Polytope of Type {12,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*1152o
if this polytope has a name.
Group : SmallGroup(1152,156063)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 48, 288, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
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 : {12,12}*576g, {12,12}*576i, {12,6}*576f
3-fold quotients : {4,12}*384d
4-fold quotients : {12,12}*288b, {12,6}*288b
6-fold quotients : {4,12}*192b, {4,6}*192b, {4,12}*192c
8-fold quotients : {6,12}*144b, {12,6}*144c, {12,3}*144
12-fold quotients : {4,12}*96a, {4,12}*96b, {4,12}*96c, {4,6}*96
16-fold quotients : {6,6}*72b
24-fold quotients : {2,12}*48, {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
32-fold quotients : {6,3}*36
36-fold quotients : {4,4}*32
48-fold quotients : {4,3}*24, {2,6}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {2,3}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 11)( 6, 12)( 7, 9)( 8, 10)( 13, 15)( 14, 16)
( 17, 23)( 18, 24)( 19, 21)( 20, 22)( 25, 27)( 26, 28)( 29, 35)( 30, 36)
( 31, 33)( 32, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)
( 49, 51)( 50, 52)( 53, 59)( 54, 60)( 55, 57)( 56, 58)( 61, 63)( 62, 64)
( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 73, 75)( 74, 76)( 77, 83)( 78, 84)
( 79, 81)( 80, 82)( 85, 87)( 86, 88)( 89, 95)( 90, 96)( 91, 93)( 92, 94)
( 97, 99)( 98,100)(101,107)(102,108)(103,105)(104,106)(109,111)(110,112)
(113,119)(114,120)(115,117)(116,118)(121,123)(122,124)(125,131)(126,132)
(127,129)(128,130)(133,135)(134,136)(137,143)(138,144)(139,141)(140,142)
(145,183)(146,184)(147,181)(148,182)(149,191)(150,192)(151,189)(152,190)
(153,187)(154,188)(155,185)(156,186)(157,195)(158,196)(159,193)(160,194)
(161,203)(162,204)(163,201)(164,202)(165,199)(166,200)(167,197)(168,198)
(169,207)(170,208)(171,205)(172,206)(173,215)(174,216)(175,213)(176,214)
(177,211)(178,212)(179,209)(180,210)(217,255)(218,256)(219,253)(220,254)
(221,263)(222,264)(223,261)(224,262)(225,259)(226,260)(227,257)(228,258)
(229,267)(230,268)(231,265)(232,266)(233,275)(234,276)(235,273)(236,274)
(237,271)(238,272)(239,269)(240,270)(241,279)(242,280)(243,277)(244,278)
(245,287)(246,288)(247,285)(248,286)(249,283)(250,284)(251,281)(252,282);;
s1 := ( 1,149)( 2,150)( 3,152)( 4,151)( 5,145)( 6,146)( 7,148)( 8,147)
( 9,153)( 10,154)( 11,156)( 12,155)( 13,173)( 14,174)( 15,176)( 16,175)
( 17,169)( 18,170)( 19,172)( 20,171)( 21,177)( 22,178)( 23,180)( 24,179)
( 25,161)( 26,162)( 27,164)( 28,163)( 29,157)( 30,158)( 31,160)( 32,159)
( 33,165)( 34,166)( 35,168)( 36,167)( 37,185)( 38,186)( 39,188)( 40,187)
( 41,181)( 42,182)( 43,184)( 44,183)( 45,189)( 46,190)( 47,192)( 48,191)
( 49,209)( 50,210)( 51,212)( 52,211)( 53,205)( 54,206)( 55,208)( 56,207)
( 57,213)( 58,214)( 59,216)( 60,215)( 61,197)( 62,198)( 63,200)( 64,199)
( 65,193)( 66,194)( 67,196)( 68,195)( 69,201)( 70,202)( 71,204)( 72,203)
( 73,221)( 74,222)( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)
( 81,225)( 82,226)( 83,228)( 84,227)( 85,245)( 86,246)( 87,248)( 88,247)
( 89,241)( 90,242)( 91,244)( 92,243)( 93,249)( 94,250)( 95,252)( 96,251)
( 97,233)( 98,234)( 99,236)(100,235)(101,229)(102,230)(103,232)(104,231)
(105,237)(106,238)(107,240)(108,239)(109,257)(110,258)(111,260)(112,259)
(113,253)(114,254)(115,256)(116,255)(117,261)(118,262)(119,264)(120,263)
(121,281)(122,282)(123,284)(124,283)(125,277)(126,278)(127,280)(128,279)
(129,285)(130,286)(131,288)(132,287)(133,269)(134,270)(135,272)(136,271)
(137,265)(138,266)(139,268)(140,267)(141,273)(142,274)(143,276)(144,275);;
s2 := ( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)( 8, 22)
( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)
( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)
( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)
( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)( 78, 96)
( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)(101,105)
(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)(113,129)
(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)(134,136)
(137,141)(138,144)(139,143)(140,142)(145,265)(146,268)(147,267)(148,266)
(149,273)(150,276)(151,275)(152,274)(153,269)(154,272)(155,271)(156,270)
(157,253)(158,256)(159,255)(160,254)(161,261)(162,264)(163,263)(164,262)
(165,257)(166,260)(167,259)(168,258)(169,277)(170,280)(171,279)(172,278)
(173,285)(174,288)(175,287)(176,286)(177,281)(178,284)(179,283)(180,282)
