Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768n
if this polytope has a name.
Group : SmallGroup(768,1086335)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 192, 48
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6}*384e
   4-fold quotients : {8,3}*192
   8-fold quotients : {4,6}*96
   16-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {4,3}*24, {2,6}*24
   64-fold quotients : {2,3}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,124)(  2,123)(  3,122)(  4,121)(  5,128)(  6,127)(  7,126)(  8,125)
(  9,116)( 10,115)( 11,114)( 12,113)( 13,120)( 14,119)( 15,118)( 16,117)
( 17,110)( 18,109)( 19,112)( 20,111)( 21,106)( 22,105)( 23,108)( 24,107)
( 25,102)( 26,101)( 27,104)( 28,103)( 29, 98)( 30, 97)( 31,100)( 32, 99)
( 33,156)( 34,155)( 35,154)( 36,153)( 37,160)( 38,159)( 39,158)( 40,157)
( 41,148)( 42,147)( 43,146)( 44,145)( 45,152)( 46,151)( 47,150)( 48,149)
( 49,142)( 50,141)( 51,144)( 52,143)( 53,138)( 54,137)( 55,140)( 56,139)
( 57,134)( 58,133)( 59,136)( 60,135)( 61,130)( 62,129)( 63,132)( 64,131)
( 65,188)( 66,187)( 67,186)( 68,185)( 69,192)( 70,191)( 71,190)( 72,189)
( 73,180)( 74,179)( 75,178)( 76,177)( 77,184)( 78,183)( 79,182)( 80,181)
( 81,174)( 82,173)( 83,176)( 84,175)( 85,170)( 86,169)( 87,172)( 88,171)
( 89,166)( 90,165)( 91,168)( 92,167)( 93,162)( 94,161)( 95,164)( 96,163)
(193,316)(194,315)(195,314)(196,313)(197,320)(198,319)(199,318)(200,317)
(201,308)(202,307)(203,306)(204,305)(205,312)(206,311)(207,310)(208,309)
(209,302)(210,301)(211,304)(212,303)(213,298)(214,297)(215,300)(216,299)
(217,294)(218,293)(219,296)(220,295)(221,290)(222,289)(223,292)(224,291)
(225,348)(226,347)(227,346)(228,345)(229,352)(230,351)(231,350)(232,349)
(233,340)(234,339)(235,338)(236,337)(237,344)(238,343)(239,342)(240,341)
(241,334)(242,333)(243,336)(244,335)(245,330)(246,329)(247,332)(248,331)
(249,326)(250,325)(251,328)(252,327)(253,322)(254,321)(255,324)(256,323)
(257,380)(258,379)(259,378)(260,377)(261,384)(262,383)(263,382)(264,381)
(265,372)(266,371)(267,370)(268,369)(269,376)(270,375)(271,374)(272,373)
(273,366)(274,365)(275,368)(276,367)(277,362)(278,361)(279,364)(280,363)
(281,358)(282,357)(283,360)(284,359)(285,354)(286,353)(287,356)(288,355);;
s1 := (  1,289)(  2,290)(  3,292)(  4,291)(  5,294)(  6,293)(  7,295)(  8,296)
(  9,304)( 10,303)( 11,301)( 12,302)( 13,299)( 14,300)( 15,298)( 16,297)
( 17,313)( 18,314)( 19,316)( 20,315)( 21,318)( 22,317)( 23,319)( 24,320)
( 25,305)( 26,306)( 27,308)( 28,307)( 29,310)( 30,309)( 31,311)( 32,312)
( 33,353)( 34,354)( 35,356)( 36,355)( 37,358)( 38,357)( 39,359)( 40,360)
( 41,368)( 42,367)( 43,365)( 44,366)( 45,363)( 46,364)( 47,362)( 48,361)
( 49,377)( 50,378)( 51,380)( 52,379)( 53,382)( 54,381)( 55,383)( 56,384)
( 57,369)( 58,370)( 59,372)( 60,371)( 61,374)( 62,373)( 63,375)( 64,376)
( 65,321)( 66,322)( 67,324)( 68,323)( 69,326)( 70,325)( 71,327)( 72,328)
( 73,336)( 74,335)( 75,333)( 76,334)( 77,331)( 78,332)( 79,330)( 80,329)
( 81,345)( 82,346)( 83,348)( 84,347)( 85,350)( 86,349)( 87,351)( 88,352)
( 89,337)( 90,338)( 91,340)( 92,339)( 93,342)( 94,341)( 95,343)( 96,344)
( 97,199)( 98,200)( 99,198)(100,197)(101,196)(102,195)(103,193)(104,194)
(105,202)(106,201)(107,203)(108,204)(109,205)(110,206)(111,208)(112,207)
(113,223)(114,224)(115,222)(116,221)(117,220)(118,219)(119,217)(120,218)
(121,215)(122,216)(123,214)(124,213)(125,212)(126,211)(127,209)(128,210)
(129,263)(130,264)(131,262)(132,261)(133,260)(134,259)(135,257)(136,258)
(137,266)(138,265)(139,267)(140,268)(141,269)(142,270)(143,272)(144,271)
(145,287)(146,288)(147,286)(148,285)(149,284)(150,283)(151,281)(152,282)
(153,279)(154,280)(155,278)(156,277)(157,276)(158,275)(159,273)(160,274)
(161,231)(162,232)(163,230)(164,229)(165,228)(166,227)(167,225)(168,226)
(169,234)(170,233)(171,235)(172,236)(173,237)(174,238)(175,240)(176,239)
(177,255)(178,256)(179,254)(180,253)(181,252)(182,251)(183,249)(184,250)
(185,247)(186,248)(187,246)(188,245)(189,244)(190,243)(191,241)(192,242);;
s2 := (  1,161)(  2,163)(  3,162)(  4,164)(  5,168)(  6,166)(  7,167)(  8,165)
(  9,182)( 10,184)( 11,181)( 12,183)( 13,179)( 14,177)( 15,180)( 16,178)
( 17,174)( 18,176)( 19,173)( 20,175)( 21,171)( 22,169)( 23,172)( 24,170)
( 25,191)( 26,189)( 27,192)( 28,190)( 29,186)( 30,188)( 31,185)( 32,187)
( 33,129)( 34,131)( 35,130)( 36,132)( 37,136)( 38,134)( 39,135)( 40,133)
( 41,150)( 42,152)( 43,149)( 44,151)( 45,147)( 46,145)( 47,148)( 48,146)
( 49,142)( 50,144)( 51,141)( 52,143)( 53,139)( 54,137)( 55,140)( 56,138)
( 57,159)( 58,157)( 59,160)( 60,158)( 61,154)( 62,156)( 63,153)( 64,155)
( 65, 97)( 66, 99)( 67, 98)( 68,100)( 69,104)( 70,102)( 71,103)( 72,101)
( 73,118)( 74,120)( 75,117)( 76,119)( 77,115)( 78,113)( 79,116)( 80,114)
( 81,110)( 82,112)( 83,109)( 84,111)( 85,107)( 86,105)( 87,108)( 88,106)
( 89,127)( 90,125)( 91,128)( 92,126)( 93,122)( 94,124)( 95,121)( 96,123)
(193,353)(194,355)(195,354)(196,356)(197,360)(198,358)(199,359)(200,357)
(201,374)(202,376)(203,373)(204,375)(205,371)(206,369)(207,372)(208,370)
(209,366)(210,368)(211,365)(212,367)(213,363)(214,361)(215,364)(216,362)
(217,383)(218,381)(219,384)(220,382)(221,378)(222,380)(223,377)(224,379)
(225,321)(226,323)(227,322)(228,324)(229,328)(230,326)(231,327)(232,325)
(233,342)(234,344)(235,341)(236,343)(237,339)(238,337)(239,340)(240,338)
(241,334)(242,336)(243,333)(244,335)(245,331)(246,329)(247,332)(248,330)
(249,351)(250,349)(251,352)(252,350)(253,346)(254,348)(255,345)(256,347)
(257,289)(258,291)(259,290)(260,292)(261,296)(262,294)(263,295)(264,293)
(265,310)(266,312)(267,309)(268,311)(269,307)(270,305)(271,308)(272,306)
