834923055&{}:{}&1.167669846111&,\\ P_{\mathbf{2c}}&{}\approx{}&0.962172809687&{}:{}&0.106908089965&{}:{}&-0.069080899652&,\\ P_{\mathbf{3c}}&{}\approx{}&-0.008668979678&{}:{}&-0.078020817101&{}:{}&1.086689796779&,\\ P_{\mathbf{4c}}&{}\approx{}&0.106908089965&{}:{}&0.962172809687&{}:{}&-0.069080899652&,\\ P_{\mathbf{5c}}&{}\approx{}&-0.078020817101&{}:{}&-0.008668979678&{}:{}&1.086689796779&,\\ P_{\mathbf{6c}}&{}\approx{}&0.518617531751&{}:{}&0.518617531751&{}:{}&-0.037235063502&,\\ P_{\mathbf{7c}}&{}\approx{}&-0.008106760913&{}:{}&-0.008106760913&{}:{}&1.016213521826&. \end{alignedat} \] \[ \begin{alignedat}{4} P^-&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ P^-_{\mathbf{1}}&{}\approx{}&-0.014783929292&{}:{}&-0.014783929292&{}:{}&1.029567858583&,\\ P^-_{\mathbf{2}}&{}\approx{}&-0.014783929292&{}:{}&1.029567858583&{}:{}&-0.014783929292&,\\ P^-_{\mathbf{3}}&{}\approx{}&-0.218757047773&{}:{}&0.609378523886&{}:{}&0.609378523886&,\\ P^-_{\mathbf{4}}&{}\approx{}&1.029567858583&{}:{}&-0.014783929292&{}:{}&-0.014783929292&,\\ P^-_{\mathbf{5}}&{}\approx{}&0.609378523886&{}:{}&-0.218757047773&{}:{}&0.609378523886&,\\ P^-_{\mathbf{6}}&{}\approx{}&0.609378523886&{}:{}&0.609378523886&{}:{}&-0.218757047773&,\\ P^-_{\mathbf{7}}&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ P^-_{\mathbf{a}}&{}\approx{}&-0.348308999953&{}:{}&0.674154499977&{}:{}&0.674154499977&,\\ P^-_{\mathbf{1a}}&{}\approx{}&0.018441753337&{}:{}&0.958616393184&{}:{}&0.022941853479&,\\ P^-_{\mathbf{2a}}&{}\approx{}&0.018441753337&{}:{}&0.022941853479&{}:{}&0.958616393184&,\\ P^-_{\mathbf{3a}}&{}\approx{}&0.118146029605&{}:{}&0.440926985198&{}:{}&0.440926985198&,\\ P^-_{\mathbf{4a}}&{}\approx{}&0.651084739626&{}:{}&0.174457630187&{}:{}&0.174457630187&,\\ P^-_{\mathbf{5a}}&{}\approx{}&0.902075806737&{}:{}&0.080570161309&{}:{}&0.017354031954&,\\ P^-_{\mathbf{6a}}&{}\approx{}&0.902075806737&{}:{}&0.017354031954&{}:{}&0.080570161309&,\\ P^-_{\mathbf{7a}}&{}\approx{}&0.957004652127&{}:{}&0.021497673936&{}:{}&0.021497673936&,\\ P^-_{\mathbf{b}}&{}\approx{}&0.674154499977&{}:{}&-0.348308999953&{}:{}&0.674154499977&,\\ P^-_{\mathbf{1b}}&{}\approx{}&0.958616393184&{}:{}&0.018441753337&{}:{}&0.022941853479&,\\ P^-_{\mathbf{2b}}&{}\approx{}&0.174457630187&{}:{}&0.651084739626&{}:{}&0.174457630187&,\\ P^-_{\mathbf{3b}}&{}\approx{}&0.080570161309&{}:{}&0.902075806737&{}:{}&0.017354031954&,\\ P^-_{\mathbf{4b}}&{}\approx{}&0.022941853479&{}:{}&0.018441753337&{}:{}&0.958616393184&,\\ P^-_{\mathbf{5b}}&{}\approx{}&0.440926985198&{}:{}&0.118146029605&{}:{}&0.440926985198&,\\ P^-_{\mathbf{6b}}&{}\approx{}&0.017354031954&{}:{}&0.902075806737&{}:{}&0.080570161309&,\\ P^-_{\mathbf{7b}}&{}\approx{}&0.021497673936&{}:{}&0.957004652127&{}:{}&0.021497673936&,\\ P^-_{\mathbf{c}}&{}\approx{}&0.674154499977&{}:{}&0.674154499977&{}:{}&-0.348308999953&,\\ P^-_{\mathbf{1c}}&{}\approx{}&0.174457630187&{}:{}&0.174457630187&{}:{}&0.651084739626&,\\ P^-_{\mathbf{2c}}&{}\approx{}&0.958616393184&{}:{}&0.022941853479&{}:{}&0.018441753337&,\\ P^-_{\mathbf{3c}}&{}\approx{}&0.080570161309&{}:{}&0.017354031954&{}:{}&0.902075806737&,\\ P^-_{\mathbf{4c}}&{}\approx{}&0.022941853479&{}:{}&0.958616393184&{}:{}&0.018441753337&,\\ P^-_{\mathbf{5c}}&{}\approx{}&0.017354031954&{}:{}&0.080570161309&{}:{}&0.902075806737&,\\ P^-_{\mathbf{6c}}&{}\approx{}&0.440926985198&{}:{}&0.440926985198&{}:{}&0.118146029605&,\\ P^-_{\mathbf{7c}}&{}\approx{}&0.021497673936&{}:{}&0.021497673936&{}:{}&0.957004652127&. \end{alignedat} \] \[ \begin{alignedat}{4} P^+&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ P^+_{\mathbf{1}}&{}\approx{}&0.022839075352&{}:{}&0.022839075352&{}:{}&0.954321849295&,\\ P^+_{\mathbf{2}}&{}\approx{}&0.022839075352&{}:{}&0.954321849295&{}:{}&0.022839075352&,\\ P^+_{\mathbf{3}}&{}\approx{}&0.097224542457&{}:{}&0.451387728771&{}:{}&0.451387728771&,\\ P^+_{\mathbf{4}}&{}\approx{}&0.954321849295&{}:{}&0.022839075352&{}:{}&0.022839075352&,\\ P^+_{\mathbf{5}}&{}\approx{}&0.451387728771&{}:{}&0.097224542457&{}:{}&0.451387728771&,\\ P^+_{\mathbf{6}}&{}\approx{}&0.451387728771&{}:{}&0.451387728771&{}:{}&0.097224542457&,\\ P^+_{\mathbf{7}}&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ P^+_{\mathbf{a}}&{}\approx{}&-0.563652960290&{}:{}&0.781826480145&{}:{}&0.781826480145&,\\ P^+_{\mathbf{1a}}&{}\approx{}&-0.142751000530&{}:{}&0.965166338260&{}:{}&0.177584662270&,\\ P^+_{\mathbf{2a}}&{}\approx{}&-0.142751000530&{}:{}&0.177584662270&{}:{}&0.965166338260&,\\ P^+_{\mathbf{3a}}&{}\approx{}&-0.154700538379&{}:{}&0.577350269190&{}:{}&0.577350269190&,\\ P^+_{\mathbf{4a}}&{}\approx{}&2.154700538379&{}:{}&-0.577350269190&{}:{}&-0.577350269190&,\\ P^+_{\mathbf{5a}}&{}\approx{}&1.310992966503&{}:{}&-0.117093168886&{}:{}&-0.193899797618&,\\ P^+_{\mathbf{6a}}&{}\approx{}&1.310992966503&{}:{}&-0.193899797618&{}:{}&-0.117093168886&,\\ P^+_{\mathbf{7a}}&{}\approx{}&1.079116877816&{}:{}&-0.039558438908&{}:{}&-0.039558438908&,\\ P^+_{\mathbf{b}}&{}\approx{}&0.781826480145&{}:{}&-0.563652960290&{}:{}&0.781826480145&,\\ P^+_{\mathbf{1b}}&{}\approx{}&0.965166338260&{}:{}&-0.142751000530&{}:{}&0.177584662270&,\\ P^+_{\mathbf{2b}}&{}\approx{}&-0.577350269190&{}:{}&2.154700538379&{}:{}&-0.577350269190&,\\ P^+_{\mathbf{3b}}&{}\approx{}&-0.117093168886&{}:{}&1.310992966503&{}:{}&-0.193899797618&,\\ P^+_{\mathbf{4b}}&{}\approx{}&0.177584662270&{}:{}&-0.142751000530&{}:{}&0.965166338260&,\\ P^+_{\mathbf{5b}}&{}\approx{}&0.577350269190&{}:{}&-0.154700538379&{}:{}&0.577350269190&,\\ P^+_{\mathbf{6b}}&{}\approx{}&-0.193899797618&{}:{}&1.310992966503&{}:{}&-0.117093168886&,\\ P^+_{\mathbf{7b}}&{}\approx{}&-0.039558438908&{}:{}&1.079116877816&{}:{}&-0.039558438908&,\\ P^+_{\mathbf{c}}&{}\approx{}&0.781826480145&{}:{}&0.781826480145&{}:{}&-0.563652960290&,\\ P^+_{\mathbf{1c}}&{}\approx{}&-0.577350269190&{}:{}&-0.577350269190&{}:{}&2.154700538379&,\\ P^+_{\mathbf{2c}}&{}\approx{}&0.965166338260&{}:{}&0.177584662270&{}:{}&-0.142751000530&,\\ P^+_{\mathbf{3c}}&{}\approx{}&-0.117093168886&{}:{}&-0.193899797618&{}:{}&1.310992966503&,\\ P^+_{\mathbf{4c}}&{}\approx{}&0.177584662270&{}:{}&0.965166338260&{}:{}&-0.142751000530&,\\ P^+_{\mathbf{5c}}&{}\approx{}&-0.193899797618&{}:{}&-0.117093168886&{}:{}&1.310992966503&,\\ P^+_{\mathbf{6c}}&{}\approx{}&0.577350269190&{}:{}&0.577350269190&{}:{}&-0.154700538379&,\\ P^+_{\mathbf{7c}}&{}\approx{}&-0.039558438908&{}:{}&-0.039558438908&{}:{}&1.079116877816&. \end{alignedat} \] \[ \begin{alignedat}{4} Q&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ Q_{\mathbf{1}}&{}\approx{}&-0.083834923055&{}:{}&-0.083834923055&{}:{}&1.167669846111&,\\ Q_{\mathbf{2}}&{}\approx{}&-0.083834923055&{}:{}&1.167669846111&{}:{}&-0.083834923055&,\\ Q_{\mathbf{3}}&{}\approx{}&-0.037235063502&{}:{}&0.518617531751&{}:{}&0.518617531751&,\\ Q_{\mathbf{4}}&{}\approx{}&1.167669846111&{}:{}&-0.083834923055&{}:{}&-0.083834923055&,\\ Q_{\mathbf{5}}&{}\approx{}&0.518617531751&{}:{}&-0.037235063502&{}:{}&0.518617531751&,\\ Q_{\mathbf{6}}&{}\approx{}&0.518617531751&{}:{}&0.518617531751&{}:{}&-0.037235063502&,\\ Q_{\mathbf{7}}&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ Q_{\mathbf{a}}&{}\approx{}&-0.302169479252&{}:{}&0.651084739626&{}:{}&0.651084739626&,\\ Q_{\mathbf{1a}}&{}\approx{}&0.188345160884&{}:{}&1.217482258674&{}:{}&-0.405827419558&,\\ Q_{\mathbf{2a}}&{}\approx{}&0.188345160884&{}:{}&-0.405827419558&{}:{}&1.217482258674&,\\ Q_{\mathbf{3a}}&{}\approx{}&0.071796769724&{}:{}&0.464101615138&{}:{}&0.464101615138&,\\ Q_{\mathbf{4a}}&{}\approx{}&13.928203230276&{}:{}&-6.464101615138&{}:{}&-6.464101615138&,\\ Q_{\mathbf{5a}}&{}\approx{}&1.448018475480&{}:{}&0.224009237740&{}:{}&-0.672027713219&,\\ Q_{\mathbf{6a}}&{}\approx{}&1.448018475480&{}:{}&-0.672027713219&{}:{}&0.224009237740&,\\ Q_{\mathbf{7a}}&{}\approx{}&0.763707940790&{}:{}&0.118146029605&{}:{}&0.118146029605&,\\ Q_{\mathbf{b}}&{}\approx{}&0.651084739626&{}:{}&-0.302169479252&{}:{}&0.651084739626&,\\ Q_{\mathbf{1b}}&{}\approx{}&1.217482258674&{}:{}&0.188345160884&{}:{}&-0.405827419558&,\\ Q_{\mathbf{2b}}&{}\approx{}&-6.464101615138&{}:{}&13.928203230276&{}:{}&-6.464101615138&,\\ Q_{\mathbf{3b}}&{}\approx{}&0.224009237740&{}:{}&1.448018475480&{}:{}&-0.672027713219&,\\ Q_{\mathbf{4b}}&{}\approx{}&-0.405827419558&{}:{}&0.188345160884&{}:{}&1.217482258674&,\\ Q_{\mathbf{5b}}&{}\approx{}&0.464101615138&{}:{}&0.071796769724&{}:{}&0.464101615138&,\\ Q_{\mathbf{6b}}&{}\approx{}&-0.672027713219&{}:{}&1.448018475480&{}:{}&0.224009237740&,\\ Q_{\mathbf{7b}}&{}\approx{}&0.118146029605&{}:{}&0.763707940790&{}:{}&0.118146029605&,\\ Q_{\mathbf{c}}&{}\approx{}&0.651084739626&{}:{}&0.651084739626&{}:{}&-0.302169479252&,\\ Q_{\mathbf{1c}}&{}\approx{}&-6.464101615138&{}:{}&-6.464101615138&{}:{}&13.928203230276&,\\ Q_{\mathbf{2c}}&{}\approx{}&1.217482258674&{}:{}&-0.405827419558&{}:{}&0.188345160884&,\\ Q_{\mathbf{3c}}&{}\approx{}&0.224009237740&{}:{}&-0.672027713219&{}:{}&1.448018475480&,\\ Q_{\mathbf{4c}}&{}\approx{}&-0.405827419558&{}:{}&1.217482258674&{}:{}&0.188345160884&,\\ Q_{\mathbf{5c}}&{}\approx{}&-0.672027713219&{}:{}&0.224009237740&{}:{}&1.448018475480&,\\ Q_{\mathbf{6c}}&{}\approx{}&0.464101615138&{}:{}&0.464101615138&{}:{}&0.071796769724&,\\ Q_{\mathbf{7c}}&{}\approx{}&0.118146029605&{}:{}&0.118146029605&{}:{}&0.763707940790&. \end{alignedat} \] \[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ I^\prime_{\mathbf{1}}&{}\approx{}&0.062781720295&{}:{}&0.062781720295&{}:{}&0.874436559411&,\\ I^\prime_{\mathbf{2}}&{}\approx{}&0.062781720295&{}:{}&0.874436559411&{}:{}&0.062781720295&,\\ I^\prime_{\mathbf{3}}&{}\approx{}&0.034654349680&{}:{}&0.482672825160&{}:{}&0.482672825160&,\\ I^\prime_{\mathbf{4}}&{}\approx{}&0.874436559411&{}:{}&0.062781720295&{}:{}&0.062781720295&,\\ I^\prime_{\mathbf{5}}&{}\approx{}&0.482672825160&{}:{}&0.034654349680&{}:{}&0.482672825160&,\\ I^\prime_{\mathbf{6}}&{}\approx{}&0.482672825160&{}:{}&0.482672825160&{}:{}&0.034654349680&,\\ I^\prime_{\mathbf{7}}&{}\approx{}&0.333333333333&{}:{}&0.333333333333&{}:{}&0.333333333333&,\\ I^\prime_{\mathbf{a}}&{}\approx{}&-0.672027713219&{}:{}&0.836013856610&{}:{}&0.836013856610&,\\ I^\prime_{\mathbf{1a}}&{}\approx{}&-0.251504769166&{}:{}&0.938628576875&{}:{}&0.312876192292&,\\ I^\prime_{\mathbf{2a}}&{}\approx{}&-0.251504769166&{}:{}&0.312876192292&{}:{}&0.938628576875&,\\ I^\prime_{\mathbf{3a}}&{}\approx{}&-0.154700538379&{}:{}&0.577350269190&{}:{}&0.577350269190&,\\ I^\prime_{\mathbf{4a}}&{}\approx{}&2.154700538379&{}:{}&-0.577350269190&{}:{}&-0.577350269190&,\\ I^\prime_{\mathbf{5a}}&{}\approx{}&1.555852595253&{}:{}&-0.138963148813&{}:{}&-0.416889446440&,\\ I^\prime_{\mathbf{6a}}&{}\approx{}&1.555852595253&{}:{}&-0.416889446440&{}:{}&-0.138963148813&,\\ I^\prime_{\mathbf{7a}}&{}\approx{}&1.217482258674&{}:{}&-0.108741129337&{}:{}&-0.108741129337&,\\ I^\prime_{\mathbf{b}}&{}\approx{}&0.836013856610&{}:{}&-0.672027713219&{}:{}&0.836013856610&,\\ I^\prime_{\mathbf{1b}}&{}\approx{}&0.938628576875&{}:{}&-0.251504769166&{}:{}&0.312876192292&,\\ I^\prime_{\mathbf{2b}}&{}\approx{}&-0.577350269190&{}:{}&2.154700538379&{}:{}&-0.577350269190&,\\ I^\prime_{\mathbf{3b}}&{}\approx{}&-0.138963148813&{}:{}&1.555852595253&{}:{}&-0.416889446440&,\\ I^\prime_{\mathbf{4b}}&{}\approx{}&0.312876192292&{}:{}&-0.251504769166&{}:{}&0.938628576875&,\\ I^\prime_{\mathbf{5b}}&{}\approx{}&0.577350269190&{}:{}&-0.154700538379&{}:{}&0.577350269190&,\\ I^\prime_{\mathbf{6b}}&{}\approx{}&-0.416889446440&{}:{}&1.555852595253&{}:{}&-0.138963148813&,\\ I^\prime_{\mathbf{7b}}&{}\approx{}&-0.108741129337&{}:{}&1.217482258674&{}:{}&-0.108741129337&,\\ I^\prime_{\mathbf{c}}&{}\approx{}&0.836013856610&{}:{}&0.836013856610&{}:{}&-0.672027713219&,\\ I^\prime_{\mathbf{1c}}&{}\approx{}&-0.577350269190&{}:{}&-0.577350269190&{}:{}&2.154700538379&,\\ I^\prime_{\mathbf{2c}}&{}\approx{}&0.938628576875&{}:{}&0.312876192292&{}:{}&-0.251504769166&,\\ I^\prime_{\mathbf{3c}}&{}\approx{}&-0.138963148813&{}:{}&-0.416889446440&{}:{}&1.555852595253&,\\ I^\prime_{\mathbf{4c}}&{}\approx{}&0.312876192292&{}:{}&0.938628576875&{}:{}&-0.251504769166&,\\ I^\prime_{\mathbf{5c}}&{}\approx{}&-0.416889446440&{}:{}&-0.138963148813&{}:{}&1.555852595253&,\\ I^\prime_{\mathbf{6c}}&{}\approx{}&0.577350269190&{}:{}&0.577350269190&{}:{}&-0.154700538379&,\\ I^\prime_{\mathbf{7c}}&{}\approx{}&-0.108741129337&{}:{}&-0.108741129337&{}:{}&1.217482258674&. \end{alignedat} \]

Central Triangles and their Extraversions

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.577350269190&{}:{}&0.211324865405&{}:{}&0.211324865405&,\\B^\prime&{}\approx{}&0.211324865405&{}:{}&0.577350269190&{}:{}&0.211324865405&,\\C^\prime&{}\approx{}&0.211324865405&{}:{}&0.211324865405&{}:{}&0.577350269190&,\\[.5em] A^\prime_{\mathbf{1}}&{}\approx{}&-0.577350269190&{}:{}&0.788675134595&{}:{}&0.788675134595&,\\B^\prime_{\mathbf{1}}&{}\approx{}&0.788675134595&{}:{}&-0.577350269190&{}:{}&0.788675134595&,\\C^\prime_{\mathbf{1}}&{}\approx{}&0.018874775675&{}:{}&0.018874775675&{}:{}&0.962250448649&,\\[.5em] A^\prime_{\mathbf{2}}&{}\approx{}&-0.577350269190&{}:{}&0.788675134595&{}:{}&0.788675134595&,\\B^\prime_{\mathbf{2}}&{}\approx{}&0.018874775675&{}:{}&0.962250448649&{}:{}&0.018874775675&,\\C^\prime_{\mathbf{2}}&{}\approx{}&0.788675134595&{}:{}&0.788675134595&{}:{}&-0.577350269190&,\\[.5em] A^\prime_{\mathbf{3}}&{}\approx{}&-0.962250448649&{}:{}&0.981125224325&{}:{}&0.981125224325&,\\B^\prime_{\mathbf{3}}&{}\approx{}&0.211324865405&{}:{}&0.577350269190&{}:{}&0.211324865405&,\\C^\prime_{\mathbf{3}}&{}\approx{}&0.211324865405&{}:{}&0.211324865405&{}:{}&0.577350269190&,\\[.5em] A^\prime_{\mathbf{4}}&{}\approx{}&0.962250448649&{}:{}&0.018874775675&{}:{}&0.018874775675&,\\B^\prime_{\mathbf{4}}&{}\approx{}&0.788675134595&{}:{}&-0.577350269190&{}:{}&0.788675134595&,\\C^\prime_{\mathbf{4}}&{}\approx{}&0.788675134595&{}:{}&0.788675134595&{}:{}&-0.577350269190&,\\[.5em] A^\prime_{\mathbf{5}}&{}\approx{}&0.577350269190&{}:{}&0.211324865405&{}:{}&0.211324865405&,\\B^\prime_{\mathbf{5}}&{}\approx{}&0.981125224325&{}:{}&-0.962250448649&{}:{}&0.981125224325&,\\C^\prime_{\mathbf{5}}&{}\approx{}&0.211324865405&{}:{}&0.211324865405&{}:{}&0.577350269190&,\\[.5em] A^\prime_{\mathbf{6}}&{}\approx{}&0.577350269190&{}:{}&0.211324865405&{}:{}&0.211324865405&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.211324865405&{}:{}&0.577350269190&{}:{}&0.211324865405&,\\C^\prime_{\mathbf{6}}&{}\approx{}&0.981125224325&{}:{}&0.981125224325&{}:{}&-0.962250448649&,\\[.5em] A^\prime_{\mathbf{7}}&{}\approx{}&-0.577350269190&{}:{}&0.788675134595&{}:{}&0.788675134595&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.788675134595&{}:{}&-0.577350269190&{}:{}&0.788675134595&,\\C^\prime_{\mathbf{7}}&{}\approx{}&0.788675134595&{}:{}&0.788675134595&{}:{}&-0.577350269190&,\\[.5em] A^\prime_{\mathbf{a}}&{}\approx{}&-2.398717474236&{}:{}&1.699358737118&{}:{}&1.699358737118&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.366025403784&{}:{}&1.000000000000&{}:{}&0.366025403784&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.366025403784&{}:{}&0.366025403784&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{1a}}&{}\approx{}&0.089316397477&{}:{}&0.455341801261&{}:{}&0.455341801261&,\\B^\prime_{\mathbf{1a}}&{}\approx{}&-0.098076211353&{}:{}&1.000000000000&{}:{}&0.098076211353&,\\C^\prime_{\mathbf{1a}}&{}\approx{}&-4.098076211353&{}:{}&4.098076211353&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{2a}}&{}\approx{}&0.089316397477&{}:{}&0.455341801261&{}:{}&0.455341801261&,\\B^\prime_{\mathbf{2a}}&{}\approx{}&-4.098076211353&{}:{}&1.000000000000&{}:{}&4.098076211353&,\\C^\prime_{\mathbf{2a}}&{}\approx{}&-0.098076211353&{}:{}&0.098076211353&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{3a}}&{}\approx{}&0.267949192431&{}:{}&0.366025403784&{}:{}&0.366025403784&,\\B^\prime_{\mathbf{3a}}&{}\approx{}&-0.366025403784&{}:{}&1.000000000000&{}:{}&0.366025403784&,\\C^\prime_{\mathbf{3a}}&{}\approx{}&-0.366025403784&{}:{}&0.366025403784&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{4a}}&{}\approx{}&3.732050807569&{}:{}&-1.366025403784&{}:{}&-1.366025403784&,\\B^\prime_{\mathbf{4a}}&{}\approx{}&1.366025403784&{}:{}&1.000000000000&{}:{}&-1.366025403784&,\\C^\prime_{\mathbf{4a}}&{}\approx{}&1.366025403784&{}:{}&-1.366025403784&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{5a}}&{}\approx{}&1.244016935856&{}:{}&-0.122008467928&{}:{}&-0.122008467928&,\\B^\prime_{\mathbf{5a}}&{}\approx{}&1.098076211353&{}:{}&1.000000000000&{}:{}&-1.098076211353&,\\C^\prime_{\mathbf{5a}}&{}\approx{}&5.098076211353&{}:{}&-5.098076211353&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{6a}}&{}\approx{}&1.244016935856&{}:{}&-0.122008467928&{}:{}&-0.122008467928&,\\B^\prime_{\mathbf{6a}}&{}\approx{}&5.098076211353&{}:{}&1.000000000000&{}:{}&-5.098076211353&,\\C^\prime_{\mathbf{6a}}&{}\approx{}&1.098076211353&{}:{}&-1.098076211353&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{7a}}&{}\approx{}&1.065384140902&{}:{}&-0.032692070451&{}:{}&-0.032692070451&,\\B^\prime_{\mathbf{7a}}&{}\approx{}&1.366025403784&{}:{}&1.000000000000&{}:{}&-1.366025403784&,\\C^\prime_{\mathbf{7a}}&{}\approx{}&1.366025403784&{}:{}&-1.366025403784&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{b}}&{}\approx{}&1.000000000000&{}:{}&-0.366025403784&{}:{}&0.366025403784&,\\B^\prime_{\mathbf{b}}&{}\approx{}&1.699358737118&{}:{}&-2.398717474236&{}:{}&1.699358737118&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.366025403784&{}:{}&-0.366025403784&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{1b}}&{}\approx{}&1.000000000000&{}:{}&-0.098076211353&{}:{}&0.098076211353&,\\B^\prime_{\mathbf{1b}}&{}\approx{}&0.455341801261&{}:{}&0.089316397477&{}:{}&0.455341801261&,\\C^\prime_{\mathbf{1b}}&{}\approx{}&4.098076211353&{}:{}&-4.098076211353&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{2b}}&{}\approx{}&1.000000000000&{}:{}&1.366025403784&{}:{}&-1.366025403784&,\\B^\prime_{\mathbf{2b}}&{}\approx{}&-1.366025403784&{}:{}&3.732050807569&{}:{}&-1.366025403784&,\\C^\prime_{\mathbf{2b}}&{}\approx{}&-1.366025403784&{}:{}&1.366025403784&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{3b}}&{}\approx{}&1.000000000000&{}:{}&1.098076211353&{}:{}&-1.098076211353&,\\B^\prime_{\mathbf{3b}}&{}\approx{}&-0.122008467928&{}:{}&1.244016935856&{}:{}&-0.122008467928&,\\C^\prime_{\mathbf{3b}}&{}\approx{}&-5.098076211353&{}:{}&5.098076211353&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{4b}}&{}\approx{}&1.000000000000&{}:{}&-4.098076211353&{}:{}&4.098076211353&,\\B^\prime_{\mathbf{4b}}&{}\approx{}&0.455341801261&{}:{}&0.089316397477&{}:{}&0.455341801261&,\\C^\prime_{\mathbf{4b}}&{}\approx{}&0.098076211353&{}:{}&-0.098076211353&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{5b}}&{}\approx{}&1.000000000000&{}:{}&-0.366025403784&{}:{}&0.366025403784&,\\B^\prime_{\mathbf{5b}}&{}\approx{}&0.366025403784&{}:{}&0.267949192431&{}:{}&0.366025403784&,\\C^\prime_{\mathbf{5b}}&{}\approx{}&0.366025403784&{}:{}&-0.366025403784&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{6b}}&{}\approx{}&1.000000000000&{}:{}&5.098076211353&{}:{}&-5.098076211353&,\\B^\prime_{\mathbf{6b}}&{}\approx{}&-0.122008467928&{}:{}&1.244016935856&{}:{}&-0.122008467928&,\\C^\prime_{\mathbf{6b}}&{}\approx{}&-1.098076211353&{}:{}&1.098076211353&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{7b}}&{}\approx{}&1.000000000000&{}:{}&1.366025403784&{}:{}&-1.366025403784&,\\B^\prime_{\mathbf{7b}}&{}\approx{}&-0.032692070451&{}:{}&1.065384140902&{}:{}&-0.032692070451&,\\C^\prime_{\mathbf{7b}}&{}\approx{}&-1.366025403784&{}:{}&1.366025403784&{}:{}&1.000000000000&,\\[.5em] A^\prime_{\mathbf{c}}&{}\approx{}&1.000000000000&{}:{}&0.366025403784&{}:{}&-0.366025403784&,\\B^\prime_{\mathbf{c}}&{}\approx{}&0.366025403784&{}:{}&1.000000000000&{}:{}&-0.366025403784&,\\C^\prime_{\mathbf{c}}&{}\approx{}&1.699358737118&{}:{}&1.699358737118&{}:{}&-2.398717474236&,\\[.5em] A^\prime_{\mathbf{1c}}&{}\approx{}&1.000000000000&{}:{}&-1.366025403784&{}:{}&1.366025403784&,\\B^\prime_{\mathbf{1c}}&{}\approx{}&-1.366025403784&{}:{}&1.000000000000&{}:{}&1.366025403784&,\\C^\prime_{\mathbf{1c}}&{}\approx{}&-1.366025403784&{}:{}&-1.366025403784&{}:{}&3.732050807569&,\\[.5em] A^\prime_{\mathbf{2c}}&{}\approx{}&1.000000000000&{}:{}&0.098076211353&{}:{}&-0.098076211353&,\\B^\prime_{\mathbf{2c}}&{}\approx{}&4.098076211353&{}:{}&1.000000000000&{}:{}&-4.098076211353&,\\C^\prime_{\mathbf{2c}}&{}\approx{}&0.455341801261&{}:{}&0.455341801261&{}:{}&0.089316397477&,\\[.5em] A^\prime_{\mathbf{3c}}&{}\approx{}&1.000000000000&{}:{}&-1.098076211353&{}:{}&1.098076211353&,\\B^\prime_{\mathbf{3c}}&{}\approx{}&-5.098076211353&{}:{}&1.000000000000&{}:{}&5.098076211353&,\\C^\prime_{\mathbf{3c}}&{}\approx{}&-0.122008467928&{}:{}&-0.122008467928&{}:{}&1.244016935856&,\\[.5em] A^\prime_{\mathbf{4c}}&{}\approx{}&1.000000000000&{}:{}&4.098076211353&{}:{}&-4.098076211353&,\\B^\prime_{\mathbf{4c}}&{}\approx{}&0.098076211353&{}:{}&1.000000000000&{}:{}&-0.098076211353&,\\C^\prime_{\mathbf{4c}}&{}\approx{}&0.455341801261&{}:{}&0.455341801261&{}:{}&0.089316397477&,\\[.5em] A^\prime_{\mathbf{5c}}&{}\approx{}&1.000000000000&{}:{}&-5.098076211353&{}:{}&5.098076211353&,\\B^\prime_{\mathbf{5c}}&{}\approx{}&-1.098076211353&{}:{}&1.000000000000&{}:{}&1.098076211353&,\\C^\prime_{\mathbf{5c}}&{}\approx{}&-0.122008467928&{}:{}&-0.122008467928&{}:{}&1.244016935856&,\\[.5em] A^\prime_{\mathbf{6c}}&{}\approx{}&1.000000000000&{}:{}&0.366025403784&{}:{}&-0.366025403784&,\\B^\prime_{\mathbf{6c}}&{}\approx{}&0.366025403784&{}:{}&1.000000000000&{}:{}&-0.366025403784&,\\C^\prime_{\mathbf{6c}}&{}\approx{}&0.366025403784&{}:{}&0.366025403784&{}:{}&0.267949192431&,\\[.5em] A^\prime_{\mathbf{7c}}&{}\approx{}&1.000000000000&{}:{}&-1.366025403784&{}:{}&1.366025403784&,\\B^\prime_{\mathbf{7c}}&{}\approx{}&-1.366025403784&{}:{}&1.000000000000&{}:{}&1.366025403784&,\\C^\prime_{\mathbf{7c}}&{}\approx{}&-0.032692070451&{}:{}&-0.032692070451&{}:{}&1.065384140902&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime}&{}\approx{}&0.211324865405&{}:{}&0.394337567297&{}:{}&0.394337567297&,\\B^{\prime\prime}&{}\approx{}&0.394337567297&{}:{}&0.211324865405&{}:{}&0.394337567297&,\\C^{\prime\prime}&{}\approx{}&0.394337567297&{}:{}&0.394337567297&{}:{}&0.211324865405&,\\[.5em] A^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.036867235218&{}:{}&0.004939272952&{}:{}&0.958193491830&,\\B^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.004939272952&{}:{}&0.036867235218&{}:{}&0.958193491830&,\\C^{\prime\prime}_{\mathbf{1}}&{}\approx{}&0.105662432703&{}:{}&0.105662432703&{}:{}&0.788675134595&,\\[.5em] A^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.036867235218&{}:{}&0.958193491830&{}:{}&0.004939272952&,\\B^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.105662432703&{}:{}&0.788675134595&{}:{}&0.105662432703&,\\C^{\prime\prime}_{\mathbf{2}}&{}\approx{}&0.004939272952&{}:{}&0.958193491830&{}:{}&0.036867235218&,\\[.5em] A^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.211324865405&{}:{}&0.394337567297&{}:{}&0.394337567297&,\\B^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.003344969709&{}:{}&0.347748149397&{}:{}&0.648906880894&,\\C^{\prime\prime}_{\mathbf{3}}&{}\approx{}&0.003344969709&{}:{}&0.648906880894&{}:{}&0.347748149397&,\\[.5em] A^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.788675134595&{}:{}&0.105662432703&{}:{}&0.105662432703&,\\B^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.958193491830&{}:{}&0.036867235218&{}:{}&0.004939272952&,\\C^{\prime\prime}_{\mathbf{4}}&{}\approx{}&0.958193491830&{}:{}&0.004939272952&{}:{}&0.036867235218&,\\[.5em] A^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.347748149397&{}:{}&0.003344969709&{}:{}&0.648906880894&,\\B^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.394337567297&{}:{}&0.211324865405&{}:{}&0.394337567297&,\\C^{\prime\prime}_{\mathbf{5}}&{}\approx{}&0.648906880894&{}:{}&0.003344969709&{}:{}&0.347748149397&,\\[.5em] A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.347748149397&{}:{}&0.648906880894&{}:{}&0.003344969709&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.648906880894&{}:{}&0.347748149397&{}:{}&0.003344969709&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.394337567297&{}:{}&0.394337567297&{}:{}&0.211324865405&,\\[.5em] A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.788675134595&{}:{}&0.105662432703&{}:{}&0.105662432703&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.105662432703&{}:{}&0.788675134595&{}:{}&0.105662432703&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.105662432703&{}:{}&0.105662432703&{}:{}&0.788675134595&,\\[.5em] A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.366025403784&{}:{}&0.683012701892&{}:{}&0.683012701892&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.726257150084&{}:{}&0.602317462994&{}:{}&1.123939687090&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.726257150084&{}:{}&1.123939687090&{}:{}&0.602317462994&,\\[.5em] A^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.191567773597&{}:{}&1.072410996238&{}:{}&0.119156777360&,\\B^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.329422863406&{}:{}&0.819615242271&{}:{}&0.509807621135&,\\C^{\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.064866672287&{}:{}&0.903476194491&{}:{}&0.161390477796&,\\[.5em] A^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.191567773597&{}:{}&0.119156777360&{}:{}&1.072410996238&,\\B^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.064866672287&{}:{}&0.161390477796&{}:{}&0.903476194491&,\\C^{\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.329422863406&{}:{}&0.509807621135&{}:{}&0.819615242271&,\\[.5em] A^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.366025403784&{}:{}&0.683012701892&{}:{}&0.683012701892&,\\B^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.049038105677&{}:{}&0.366025403784&{}:{}&0.683012701892&,\\C^{\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.049038105677&{}:{}&0.683012701892&{}:{}&0.366025403784&,\\[.5em] A^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.366025403784&{}:{}&-0.183012701892&{}:{}&-0.183012701892&,\\B^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&2.549038105677&{}:{}&-1.366025403784&{}:{}&-0.183012701892&,\\C^{\prime\prime}_{\mathbf{4a}}&{}\approx{}&2.549038105677&{}:{}&-0.183012701892&{}:{}&-1.366025403784&,\\[.5em] A^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.806952388982&{}:{}&-0.080695238898&{}:{}&-0.726257150084&,\\B^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.334097441518&{}:{}&-0.238313554719&{}:{}&-0.095783886799&,\\C^{\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.229422863406&{}:{}&-0.009807621135&{}:{}&-0.219615242271&,\\[.5em] A^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.806952388982&{}:{}&-0.726257150084&{}:{}&-0.080695238898&,\\B^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.229422863406&{}:{}&-0.219615242271&{}:{}&-0.009807621135&,\\C^{\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.334097441518&{}:{}&-0.095783886799&{}:{}&-0.238313554719&,\\[.5em] A^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.366025403784&{}:{}&-0.183012701892&{}:{}&-0.183012701892&,\\B^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.072410996238&{}:{}&-0.063855924532&{}:{}&-0.008555071705&,\\C^{\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.072410996238&{}:{}&-0.008555071705&{}:{}&-0.063855924532&,\\[.5em] A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.602317462994&{}:{}&-0.726257150084&{}:{}&1.123939687090&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.683012701892&{}:{}&-0.366025403784&{}:{}&0.683012701892&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&1.123939687090&{}:{}&-0.726257150084&{}:{}&0.602317462994&,\\[.5em] A^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.819615242271&{}:{}&-0.329422863406&{}:{}&0.509807621135&,\\B^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.072410996238&{}:{}&-0.191567773597&{}:{}&0.119156777360&,\\C^{\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.903476194491&{}:{}&-0.064866672287&{}:{}&0.161390477796&,\\[.5em] A^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-1.366025403784&{}:{}&2.549038105677&{}:{}&-0.183012701892&,\\B^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.183012701892&{}:{}&1.366025403784&{}:{}&-0.183012701892&,\\C^{\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.183012701892&{}:{}&2.549038105677&{}:{}&-1.366025403784&,\\[.5em] A^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.238313554719&{}:{}&1.334097441518&{}:{}&-0.095783886799&,\\B^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.080695238898&{}:{}&1.806952388982&{}:{}&-0.726257150084&,\\C^{\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.009807621135&{}:{}&1.229422863406&{}:{}&-0.219615242271&,\\[.5em] A^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.161390477796&{}:{}&-0.064866672287&{}:{}&0.903476194491&,\\B^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.119156777360&{}:{}&-0.191567773597&{}:{}&1.072410996238&,\\C^{\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.509807621135&{}:{}&-0.329422863406&{}:{}&0.819615242271&,\\[.5em] A^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.366025403784&{}:{}&-0.049038105677&{}:{}&0.683012701892&,\\B^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.683012701892&{}:{}&-0.366025403784&{}:{}&0.683012701892&,\\C^{\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.683012701892&{}:{}&-0.049038105677&{}:{}&0.366025403784&,\\[.5em] A^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.219615242271&{}:{}&1.229422863406&{}:{}&-0.009807621135&,\\B^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.726257150084&{}:{}&1.806952388982&{}:{}&-0.080695238898&,\\C^{\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.095783886799&{}:{}&1.334097441518&{}:{}&-0.238313554719&,\\[.5em] A^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.063855924532&{}:{}&1.072410996238&{}:{}&-0.008555071705&,\\B^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.183012701892&{}:{}&1.366025403784&{}:{}&-0.183012701892&,\\C^{\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.008555071705&{}:{}&1.072410996238&{}:{}&-0.063855924532&,\\[.5em] A^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.602317462994&{}:{}&1.123939687090&{}:{}&-0.726257150084&,\\B^{\prime\prime}_{\mathbf{c}}&{}\approx{}&1.123939687090&{}:{}&0.602317462994&{}:{}&-0.726257150084&,\\C^{\prime\prime}_{\mathbf{c}}&{}\approx{}&0.683012701892&{}:{}&0.683012701892&{}:{}&-0.366025403784&,\\[.5em] A^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-1.366025403784&{}:{}&-0.183012701892&{}:{}&2.549038105677&,\\B^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.183012701892&{}:{}&-1.366025403784&{}:{}&2.549038105677&,\\C^{\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.183012701892&{}:{}&-0.183012701892&{}:{}&1.366025403784&,\\[.5em] A^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.819615242271&{}:{}&0.509807621135&{}:{}&-0.329422863406&,\\B^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.903476194491&{}:{}&0.161390477796&{}:{}&-0.064866672287&,\\C^{\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.072410996238&{}:{}&0.119156777360&{}:{}&-0.191567773597&,\\[.5em] A^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.238313554719&{}:{}&-0.095783886799&{}:{}&1.334097441518&,\\B^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.009807621135&{}:{}&-0.219615242271&{}:{}&1.229422863406&,\\C^{\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.080695238898&{}:{}&-0.726257150084&{}:{}&1.806952388982&,\\[.5em] A^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.161390477796&{}:{}&0.903476194491&{}:{}&-0.064866672287&,\\B^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.509807621135&{}:{}&0.819615242271&{}:{}&-0.329422863406&,\\C^{\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.119156777360&{}:{}&1.072410996238&{}:{}&-0.191567773597&,\\[.5em] A^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.219615242271&{}:{}&-0.009807621135&{}:{}&1.229422863406&,\\B^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.095783886799&{}:{}&-0.238313554719&{}:{}&1.334097441518&,\\C^{\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.726257150084&{}:{}&-0.080695238898&{}:{}&1.806952388982&,\\[.5em] A^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.366025403784&{}:{}&0.683012701892&{}:{}&-0.049038105677&,\\B^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.683012701892&{}:{}&0.366025403784&{}:{}&-0.049038105677&,\\C^{\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.683012701892&{}:{}&0.683012701892&{}:{}&-0.366025403784&,\\[.5em] A^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.063855924532&{}:{}&-0.008555071705&{}:{}&1.072410996238&,\\B^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.008555071705&{}:{}&-0.063855924532&{}:{}&1.072410996238&,\\C^{\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.183012701892&{}:{}&-0.183012701892&{}:{}&1.366025403784&. \end{alignedat} \] \[ \begin{alignedat}{4} A^{\prime\prime\prime}&{}\approx{}&0.154700538379&{}:{}&0.422649730810&{}:{}&0.422649730810&,\\B^{\prime\prime\prime}&{}\approx{}&0.422649730810&{}:{}&0.154700538379&{}:{}&0.422649730810&,\\C^{\prime\prime\prime}&{}\approx{}&0.422649730810&{}:{}&0.422649730810&{}:{}&0.154700538379&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&0.019512685773&{}:{}&-0.014284277378&{}:{}&0.994771591605&,\\B^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&-0.014284277378&{}:{}&0.019512685773&{}:{}&0.994771591605&,\\C^{\prime\prime\prime}_{\mathbf{1}}&{}\approx{}&1.577350269190&{}:{}&1.577350269190&{}:{}&-2.154700538379&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&0.019512685773&{}:{}&0.994771591605&{}:{}&-0.014284277378&,\\B^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&1.577350269190&{}:{}&-2.154700538379&{}:{}&1.577350269190&,\\C^{\prime\prime\prime}_{\mathbf{2}}&{}\approx{}&-0.014284277378&{}:{}&0.994771591605&{}:{}&0.019512685773&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&0.154700538379&{}:{}&0.422649730810&{}:{}&0.422649730810&,\\B^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.356473719264&{}:{}&0.363466037631&{}:{}&0.993007681634&,\\C^{\prime\prime\prime}_{\mathbf{3}}&{}\approx{}&-0.356473719264&{}:{}&0.993007681634&{}:{}&0.363466037631&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&-2.154700538379&{}:{}&1.577350269190&{}:{}&1.577350269190&,\\B^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.994771591605&{}:{}&0.019512685773&{}:{}&-0.014284277378&,\\C^{\prime\prime\prime}_{\mathbf{4}}&{}\approx{}&0.994771591605&{}:{}&-0.014284277378&{}:{}&0.019512685773&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.363466037631&{}:{}&-0.356473719264&{}:{}&0.993007681634&,\\B^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.422649730810&{}:{}&0.154700538379&{}:{}&0.422649730810&,\\C^{\prime\prime\prime}_{\mathbf{5}}&{}\approx{}&0.993007681634&{}:{}&-0.356473719264&{}:{}&0.363466037631&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.363466037631&{}:{}&0.993007681634&{}:{}&-0.356473719264&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.993007681634&{}:{}&0.363466037631&{}:{}&-0.356473719264&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.422649730810&{}:{}&0.422649730810&{}:{}&0.154700538379&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-2.154700538379&{}:{}&1.577350269190&{}:{}&1.577350269190&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&1.577350269190&{}:{}&-2.154700538379&{}:{}&1.577350269190&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&1.577350269190&{}:{}&1.577350269190&{}:{}&-2.154700538379&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.224009237740&{}:{}&0.612004618870&{}:{}&0.612004618870&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.608290376865&{}:{}&0.430940107676&{}:{}&1.177350269190&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.608290376865&{}:{}&1.177350269190&{}:{}&0.430940107676&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&-0.105930302945&{}:{}&1.080081515006&{}:{}&0.025848787939&,\\B^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&0.136200941605&{}:{}&0.694362780359&{}:{}&0.169436278036&,\\C^{\prime\prime\prime}_{\mathbf{1a}}&{}\approx{}&0.017217975236&{}:{}&0.895003474807&{}:{}&0.087778549957&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&-0.105930302945&{}:{}&0.025848787939&{}:{}&1.080081515006&,\\B^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.017217975236&{}:{}&0.087778549957&{}:{}&0.895003474807&,\\C^{\prime\prime\prime}_{\mathbf{2a}}&{}\approx{}&0.136200941605&{}:{}&0.169436278036&{}:{}&0.694362780359&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&-0.224009237740&{}:{}&0.612004618870&{}:{}&0.612004618870&,\\B^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.163986143390&{}:{}&0.224009237740&{}:{}&0.612004618870&,\\C^{\prime\prime\prime}_{\mathbf{3a}}&{}\approx{}&0.163986143390&{}:{}&0.612004618870&{}:{}&0.224009237740&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&0.405827419558&{}:{}&0.297086290221&{}:{}&0.297086290221&,\\B^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.108741129337&{}:{}&-0.405827419558&{}:{}&0.297086290221&,\\C^{\prime\prime\prime}_{\mathbf{4a}}&{}\approx{}&1.108741129337&{}:{}&0.297086290221&{}:{}&-0.405827419558&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&0.474645386743&{}:{}&0.432251770720&{}:{}&0.093102842536&,\\B^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.085585763082&{}:{}&-0.106470138742&{}:{}&0.020884375660&,\\C^{\prime\prime\prime}_{\mathbf{5a}}&{}\approx{}&1.008837226334&{}:{}&0.090105706697&{}:{}&-0.098942933031&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&0.474645386743&{}:{}&0.093102842536&{}:{}&0.432251770720&,\\B^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.008837226334&{}:{}&-0.098942933031&{}:{}&0.090105706697&,\\C^{\prime\prime\prime}_{\mathbf{6a}}&{}\approx{}&1.085585763082&{}:{}&0.020884375660&{}:{}&-0.106470138742&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&0.405827419558&{}:{}&0.297086290221&{}:{}&0.297086290221&,\\B^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.008290376865&{}:{}&-0.030940107676&{}:{}&0.022649730810&,\\C^{\prime\prime\prime}_{\mathbf{7a}}&{}\approx{}&1.008290376865&{}:{}&0.022649730810&{}:{}&-0.030940107676&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.430940107676&{}:{}&-0.608290376865&{}:{}&1.177350269190&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.612004618870&{}:{}&-0.224009237740&{}:{}&0.612004618870&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&1.177350269190&{}:{}&-0.608290376865&{}:{}&0.430940107676&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.694362780359&{}:{}&0.136200941605&{}:{}&0.169436278036&,\\B^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&1.080081515006&{}:{}&-0.105930302945&{}:{}&0.025848787939&,\\C^{\prime\prime\prime}_{\mathbf{1b}}&{}\approx{}&0.895003474807&{}:{}&0.017217975236&{}:{}&0.087778549957&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&-0.405827419558&{}:{}&1.108741129337&{}:{}&0.297086290221&,\\B^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.297086290221&{}:{}&0.405827419558&{}:{}&0.297086290221&,\\C^{\prime\prime\prime}_{\mathbf{2b}}&{}\approx{}&0.297086290221&{}:{}&1.108741129337&{}:{}&-0.405827419558&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&-0.106470138742&{}:{}&1.085585763082&{}:{}&0.020884375660&,\\B^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.432251770720&{}:{}&0.474645386743&{}:{}&0.093102842536&,\\C^{\prime\prime\prime}_{\mathbf{3b}}&{}\approx{}&0.090105706697&{}:{}&1.008837226334&{}:{}&-0.098942933031&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.087778549957&{}:{}&0.017217975236&{}:{}&0.895003474807&,\\B^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.025848787939&{}:{}&-0.105930302945&{}:{}&1.080081515006&,\\C^{\prime\prime\prime}_{\mathbf{4b}}&{}\approx{}&0.169436278036&{}:{}&0.136200941605&{}:{}&0.694362780359&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.224009237740&{}:{}&0.163986143390&{}:{}&0.612004618870&,\\B^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.612004618870&{}:{}&-0.224009237740&{}:{}&0.612004618870&,\\C^{\prime\prime\prime}_{\mathbf{5b}}&{}\approx{}&0.612004618870&{}:{}&0.163986143390&{}:{}&0.224009237740&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&-0.098942933031&{}:{}&1.008837226334&{}:{}&0.090105706697&,\\B^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.093102842536&{}:{}&0.474645386743&{}:{}&0.432251770720&,\\C^{\prime\prime\prime}_{\mathbf{6b}}&{}\approx{}&0.020884375660&{}:{}&1.085585763082&{}:{}&-0.106470138742&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&-0.030940107676&{}:{}&1.008290376865&{}:{}&0.022649730810&,\\B^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.297086290221&{}:{}&0.405827419558&{}:{}&0.297086290221&,\\C^{\prime\prime\prime}_{\mathbf{7b}}&{}\approx{}&0.022649730810&{}:{}&1.008290376865&{}:{}&-0.030940107676&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.430940107676&{}:{}&1.177350269190&{}:{}&-0.608290376865&,\\B^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&1.177350269190&{}:{}&0.430940107676&{}:{}&-0.608290376865&,\\C^{\prime\prime\prime}_{\mathbf{c}}&{}\approx{}&0.612004618870&{}:{}&0.612004618870&{}:{}&-0.224009237740&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&-0.405827419558&{}:{}&0.297086290221&{}:{}&1.108741129337&,\\B^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.297086290221&{}:{}&-0.405827419558&{}:{}&1.108741129337&,\\C^{\prime\prime\prime}_{\mathbf{1c}}&{}\approx{}&0.297086290221&{}:{}&0.297086290221&{}:{}&0.405827419558&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.694362780359&{}:{}&0.169436278036&{}:{}&0.136200941605&,\\B^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&0.895003474807&{}:{}&0.087778549957&{}:{}&0.017217975236&,\\C^{\prime\prime\prime}_{\mathbf{2c}}&{}\approx{}&1.080081515006&{}:{}&0.025848787939&{}:{}&-0.105930302945&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&-0.106470138742&{}:{}&0.020884375660&{}:{}&1.085585763082&,\\B^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.090105706697&{}:{}&-0.098942933031&{}:{}&1.008837226334&,\\C^{\prime\prime\prime}_{\mathbf{3c}}&{}\approx{}&0.432251770720&{}:{}&0.093102842536&{}:{}&0.474645386743&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.087778549957&{}:{}&0.895003474807&{}:{}&0.017217975236&,\\B^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.169436278036&{}:{}&0.694362780359&{}:{}&0.136200941605&,\\C^{\prime\prime\prime}_{\mathbf{4c}}&{}\approx{}&0.025848787939&{}:{}&1.080081515006&{}:{}&-0.105930302945&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&-0.098942933031&{}:{}&0.090105706697&{}:{}&1.008837226334&,\\B^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&0.020884375660&{}:{}&-0.106470138742&{}:{}&1.085585763082&,\\C^{\prime\prime\prime}_{\mathbf{5c}}&{}\approx{}&0.093102842536&{}:{}&0.432251770720&{}:{}&0.474645386743&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.224009237740&{}:{}&0.612004618870&{}:{}&0.163986143390&,\\B^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.612004618870&{}:{}&0.224009237740&{}:{}&0.163986143390&,\\C^{\prime\prime\prime}_{\mathbf{6c}}&{}\approx{}&0.612004618870&{}:{}&0.612004618870&{}:{}&-0.224009237740&,\\[.5em] A^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&-0.030940107676&{}:{}&0.022649730810&{}:{}&1.008290376865&,\\B^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.022649730810&{}:{}&-0.030940107676&{}:{}&1.008290376865&,\\C^{\prime\prime\prime}_{\mathbf{7c}}&{}\approx{}&0.297086290221&{}:{}&0.297086290221&{}:{}&0.405827419558&. \end{alignedat} \] \[ \begin{alignedat}{4} A^*&{}\approx{}&0.000000000000&{}:{}&0.500000000000&{}:{}&0.500000000000&,\\B^*&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1}}&{}\approx{}&0.000000000000&{}:{}&-0.077350269190&{}:{}&1.077350269190&,\\B^*_{\mathbf{1}}&{}\approx{}&-0.077350269190&{}:{}&0.000000000000&{}:{}&1.077350269190&,\\C^*_{\mathbf{1}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2}}&{}\approx{}&0.000000000000&{}:{}&1.077350269190&{}:{}&-0.077350269190&,\\B^*_{\mathbf{2}}&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*_{\mathbf{2}}&{}\approx{}&-0.077350269190&{}:{}&1.077350269190&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3}}&{}\approx{}&0.000000000000&{}:{}&0.500000000000&{}:{}&0.500000000000&,\\B^*_{\mathbf{3}}&{}\approx{}&-0.077350269190&{}:{}&0.000000000000&{}:{}&1.077350269190&,\\C^*_{\mathbf{3}}&{}\approx{}&-0.077350269190&{}:{}&1.077350269190&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4}}&{}\approx{}&0.000000000000&{}:{}&0.500000000000&{}:{}&0.500000000000&,\\B^*_{\mathbf{4}}&{}\approx{}&1.077350269190&{}:{}&0.000000000000&{}:{}&-0.077350269190&,\\C^*_{\mathbf{4}}&{}\approx{}&1.077350269190&{}:{}&-0.077350269190&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5}}&{}\approx{}&0.000000000000&{}:{}&-0.077350269190&{}:{}&1.077350269190&,\\B^*_{\mathbf{5}}&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*_{\mathbf{5}}&{}\approx{}&1.077350269190&{}:{}&-0.077350269190&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.077350269190&{}:{}&-0.077350269190&,\\B^*_{\mathbf{6}}&{}\approx{}&1.077350269190&{}:{}&0.000000000000&{}:{}&-0.077350269190&,\\C^*_{\mathbf{6}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.500000000000&{}:{}&0.500000000000&,\\B^*_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.500000000000&{}:{}&0.500000000000&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.866025403784&{}:{}&0.000000000000&{}:{}&1.866025403784&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.866025403784&{}:{}&1.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1a}}&{}\approx{}&0.000000000000&{}:{}&1.500000000000&{}:{}&-0.500000000000&,\\B^*_{\mathbf{1a}}&{}\approx{}&-0.866025403784&{}:{}&0.000000000000&{}:{}&1.866025403784&,\\C^*_{\mathbf{1a}}&{}\approx{}&0.133974596216&{}:{}&0.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2a}}&{}\approx{}&0.000000000000&{}:{}&-0.500000000000&{}:{}&1.500000000000&,\\B^*_{\mathbf{2a}}&{}\approx{}&0.133974596216&{}:{}&0.000000000000&{}:{}&0.866025403784&,\\C^*_{\mathbf{2a}}&{}\approx{}&-0.866025403784&{}:{}&1.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3a}}&{}\approx{}&0.000000000000&{}:{}&0.500000000000&{}:{}&0.500000000000&,\\B^*_{\mathbf{3a}}&{}\approx{}&0.133974596216&{}:{}&0.000000000000&{}:{}&0.866025403784&,\\C^*_{\mathbf{3a}}&{}\approx{}&0.133974596216&{}:{}&0.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4a}}&{}\approx{}&0.000000000000&{}:{}&0.500000000000&{}:{}&0.500000000000&,\\B^*_{\mathbf{4a}}&{}\approx{}&1.866025403784&{}:{}&0.000000000000&{}:{}&-0.866025403784&,\\C^*_{\mathbf{4a}}&{}\approx{}&1.866025403784&{}:{}&-0.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5a}}&{}\approx{}&0.000000000000&{}:{}&-0.500000000000&{}:{}&1.500000000000&,\\B^*_{\mathbf{5a}}&{}\approx{}&1.866025403784&{}:{}&0.000000000000&{}:{}&-0.866025403784&,\\C^*_{\mathbf{5a}}&{}\approx{}&0.866025403784&{}:{}&0.133974596216&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6a}}&{}\approx{}&0.000000000000&{}:{}&1.500000000000&{}:{}&-0.500000000000&,\\B^*_{\mathbf{6a}}&{}\approx{}&0.866025403784&{}:{}&0.000000000000&{}:{}&0.133974596216&,\\C^*_{\mathbf{6a}}&{}\approx{}&1.866025403784&{}:{}&-0.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7a}}&{}\approx{}&0.000000000000&{}:{}&0.500000000000&{}:{}&0.500000000000&,\\B^*_{\mathbf{7a}}&{}\approx{}&0.866025403784&{}:{}&0.000000000000&{}:{}&0.133974596216&,\\C^*_{\mathbf{7a}}&{}\approx{}&0.866025403784&{}:{}&0.133974596216&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-0.866025403784&{}:{}&1.866025403784&,\\B^*_{\mathbf{b}}&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*_{\mathbf{b}}&{}\approx{}&1.866025403784&{}:{}&-0.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1b}}&{}\approx{}&0.000000000000&{}:{}&-0.866025403784&{}:{}&1.866025403784&,\\B^*_{\mathbf{1b}}&{}\approx{}&1.500000000000&{}:{}&0.000000000000&{}:{}&-0.500000000000&,\\C^*_{\mathbf{1b}}&{}\approx{}&0.866025403784&{}:{}&0.133974596216&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2b}}&{}\approx{}&0.000000000000&{}:{}&1.866025403784&{}:{}&-0.866025403784&,\\B^*_{\mathbf{2b}}&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*_{\mathbf{2b}}&{}\approx{}&-0.866025403784&{}:{}&1.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3b}}&{}\approx{}&0.000000000000&{}:{}&1.866025403784&{}:{}&-0.866025403784&,\\B^*_{\mathbf{3b}}&{}\approx{}&-0.500000000000&{}:{}&0.000000000000&{}:{}&1.500000000000&,\\C^*_{\mathbf{3b}}&{}\approx{}&0.133974596216&{}:{}&0.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4b}}&{}\approx{}&0.000000000000&{}:{}&0.133974596216&{}:{}&0.866025403784&,\\B^*_{\mathbf{4b}}&{}\approx{}&-0.500000000000&{}:{}&0.000000000000&{}:{}&1.500000000000&,\\C^*_{\mathbf{4b}}&{}\approx{}&1.866025403784&{}:{}&-0.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5b}}&{}\approx{}&0.000000000000&{}:{}&0.133974596216&{}:{}&0.866025403784&,\\B^*_{\mathbf{5b}}&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*_{\mathbf{5b}}&{}\approx{}&0.866025403784&{}:{}&0.133974596216&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6b}}&{}\approx{}&0.000000000000&{}:{}&0.866025403784&{}:{}&0.133974596216&,\\B^*_{\mathbf{6b}}&{}\approx{}&1.500000000000&{}:{}&0.000000000000&{}:{}&-0.500000000000&,\\C^*_{\mathbf{6b}}&{}\approx{}&-0.866025403784&{}:{}&1.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7b}}&{}\approx{}&0.000000000000&{}:{}&0.866025403784&{}:{}&0.133974596216&,\\B^*_{\mathbf{7b}}&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*_{\mathbf{7b}}&{}\approx{}&0.133974596216&{}:{}&0.866025403784&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{c}}&{}\approx{}&0.000000000000&{}:{}&1.866025403784&{}:{}&-0.866025403784&,\\B^*_{\mathbf{c}}&{}\approx{}&1.866025403784&{}:{}&0.000000000000&{}:{}&-0.866025403784&,\\C^*_{\mathbf{c}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{1c}}&{}\approx{}&0.000000000000&{}:{}&-0.866025403784&{}:{}&1.866025403784&,\\B^*_{\mathbf{1c}}&{}\approx{}&-0.866025403784&{}:{}&0.000000000000&{}:{}&1.866025403784&,\\C^*_{\mathbf{1c}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{2c}}&{}\approx{}&0.000000000000&{}:{}&1.866025403784&{}:{}&-0.866025403784&,\\B^*_{\mathbf{2c}}&{}\approx{}&0.866025403784&{}:{}&0.000000000000&{}:{}&0.133974596216&,\\C^*_{\mathbf{2c}}&{}\approx{}&1.500000000000&{}:{}&-0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{3c}}&{}\approx{}&0.000000000000&{}:{}&-0.866025403784&{}:{}&1.866025403784&,\\B^*_{\mathbf{3c}}&{}\approx{}&0.133974596216&{}:{}&0.000000000000&{}:{}&0.866025403784&,\\C^*_{\mathbf{3c}}&{}\approx{}&-0.500000000000&{}:{}&1.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{4c}}&{}\approx{}&0.000000000000&{}:{}&0.866025403784&{}:{}&0.133974596216&,\\B^*_{\mathbf{4c}}&{}\approx{}&1.866025403784&{}:{}&0.000000000000&{}:{}&-0.866025403784&,\\C^*_{\mathbf{4c}}&{}\approx{}&-0.500000000000&{}:{}&1.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{5c}}&{}\approx{}&0.000000000000&{}:{}&0.133974596216&{}:{}&0.866025403784&,\\B^*_{\mathbf{5c}}&{}\approx{}&-0.866025403784&{}:{}&0.000000000000&{}:{}&1.866025403784&,\\C^*_{\mathbf{5c}}&{}\approx{}&1.500000000000&{}:{}&-0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{6c}}&{}\approx{}&0.000000000000&{}:{}&0.866025403784&{}:{}&0.133974596216&,\\B^*_{\mathbf{6c}}&{}\approx{}&0.866025403784&{}:{}&0.000000000000&{}:{}&0.133974596216&,\\C^*_{\mathbf{6c}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&,\\[.5em] A^*_{\mathbf{7c}}&{}\approx{}&0.000000000000&{}:{}&0.133974596216&{}:{}&0.866025403784&,\\B^*_{\mathbf{7c}}&{}\approx{}&0.133974596216&{}:{}&0.000000000000&{}:{}&0.866025403784&,\\C^*_{\mathbf{7c}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]