(181,229)(182,232)(183,231)(184,230)(185,237)(186,240)(187,239)(188,238)
(189,233)(190,236)(191,235)(192,234)(193,217)(194,220)(195,219)(196,218)
(197,225)(198,228)(199,227)(200,226)(201,221)(202,224)(203,223)(204,222)
(205,241)(206,244)(207,243)(208,242)(209,249)(210,252)(211,251)(212,250)
(213,245)(214,248)(215,247)(216,246);;
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*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1, 3)( 2, 4)( 5, 11)( 6, 12)( 7, 9)( 8, 10)( 13, 15)
( 14, 16)( 17, 23)( 18, 24)( 19, 21)( 20, 22)( 25, 27)( 26, 28)( 29, 35)
( 30, 36)( 31, 33)( 32, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)
( 44, 46)( 49, 51)( 50, 52)( 53, 59)( 54, 60)( 55, 57)( 56, 58)( 61, 63)
( 62, 64)( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 73, 75)( 74, 76)( 77, 83)
( 78, 84)( 79, 81)( 80, 82)( 85, 87)( 86, 88)( 89, 95)( 90, 96)( 91, 93)
( 92, 94)( 97, 99)( 98,100)(101,107)(102,108)(103,105)(104,106)(109,111)
(110,112)(113,119)(114,120)(115,117)(116,118)(121,123)(122,124)(125,131)
(126,132)(127,129)(128,130)(133,135)(134,136)(137,143)(138,144)(139,141)
(140,142)(145,183)(146,184)(147,181)(148,182)(149,191)(150,192)(151,189)
(152,190)(153,187)(154,188)(155,185)(156,186)(157,195)(158,196)(159,193)
(160,194)(161,203)(162,204)(163,201)(164,202)(165,199)(166,200)(167,197)
(168,198)(169,207)(170,208)(171,205)(172,206)(173,215)(174,216)(175,213)
(176,214)(177,211)(178,212)(179,209)(180,210)(217,255)(218,256)(219,253)
(220,254)(221,263)(222,264)(223,261)(224,262)(225,259)(226,260)(227,257)
(228,258)(229,267)(230,268)(231,265)(232,266)(233,275)(234,276)(235,273)
(236,274)(237,271)(238,272)(239,269)(240,270)(241,279)(242,280)(243,277)
(244,278)(245,287)(246,288)(247,285)(248,286)(249,283)(250,284)(251,281)
(252,282);
s1 := Sym(288)!( 1,149)( 2,150)( 3,152)( 4,151)( 5,145)( 6,146)( 7,148)
( 8,147)( 9,153)( 10,154)( 11,156)( 12,155)( 13,173)( 14,174)( 15,176)
( 16,175)( 17,169)( 18,170)( 19,172)( 20,171)( 21,177)( 22,178)( 23,180)
( 24,179)( 25,161)( 26,162)( 27,164)( 28,163)( 29,157)( 30,158)( 31,160)
( 32,159)( 33,165)( 34,166)( 35,168)( 36,167)( 37,185)( 38,186)( 39,188)
( 40,187)( 41,181)( 42,182)( 43,184)( 44,183)( 45,189)( 46,190)( 47,192)
( 48,191)( 49,209)( 50,210)( 51,212)( 52,211)( 53,205)( 54,206)( 55,208)
( 56,207)( 57,213)( 58,214)( 59,216)( 60,215)( 61,197)( 62,198)( 63,200)
( 64,199)( 65,193)( 66,194)( 67,196)( 68,195)( 69,201)( 70,202)( 71,204)
( 72,203)( 73,221)( 74,222)( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)
( 80,219)( 81,225)( 82,226)( 83,228)( 84,227)( 85,245)( 86,246)( 87,248)
( 88,247)( 89,241)( 90,242)( 91,244)( 92,243)( 93,249)( 94,250)( 95,252)
( 96,251)( 97,233)( 98,234)( 99,236)(100,235)(101,229)(102,230)(103,232)
(104,231)(105,237)(106,238)(107,240)(108,239)(109,257)(110,258)(111,260)
(112,259)(113,253)(114,254)(115,256)(116,255)(117,261)(118,262)(119,264)
(120,263)(121,281)(122,282)(123,284)(124,283)(125,277)(126,278)(127,280)
(128,279)(129,285)(130,286)(131,288)(132,287)(133,269)(134,270)(135,272)
(136,271)(137,265)(138,266)(139,268)(140,267)(141,273)(142,274)(143,276)
(144,275);
s2 := Sym(288)!( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)
( 8, 22)( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)
( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)
( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)
( 66, 72)( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)
( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)
(101,105)(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)
(113,129)(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)
(134,136)(137,141)(138,144)(139,143)(140,142)(145,265)(146,268)(147,267)
(148,266)(149,273)(150,276)(151,275)(152,274)(153,269)(154,272)(155,271)
(156,270)(157,253)(158,256)(159,255)(160,254)(161,261)(162,264)(163,263)
(164,262)(165,257)(166,260)(167,259)(168,258)(169,277)(170,280)(171,279)
(172,278)(173,285)(174,288)(175,287)(176,286)(177,281)(178,284)(179,283)
(180,282)(181,229)(182,232)(183,231)(184,230)(185,237)(186,240)(187,239)
(188,238)(189,233)(190,236)(191,235)(192,234)(193,217)(194,220)(195,219)
(196,218)(197,225)(198,228)(199,227)(200,226)(201,221)(202,224)(203,223)
(204,222)(205,241)(206,244)(207,243)(208,242)(209,249)(210,252)(211,251)
(212,250)(213,245)(214,248)(215,247)(216,246);
poly := sub<Sym(288)|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*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope