History of Volumes of the hyperbolic Coxeter simplices

   number-header: $\mathrm{Vol}$ Numbers:-  '3':-    '[3,3,6]':-      number: '0.04228923360040223437588343976143834524757038781376249133406204611569156151076016758901959809284402896'-      comment: Kozma and Szirmai write this simplex as $\overline{V}_3$ and give the-        check decimal $0.0422892336\ldots$ in their Table 1.-    '[3,6,3]':-      number: '0.1691569344016089375035337590457533809902815512550499653362481844627662460430406703560783923713761158'-      comment: Kozma and Szirmai write this simplex as $\overline{Y}_3$ and give the-        check decimal $0.1691569344\ldots$ in their Table 1.-    '[6,3^[3]]':-      number: '0.5074708032048268125106012771372601429708446537651498960087445533882987381291220110682351771141283475'-      comment: Kozma and Szirmai write this simplex as $\overline{VP}_3$ and give-        the check decimal $0.5074708032\ldots$ in their Table 1.-    '[3^[3,3]]':-      number: '1.014941606409653625021202554274520285941689307530299792017489106776597476258244022136470354228256695'-      comment: Kozma and Szirmai write this simplex as $\widehat{PP}_3$ and give the-        check decimal $1.0149416064\ldots$ in their Table 1.-    '[3,3^[3]]':-      number: '0.08457846720080446875176687952287669049514077562752498266812409223138312302152033517803919618568805791'-      comment: Kozma and Szirmai write this simplex as $\overline{P}_3$ and give the-        check decimal $0.0845784672\ldots$ in their Table 1.-    '[6,3,6]':-      number: '0.2537354016024134062553006385686300714854223268825749480043722766941493690645610055341175885570641737'-      comment: Kozma and Szirmai write this simplex as $\overline{Z}_3$ and give the-        check decimal $0.2537354016\ldots$ in their Table 1.-    '[4,3,6]':-      number: '0.1057230840010055859397085994035958631189259695344062283351551152892289037769004189725489952321100724'-      comment: Kozma and Szirmai write this simplex as $\overline{BV}_3$ and give-        the check decimal $0.1057230840\ldots$ in their Table 1.-    '[4,3^[3]]':-      number: '0.2114461680020111718794171988071917262378519390688124566703102305784578075538008379450979904642201448'-      comment: Kozma and Szirmai write this simplex as $\overline{BP}_3$ and give-        the check decimal $0.2114461680\ldots$ in their Table 1.-    '[4,3^[1,1]]':-      number: '0.2114461680020111718794171988071917262378519390688124566703102305784578075538008379450979904642201448'-      comment: Kozma and Szirmai write this simplex as $\overline{DV}_3$ and give-        the check decimal $0.2114461680\ldots$ in their Table 1.-    '[3^[]x[]]':-      number: '0.4228923360040223437588343976143834524757038781376249133406204611569156151076016758901959809284402896'-      comment: Kozma and Szirmai write this simplex as $\overline{DP}_3$ and give-        the check decimal $0.4228923360\ldots$ in their Table 1.-    '[(3,6)^[2]]':-      number: '0.8457846720080446875176687952287669049514077562752498266812409223138312302152033517803919618568805791'-      comment: Kozma and Szirmai write this simplex as $\widehat{VV}_3$ and give the-        check decimal $0.8457846720\ldots$ in their Table 1.-    '[3,4,4]':-      number: '0.07633046618143491792121695957769867589784578119013934452220817663514691831468789745661304274384292552'-      comment: Kozma and Szirmai write this simplex as $\overline{R}_3$ and give the-        check decimal $0.0763304662\ldots$ in their Table 1.-    '[3,4^[1,1]]':-      number: '0.1526609323628698358424339191553973517956915623802786890444163532702938366293757949132260854876858510'-      comment: Kozma and Szirmai write this simplex as $\overline{O}_3$ and give the-        check decimal $0.1526609324\ldots$ in their Table 1.-    '[(3^2,4^2)]':-      number: '0.3053218647257396716848678383107947035913831247605573780888327065405876732587515898264521709753717021'-      comment: Kozma and Szirmai write this simplex as $\widehat{BR}_3$ and give the-        check decimal $0.3053218647\ldots$ in their Table 1.-    '[4,4,4]':-      number: '0.2289913985443047537636508787330960276935373435704180335666245299054407549440636923698391282315287766'-      comment: Kozma and Szirmai write this simplex as $\overline{N}_3$ and give the-        check decimal $0.2289913985\ldots$ in their Table 1.-    '[4^[1,1,1]]':-      number: '0.4579827970886095075273017574661920553870746871408360671332490598108815098881273847396782564630575531'-      comment: Kozma and Szirmai write this simplex as $\overline{M}_3$ and give the-        check decimal $0.4579827971\ldots$ in their Table 1.-    '[4^[4]]':-      number: '0.9159655941772190150546035149323841107741493742816721342664981196217630197762547694793565129261151062'-      comment: Kozma and Szirmai write this simplex as $\widehat{RR}_3$ and give the-        check decimal $0.9159655942\ldots$ in their Table 1.-    '[5,3,6]':-      number: '0.1715016612824999469000279964800349893678040756955395984715202632150696956462308486829963126912896437'-      comment: Kozma and Szirmai write this simplex as $\overline{HV}_3$ and give-        the check decimal $0.1715016613\ldots$ in their Table 1.-    '[5,3^[3]]':-      number: '0.3430033225649998938000559929600699787356081513910791969430405264301393912924616973659926253825792874'-      comment: Kozma and Szirmai write this simplex as $\overline{HP}_3$ and give-        the check decimal $0.3430033226\ldots$ in their Table 1.-    '[(3^3,6)]':-      number: '0.3641071003648810077218511179625890780335435014490911457147265838487516441831766328583240759519059958'-      comment: Kozma and Szirmai write this simplex as $\widehat{AV}_3$ and give the-        check decimal $0.3641071004\ldots$ in their Table 1.-    '[(3,4,3,6)]':-      number: '0.5258402692379140577613335798917157905882920634862270030080661680012334531885097372803152791544391707'-      comment: Kozma and Szirmai write this simplex as $\widehat{BV}_3$ and give the-        check decimal $0.5258402692\ldots$ in their Table 1.-    '[(3,5,3,6)]':-      number: '0.6729858045482070864989016868337961076494172338060998040665663070759617338022679831662452322170737629'-      comment: Kozma and Szirmai write this simplex as $\widehat{HV}_3$ and give the-        check decimal $0.6729858045\ldots$ in their Table 1.-    '[(3,4^3)]':-      number: '0.5562821155610392060029590597531612500704676674573281874254955747898259766273202377781400625263246846'-      comment: Kozma and Szirmai write this simplex as $\widehat{CR}_3$ and give the-        check decimal $0.5562821156\ldots$ in their Table 1.+- params:+    n: '3'+    diagram: '[3,3,6]'+  number: '0.04228923360040223437588343976143834524757038781376249133406204611569156151076016758901959809284402896'+  comment: Kozma and Szirmai write this simplex as $\overline{V}_3$. Its volume is+    $\Lambda(\pi/3)/8$.+- params:+    n: '3'+    diagram: '[3,6,3]'+  number: '0.1691569344016089375035337590457533809902815512550499653362481844627662460430406703560783923713761158'+  comment: Kozma and Szirmai write this simplex as $\overline{Y}_3$. Its volume is+    $\Lambda(\pi/3)/2$, which is the covolume of $\mathrm{PSL}_2(\mathbb{Z}[\omega])$+    in HREF{Covolumes_of_the_Bianchi_groups#-3}[the Bianchi covolume table].+- params:+    n: '3'+    diagram: '[6,3^{[3]}]'+  number: '0.5074708032048268125106012771372601429708446537651498960087445533882987381291220110682351771141283475'+  comment: Kozma and Szirmai write this simplex as $\overline{VP}_3$. Its volume is+    $3\Lambda(\pi/3)/2$.+- params:+    n: '3'+    diagram: '[3^{[3,3]}]'+  number: '1.014941606409653625021202554274520285941689307530299792017489106776597476258244022136470354228256695'+  comment: Kozma and Szirmai write this simplex as $\widehat{PP}_3$. Its volume is+    $3\Lambda(\pi/3)=\mathrm{Cl}_2(\pi/3)$.+- params:+    n: '3'+    diagram: '[3,3^{[3]}]'+  number: '0.08457846720080446875176687952287669049514077562752498266812409223138312302152033517803919618568805791'+  comment: Kozma and Szirmai write this simplex as $\overline{P}_3$. Its volume is+    $\Lambda(\pi/3)/4$.+- params:+    n: '3'+    diagram: '[6,3,6]'+  number: '0.2537354016024134062553006385686300714854223268825749480043722766941493690645610055341175885570641737'+  comment: Kozma and Szirmai write this simplex as $\overline{Z}_3$. Its volume is+    $3\Lambda(\pi/3)/4$.+- params:+    n: '3'+    diagram: '[4,3,6]'+  number: '0.1057230840010055859397085994035958631189259695344062283351551152892289037769004189725489952321100724'+  comment: Kozma and Szirmai write this simplex as $\overline{BV}_3$. Its volume is+    $5\Lambda(\pi/3)/16$.+- params:+    n: '3'+    diagram: '[4,3^{[3]}]'+  number: '0.2114461680020111718794171988071917262378519390688124566703102305784578075538008379450979904642201448'+  comment: Kozma and Szirmai write this simplex as $\overline{BP}_3$. Its volume is+    $5\Lambda(\pi/3)/8$.+- params:+    n: '3'+    diagram: '[6,3^{1,1}]'+  number: '0.2114461680020111718794171988071917262378519390688124566703102305784578075538008379450979904642201448'+  comment: Kozma and Szirmai write this simplex as $\overline{DV}_3$. Its volume is+    $5\Lambda(\pi/3)/8$.+- params:+    n: '3'+    diagram: '[3^{[]x[]}]'+  number: '0.4228923360040223437588343976143834524757038781376249133406204611569156151076016758901959809284402896'+  comment: Kozma and Szirmai write this simplex as $\overline{DP}_3$. Its volume is+    $5\Lambda(\pi/3)/4$.+- params:+    n: '3'+    diagram: '[(3,6)^{[2]}]'+  number: '0.8457846720080446875176687952287669049514077562752498266812409223138312302152033517803919618568805791'+  comment: Kozma and Szirmai write this simplex as $\widehat{VV}_3$. Its volume is+    $5\Lambda(\pi/3)/2$.+- params:+    n: '3'+    diagram: '[3,4,4]'+  number: '0.07633046618143491792121695957769867589784578119013934452220817663514691831468789745661304274384292552'+  comment: Kozma and Szirmai write this simplex as $\overline{R}_3$. Its volume is+    $\Lambda(\pi/4)/6$.+- params:+    n: '3'+    diagram: '[3,4^{1,1}]'+  number: '0.1526609323628698358424339191553973517956915623802786890444163532702938366293757949132260854876858510'+  comment: Kozma and Szirmai write this simplex as $\overline{O}_3$. Its volume is+    $\Lambda(\pi/4)/3$.+- params:+    n: '3'+    diagram: '[(3^2,4^2)]'+  number: '0.3053218647257396716848678383107947035913831247605573780888327065405876732587515898264521709753717021'+  comment: Kozma and Szirmai write this simplex as $\widehat{BR}_3$. Its volume is+    $2\Lambda(\pi/4)/3$, which is the covolume of $\mathrm{PSL}_2(\mathbb{Z}[i])$+    in HREF{Covolumes_of_the_Bianchi_groups#-4}[the Bianchi covolume table].+- params:+    n: '3'+    diagram: '[4,4,4]'+  number: '0.2289913985443047537636508787330960276935373435704180335666245299054407549440636923698391282315287766'+  comment: Kozma and Szirmai write this simplex as $\overline{N}_3$. Its volume is+    $\Lambda(\pi/4)/2$.+- params:+    n: '3'+    diagram: '[4^{1,1,1}]'+  number: '0.4579827970886095075273017574661920553870746871408360671332490598108815098881273847396782564630575531'+  comment: Kozma and Szirmai write this simplex as $\overline{M}_3$. Its volume is+    $\Lambda(\pi/4)$.+- params:+    n: '3'+    diagram: '[4^{[4]}]'+  number: '0.9159655941772190150546035149323841107741493742816721342664981196217630197762547694793565129261151062'+  comment: Kozma and Szirmai write this simplex as $\widehat{RR}_3$. Its volume is+    $2\Lambda(\pi/4)$, which is HREF{Values_of_the_Clausen_functions_at_rational_multiples_of#2,1/2}[Catalan's+    constant $G$].+- params:+    n: '3'+    diagram: '[5,3,6]'+  number: '0.1715016612824999469000279964800349893678040756955395984715202632150696956462308486829963126912896437'+  comment: Kozma and Szirmai write this simplex as $\overline{HV}_3$.+- params:+    n: '3'+    diagram: '[5,3^{[3]}]'+  number: '0.3430033225649998938000559929600699787356081513910791969430405264301393912924616973659926253825792874'+  comment: Kozma and Szirmai write this simplex as $\overline{HP}_3$.+- params:+    n: '3'+    diagram: '[(3^3,6)]'+  number: '0.3641071003648810077218511179625890780335435014490911457147265838487516441831766328583240759519059958'+  comment: Kozma and Szirmai write this simplex as $\widehat{AV}_3$.+- params:+    n: '3'+    diagram: '[(3,4,3,6)]'+  number: '0.5258402692379140577613335798917157905882920634862270030080661680012334531885097372803152791544391707'+  comment: Kozma and Szirmai write this simplex as $\widehat{BV}_3$.+- params:+    n: '3'+    diagram: '[(3,5,3,6)]'+  number: '0.6729858045482070864989016868337961076494172338060998040665663070759617338022679831662452322170737629'+  comment: Kozma and Szirmai write this simplex as $\widehat{HV}_3$.+- params:+    n: '3'+    diagram: '[(3,4^3)]'+  number: '0.5562821155610392060029590597531612500704676674573281874254955747898259766273202377781400625263246846'+  comment: Kozma and Szirmai write this simplex as $\widehat{CR}_3$.