Polytope of Type {12,8}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope