Polytope of Type {12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768e
if this polytope has a name.
Group : SmallGroup(768,1086012)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie
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 : {12,4}*384b, {6,8}*384b
4-fold quotients : {6,4}*192a
8-fold quotients : {12,4}*96b
16-fold quotients : {6,4}*48c
32-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 7)( 6, 8)( 13, 15)( 14, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)
( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)( 35, 67)( 36, 68)
( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)( 43, 75)( 44, 76)
( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)( 51, 91)( 52, 92)
( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 83)( 60, 84)
( 61, 87)( 62, 88)( 63, 85)( 64, 86)(101,103)(102,104)(109,111)(110,112)
(113,121)(114,122)(115,123)(116,124)(117,127)(118,128)(119,125)(120,126)
(129,161)(130,162)(131,163)(132,164)(133,167)(134,168)(135,165)(136,166)
(137,169)(138,170)(139,171)(140,172)(141,175)(142,176)(143,173)(144,174)
(145,185)(146,186)(147,187)(148,188)(149,191)(150,192)(151,189)(152,190)
(153,177)(154,178)(155,179)(156,180)(157,183)(158,184)(159,181)(160,182)
(193,289)(194,290)(195,291)(196,292)(197,295)(198,296)(199,293)(200,294)
(201,297)(202,298)(203,299)(204,300)(205,303)(206,304)(207,301)(208,302)
(209,313)(210,314)(211,315)(212,316)(213,319)(214,320)(215,317)(216,318)
(217,305)(218,306)(219,307)(220,308)(221,311)(222,312)(223,309)(224,310)
(225,353)(226,354)(227,355)(228,356)(229,359)(230,360)(231,357)(232,358)
(233,361)(234,362)(235,363)(236,364)(237,367)(238,368)(239,365)(240,366)
(241,377)(242,378)(243,379)(244,380)(245,383)(246,384)(247,381)(248,382)
(249,369)(250,370)(251,371)(252,372)(253,375)(254,376)(255,373)(256,374)
(257,321)(258,322)(259,323)(260,324)(261,327)(262,328)(263,325)(264,326)
(265,329)(266,330)(267,331)(268,332)(269,335)(270,336)(271,333)(272,334)
(273,345)(274,346)(275,347)(276,348)(277,351)(278,352)(279,349)(280,350)
(281,337)(282,338)(283,339)(284,340)(285,343)(286,344)(287,341)(288,342);;
s1 := ( 1,353)( 2,354)( 3,357)( 4,358)( 5,355)( 6,356)( 7,359)( 8,360)
( 9,374)( 10,373)( 11,370)( 12,369)( 13,376)( 14,375)( 15,372)( 16,371)
( 17,364)( 18,363)( 19,368)( 20,367)( 21,362)( 22,361)( 23,366)( 24,365)
( 25,384)( 26,383)( 27,380)( 28,379)( 29,382)( 30,381)( 31,378)( 32,377)
( 33,321)( 34,322)( 35,325)( 36,326)( 37,323)( 38,324)( 39,327)( 40,328)
( 41,342)( 42,341)( 43,338)( 44,337)( 45,344)( 46,343)( 47,340)( 48,339)
( 49,332)( 50,331)( 51,336)( 52,335)( 53,330)( 54,329)( 55,334)( 56,333)
( 57,352)( 58,351)( 59,348)( 60,347)( 61,350)( 62,349)( 63,346)( 64,345)
( 65,289)( 66,290)( 67,293)( 68,294)( 69,291)( 70,292)( 71,295)( 72,296)
( 73,310)( 74,309)( 75,306)( 76,305)( 77,312)( 78,311)( 79,308)( 80,307)
( 81,300)( 82,299)( 83,304)( 84,303)( 85,298)( 86,297)( 87,302)( 88,301)
( 89,320)( 90,319)( 91,316)( 92,315)( 93,318)( 94,317)( 95,314)( 96,313)
( 97,257)( 98,258)( 99,261)(100,262)(101,259)(102,260)(103,263)(104,264)
(105,278)(106,277)(107,274)(108,273)(109,280)(110,279)(111,276)(112,275)
(113,268)(114,267)(115,272)(116,271)(117,266)(118,265)(119,270)(120,269)
(121,288)(122,287)(123,284)(124,283)(125,286)(126,285)(127,282)(128,281)
(129,225)(130,226)(131,229)(132,230)(133,227)(134,228)(135,231)(136,232)
(137,246)(138,245)(139,242)(140,241)(141,248)(142,247)(143,244)(144,243)
(145,236)(146,235)(147,240)(148,239)(149,234)(150,233)(151,238)(152,237)
(153,256)(154,255)(155,252)(156,251)(157,254)(158,253)(159,250)(160,249)
(161,193)(162,194)(163,197)(164,198)(165,195)(166,196)(167,199)(168,200)
(169,214)(170,213)(171,210)(172,209)(173,216)(174,215)(175,212)(176,211)
(177,204)(178,203)(179,208)(180,207)(181,202)(182,201)(183,206)(184,205)
(185,224)(186,223)(187,220)(188,219)(189,222)(190,221)(191,218)(192,217);;
s2 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 14)( 6, 13)( 7, 16)( 8, 15)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 30)( 22, 29)( 23, 32)( 24, 31)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 46)( 38, 45)( 39, 48)( 40, 47)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 64)( 56, 63)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 78)( 70, 77)( 71, 80)( 72, 79)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 87, 96)( 88, 95)
( 97,105)( 98,106)( 99,107)(100,108)(101,110)(102,109)(103,112)(104,111)
(113,121)(114,122)(115,123)(116,124)(117,126)(118,125)(119,128)(120,127)
(129,137)(130,138)(131,139)(132,140)(133,142)(134,141)(135,144)(136,143)
(145,153)(146,154)(147,155)(148,156)(149,158)(150,157)(151,160)(152,159)
(161,169)(162,170)(163,171)(164,172)(165,174)(166,173)(167,176)(168,175)
(177,185)(178,186)(179,187)(180,188)(181,190)(182,189)(183,192)(184,191)
(193,201)(194,202)(195,203)(196,204)(197,206)(198,205)(199,208)(200,207)
(209,217)(210,218)(211,219)(212,220)(213,222)(214,221)(215,224)(216,223)
(225,233)(226,234)(227,235)(228,236)(229,238)(230,237)(231,240)(232,239)
(241,249)(242,250)(243,251)(244,252)(245,254)(246,253)(247,256)(248,255)
(257,265)(258,266)(259,267)(260,268)(261,270)(262,269)(263,272)(264,271)
(273,281)(274,282)(275,283)(276,284)(277,286)(278,285)(279,288)(280,287)
(289,297)(290,298)(291,299)(292,300)(293,302)(294,301)(295,304)(296,303)
(305,313)(306,314)(307,315)(308,316)(309,318)(310,317)(311,320)(312,319)
(321,329)(322,330)(323,331)(324,332)(325,334)(326,333)(327,336)(328,335)
(337,345)(338,346)(339,347)(340,348)(341,350)(342,349)(343,352)(344,351)
(353,361)(354,362)(355,363)(356,364)(357,366)(358,365)(359,368)(360,367)
(369,377)(370,378)(371,379)(372,380)(373,382)(374,381)(375,384)(376,383);;
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, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 5, 7)( 6, 8)( 13, 15)( 14, 16)( 17, 25)( 18, 26)( 19, 27)
( 20, 28)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)( 35, 67)
( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)( 43, 75)
( 44, 76)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)( 51, 91)
( 52, 92)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 83)
( 60, 84)( 61, 87)( 62, 88)( 63, 85)( 64, 86)(101,103)(102,104)(109,111)
(110,112)(113,121)(114,122)(115,123)(116,124)(117,127)(118,128)(119,125)
(120,126)(129,161)(130,162)(131,163)(132,164)(133,167)(134,168)(135,165)
(136,166)(137,169)(138,170)(139,171)(140,172)(141,175)(142,176)(143,173)
(144,174)(145,185)(146,186)(147,187)(148,188)(149,191)(150,192)(151,189)
(152,190)(153,177)(154,178)(155,179)(156,180)(157,183)(158,184)(159,181)
(160,182)(193,289)(194,290)(195,291)(196,292)(197,295)(198,296)(199,293)
(200,294)(201,297)(202,298)(203,299)(204,300)(205,303)(206,304)(207,301)
(208,302)(209,313)(210,314)(211,315)(212,316)(213,319)(214,320)(215,317)
(216,318)(217,305)(218,306)(219,307)(220,308)(221,311)(222,312)(223,309)
(224,310)(225,353)(226,354)(227,355)(228,356)(229,359)(230,360)(231,357)
(232,358)(233,361)(234,362)(235,363)(236,364)(237,367)(238,368)(239,365)
(240,366)(241,377)(242,378)(243,379)(244,380)(245,383)(246,384)(247,381)
(248,382)(249,369)(250,370)(251,371)(252,372)(253,375)(254,376)(255,373)
(256,374)(257,321)(258,322)(259,323)(260,324)(261,327)(262,328)(263,325)
(264,326)(265,329)(266,330)(267,331)(268,332)(269,335)(270,336)(271,333)
(272,334)(273,345)(274,346)(275,347)(276,348)(277,351)(278,352)(279,349)
(280,350)(281,337)(282,338)(283,339)(284,340)(285,343)(286,344)(287,341)
(288,342);
s1 := Sym(384)!( 1,353)( 2,354)( 3,357)( 4,358)( 5,355)( 6,356)( 7,359)
( 8,360)( 9,374)( 10,373)( 11,370)( 12,369)( 13,376)( 14,375)( 15,372)
( 16,371)( 17,364)( 18,363)( 19,368)( 20,367)( 21,362)( 22,361)( 23,366)
( 24,365)( 25,384)( 26,383)( 27,380)( 28,379)( 29,382)( 30,381)( 31,378)
( 32,377)( 33,321)( 34,322)( 35,325)( 36,326)( 37,323)( 38,324)( 39,327)
( 40,328)( 41,342)( 42,341)( 43,338)( 44,337)( 45,344)( 46,343)( 47,340)
( 48,339)( 49,332)( 50,331)( 51,336)( 52,335)( 53,330)( 54,329)( 55,334)
( 56,333)( 57,352)( 58,351)( 59,348)( 60,347)( 61,350)( 62,349)( 63,346)
( 64,345)( 65,289)( 66,290)( 67,293)( 68,294)( 69,291)( 70,292)( 71,295)
( 72,296)( 73,310)( 74,309)( 75,306)( 76,305)( 77,312)( 78,311)( 79,308)
( 80,307)( 81,300)( 82,299)( 83,304)( 84,303)( 85,298)( 86,297)( 87,302)
( 88,301)( 89,320)( 90,319)( 91,316)( 92,315)( 93,318)( 94,317)( 95,314)
( 96,313)( 97,257)( 98,258)( 99,261)(100,262)(101,259)(102,260)(103,263)
(104,264)(105,278)(106,277)(107,274)(108,273)(109,280)(110,279)(111,276)
(112,275)(113,268)(114,267)(115,272)(116,271)(117,266)(118,265)(119,270)
(120,269)(121,288)(122,287)(123,284)(124,283)(125,286)(126,285)(127,282)
(128,281)(129,225)(130,226)(131,229)(132,230)(133,227)(134,228)(135,231)
(136,232)(137,246)(138,245)(139,242)(140,241)(141,248)(142,247)(143,244)
(144,243)(145,236)(146,235)(147,240)(148,239)(149,234)(150,233)(151,238)
(152,237)(153,256)(154,255)(155,252)(156,251)(157,254)(158,253)(159,250)
(160,249)(161,193)(162,194)(163,197)(164,198)(165,195)(166,196)(167,199)
(168,200)(169,214)(170,213)(171,210)(172,209)(173,216)(174,215)(175,212)
(176,211)(177,204)(178,203)(179,208)(180,207)(181,202)(182,201)(183,206)
(184,205)(185,224)(186,223)(187,220)(188,219)(189,222)(190,221)(191,218)
(192,217);
s2 := Sym(384)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 14)( 6, 13)( 7, 16)
( 8, 15)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 30)( 22, 29)( 23, 32)
( 24, 31)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 46)( 38, 45)( 39, 48)
( 40, 47)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 64)
( 56, 63)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 78)( 70, 77)( 71, 80)
( 72, 79)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 87, 96)
( 88, 95)( 97,105)( 98,106)( 99,107)(100,108)(101,110)(102,109)(103,112)
(104,111)(113,121)(114,122)(115,123)(116,124)(117,126)(118,125)(119,128)
(120,127)(129,137)(130,138)(131,139)(132,140)(133,142)(134,141)(135,144)
(136,143)(145,153)(146,154)(147,155)(148,156)(149,158)(150,157)(151,160)
(152,159)(161,169)(162,170)(163,171)(164,172)(165,174)(166,173)(167,176)
(168,175)(177,185)(178,186)(179,187)(180,188)(181,190)(182,189)(183,192)
(184,191)(193,201)(194,202)(195,203)(196,204)(197,206)(198,205)(199,208)
(200,207)(209,217)(210,218)(211,219)(212,220)(213,222)(214,221)(215,224)
(216,223)(225,233)(226,234)(227,235)(228,236)(229,238)(230,237)(231,240)
(232,239)(241,249)(242,250)(243,251)(244,252)(245,254)(246,253)(247,256)
(248,255)(257,265)(258,266)(259,267)(260,268)(261,270)(262,269)(263,272)
(264,271)(273,281)(274,282)(275,283)(276,284)(277,286)(278,285)(279,288)
(280,287)(289,297)(290,298)(291,299)(292,300)(293,302)(294,301)(295,304)
(296,303)(305,313)(306,314)(307,315)(308,316)(309,318)(310,317)(311,320)
(312,319)(321,329)(322,330)(323,331)(324,332)(325,334)(326,333)(327,336)
(328,335)(337,345)(338,346)(339,347)(340,348)(341,350)(342,349)(343,352)
(344,351)(353,361)(354,362)(355,363)(356,364)(357,366)(358,365)(359,368)
(360,367)(369,377)(370,378)(371,379)(372,380)(373,382)(374,381)(375,384)
(376,383);
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, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope