Polytope of Type {12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768f
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}*384c
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, 10)( 2, 9)( 3, 12)( 4, 11)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 26)( 18, 25)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 42)( 34, 41)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 58)( 50, 57)( 51, 60)( 52, 59)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 74)( 66, 73)( 67, 76)( 68, 75)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 90)( 82, 89)( 83, 92)( 84, 91)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,106)( 98,105)( 99,108)(100,107)(101,109)(102,110)(103,111)(104,112)
(113,122)(114,121)(115,124)(116,123)(117,125)(118,126)(119,127)(120,128)
(129,138)(130,137)(131,140)(132,139)(133,141)(134,142)(135,143)(136,144)
(145,154)(146,153)(147,156)(148,155)(149,157)(150,158)(151,159)(152,160)
(161,170)(162,169)(163,172)(164,171)(165,173)(166,174)(167,175)(168,176)
(177,186)(178,185)(179,188)(180,187)(181,189)(182,190)(183,191)(184,192)
(193,202)(194,201)(195,204)(196,203)(197,205)(198,206)(199,207)(200,208)
(209,218)(210,217)(211,220)(212,219)(213,221)(214,222)(215,223)(216,224)
(225,234)(226,233)(227,236)(228,235)(229,237)(230,238)(231,239)(232,240)
(241,250)(242,249)(243,252)(244,251)(245,253)(246,254)(247,255)(248,256)
(257,266)(258,265)(259,268)(260,267)(261,269)(262,270)(263,271)(264,272)
(273,282)(274,281)(275,284)(276,283)(277,285)(278,286)(279,287)(280,288)
(289,298)(290,297)(291,300)(292,299)(293,301)(294,302)(295,303)(296,304)
(305,314)(306,313)(307,316)(308,315)(309,317)(310,318)(311,319)(312,320)
(321,330)(322,329)(323,332)(324,331)(325,333)(326,334)(327,335)(328,336)
(337,346)(338,345)(339,348)(340,347)(341,349)(342,350)(343,351)(344,352)
(353,362)(354,361)(355,364)(356,363)(357,365)(358,366)(359,367)(360,368)
(369,378)(370,377)(371,380)(372,379)(373,381)(374,382)(375,383)(376,384);;
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*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*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, 10)( 2, 9)( 3, 12)( 4, 11)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 26)( 18, 25)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 42)( 34, 41)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 58)( 50, 57)( 51, 60)( 52, 59)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 74)( 66, 73)( 67, 76)( 68, 75)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 90)( 82, 89)( 83, 92)( 84, 91)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,106)( 98,105)( 99,108)(100,107)(101,109)(102,110)(103,111)
(104,112)(113,122)(114,121)(115,124)(116,123)(117,125)(118,126)(119,127)
(120,128)(129,138)(130,137)(131,140)(132,139)(133,141)(134,142)(135,143)
(136,144)(145,154)(146,153)(147,156)(148,155)(149,157)(150,158)(151,159)
(152,160)(161,170)(162,169)(163,172)(164,171)(165,173)(166,174)(167,175)
(168,176)(177,186)(178,185)(179,188)(180,187)(181,189)(182,190)(183,191)
(184,192)(193,202)(194,201)(195,204)(196,203)(197,205)(198,206)(199,207)
(200,208)(209,218)(210,217)(211,220)(212,219)(213,221)(214,222)(215,223)
(216,224)(225,234)(226,233)(227,236)(228,235)(229,237)(230,238)(231,239)
(232,240)(241,250)(242,249)(243,252)(244,251)(245,253)(246,254)(247,255)
(248,256)(257,266)(258,265)(259,268)(260,267)(261,269)(262,270)(263,271)
(264,272)(273,282)(274,281)(275,284)(276,283)(277,285)(278,286)(279,287)
(280,288)(289,298)(290,297)(291,300)(292,299)(293,301)(294,302)(295,303)
(296,304)(305,314)(306,313)(307,316)(308,315)(309,317)(310,318)(311,319)
(312,320)(321,330)(322,329)(323,332)(324,331)(325,333)(326,334)(327,335)
(328,336)(337,346)(338,345)(339,348)(340,347)(341,349)(342,350)(343,351)
(344,352)(353,362)(354,361)(355,364)(356,363)(357,365)(358,366)(359,367)
(360,368)(369,378)(370,377)(371,380)(372,379)(373,381)(374,382)(375,383)
(376,384);
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*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*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