(273,302)(274,304)(275,301)(276,303)(277,299)(278,297)(279,300)(280,298)
(281,319)(282,317)(283,320)(284,318)(285,314)(286,316)(287,313)(288,315);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(384)!(  1,124)(  2,123)(  3,122)(  4,121)(  5,128)(  6,127)(  7,126)
(  8,125)(  9,116)( 10,115)( 11,114)( 12,113)( 13,120)( 14,119)( 15,118)
( 16,117)( 17,110)( 18,109)( 19,112)( 20,111)( 21,106)( 22,105)( 23,108)
( 24,107)( 25,102)( 26,101)( 27,104)( 28,103)( 29, 98)( 30, 97)( 31,100)
( 32, 99)( 33,156)( 34,155)( 35,154)( 36,153)( 37,160)( 38,159)( 39,158)
( 40,157)( 41,148)( 42,147)( 43,146)( 44,145)( 45,152)( 46,151)( 47,150)
( 48,149)( 49,142)( 50,141)( 51,144)( 52,143)( 53,138)( 54,137)( 55,140)
( 56,139)( 57,134)( 58,133)( 59,136)( 60,135)( 61,130)( 62,129)( 63,132)
( 64,131)( 65,188)( 66,187)( 67,186)( 68,185)( 69,192)( 70,191)( 71,190)
( 72,189)( 73,180)( 74,179)( 75,178)( 76,177)( 77,184)( 78,183)( 79,182)
( 80,181)( 81,174)( 82,173)( 83,176)( 84,175)( 85,170)( 86,169)( 87,172)
( 88,171)( 89,166)( 90,165)( 91,168)( 92,167)( 93,162)( 94,161)( 95,164)
( 96,163)(193,316)(194,315)(195,314)(196,313)(197,320)(198,319)(199,318)
(200,317)(201,308)(202,307)(203,306)(204,305)(205,312)(206,311)(207,310)
(208,309)(209,302)(210,301)(211,304)(212,303)(213,298)(214,297)(215,300)
(216,299)(217,294)(218,293)(219,296)(220,295)(221,290)(222,289)(223,292)
(224,291)(225,348)(226,347)(227,346)(228,345)(229,352)(230,351)(231,350)
(232,349)(233,340)(234,339)(235,338)(236,337)(237,344)(238,343)(239,342)
(240,341)(241,334)(242,333)(243,336)(244,335)(245,330)(246,329)(247,332)
(248,331)(249,326)(250,325)(251,328)(252,327)(253,322)(254,321)(255,324)
(256,323)(257,380)(258,379)(259,378)(260,377)(261,384)(262,383)(263,382)
(264,381)(265,372)(266,371)(267,370)(268,369)(269,376)(270,375)(271,374)
(272,373)(273,366)(274,365)(275,368)(276,367)(277,362)(278,361)(279,364)
(280,363)(281,358)(282,357)(283,360)(284,359)(285,354)(286,353)(287,356)
(288,355);
s1 := Sym(384)!(  1,289)(  2,290)(  3,292)(  4,291)(  5,294)(  6,293)(  7,295)
(  8,296)(  9,304)( 10,303)( 11,301)( 12,302)( 13,299)( 14,300)( 15,298)
( 16,297)( 17,313)( 18,314)( 19,316)( 20,315)( 21,318)( 22,317)( 23,319)
( 24,320)( 25,305)( 26,306)( 27,308)( 28,307)( 29,310)( 30,309)( 31,311)
( 32,312)( 33,353)( 34,354)( 35,356)( 36,355)( 37,358)( 38,357)( 39,359)
( 40,360)( 41,368)( 42,367)( 43,365)( 44,366)( 45,363)( 46,364)( 47,362)
( 48,361)( 49,377)( 50,378)( 51,380)( 52,379)( 53,382)( 54,381)( 55,383)
( 56,384)( 57,369)( 58,370)( 59,372)( 60,371)( 61,374)( 62,373)( 63,375)
( 64,376)( 65,321)( 66,322)( 67,324)( 68,323)( 69,326)( 70,325)( 71,327)
( 72,328)( 73,336)( 74,335)( 75,333)( 76,334)( 77,331)( 78,332)( 79,330)
( 80,329)( 81,345)( 82,346)( 83,348)( 84,347)( 85,350)( 86,349)( 87,351)
( 88,352)( 89,337)( 90,338)( 91,340)( 92,339)( 93,342)( 94,341)( 95,343)
( 96,344)( 97,199)( 98,200)( 99,198)(100,197)(101,196)(102,195)(103,193)
(104,194)(105,202)(106,201)(107,203)(108,204)(109,205)(110,206)(111,208)
(112,207)(113,223)(114,224)(115,222)(116,221)(117,220)(118,219)(119,217)
(120,218)(121,215)(122,216)(123,214)(124,213)(125,212)(126,211)(127,209)
(128,210)(129,263)(130,264)(131,262)(132,261)(133,260)(134,259)(135,257)
(136,258)(137,266)(138,265)(139,267)(140,268)(141,269)(142,270)(143,272)
(144,271)(145,287)(146,288)(147,286)(148,285)(149,284)(150,283)(151,281)
(152,282)(153,279)(154,280)(155,278)(156,277)(157,276)(158,275)(159,273)
(160,274)(161,231)(162,232)(163,230)(164,229)(165,228)(166,227)(167,225)
(168,226)(169,234)(170,233)(171,235)(172,236)(173,237)(174,238)(175,240)
(176,239)(177,255)(178,256)(179,254)(180,253)(181,252)(182,251)(183,249)
(184,250)(185,247)(186,248)(187,246)(188,245)(189,244)(190,243)(191,241)
(192,242);
s2 := Sym(384)!(  1,161)(  2,163)(  3,162)(  4,164)(  5,168)(  6,166)(  7,167)
(  8,165)(  9,182)( 10,184)( 11,181)( 12,183)( 13,179)( 14,177)( 15,180)
( 16,178)( 17,174)( 18,176)( 19,173)( 20,175)( 21,171)( 22,169)( 23,172)
( 24,170)( 25,191)( 26,189)( 27,192)( 28,190)( 29,186)( 30,188)( 31,185)
( 32,187)( 33,129)( 34,131)( 35,130)( 36,132)( 37,136)( 38,134)( 39,135)
( 40,133)( 41,150)( 42,152)( 43,149)( 44,151)( 45,147)( 46,145)( 47,148)
( 48,146)( 49,142)( 50,144)( 51,141)( 52,143)( 53,139)( 54,137)( 55,140)
( 56,138)( 57,159)( 58,157)( 59,160)( 60,158)( 61,154)( 62,156)( 63,153)
( 64,155)( 65, 97)( 66, 99)( 67, 98)( 68,100)( 69,104)( 70,102)( 71,103)
( 72,101)( 73,118)( 74,120)( 75,117)( 76,119)( 77,115)( 78,113)( 79,116)
( 80,114)( 81,110)( 82,112)( 83,109)( 84,111)( 85,107)( 86,105)( 87,108)
( 88,106)( 89,127)( 90,125)( 91,128)( 92,126)( 93,122)( 94,124)( 95,121)
( 96,123)(193,353)(194,355)(195,354)(196,356)(197,360)(198,358)(199,359)
(200,357)(201,374)(202,376)(203,373)(204,375)(205,371)(206,369)(207,372)
(208,370)(209,366)(210,368)(211,365)(212,367)(213,363)(214,361)(215,364)
(216,362)(217,383)(218,381)(219,384)(220,382)(221,378)(222,380)(223,377)
(224,379)(225,321)(226,323)(227,322)(228,324)(229,328)(230,326)(231,327)
(232,325)(233,342)(234,344)(235,341)(236,343)(237,339)(238,337)(239,340)
(240,338)(241,334)(242,336)(243,333)(244,335)(245,331)(246,329)(247,332)
(248,330)(249,351)(250,349)(251,352)(252,350)(253,346)(254,348)(255,345)
(256,347)(257,289)(258,291)(259,290)(260,292)(261,296)(262,294)(263,295)
(264,293)(265,310)(266,312)(267,309)(268,311)(269,307)(270,305)(271,308)
(272,306)(273,302)(274,304)(275,301)(276,303)(277,299)(278,297)(279,300)
(280,298)(281,319)(282,317)(283,320)(284,318)(285,314)(286,316)(287,313)
(288,315);
poly := sub<Sym(384)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope