Questions?
See the FAQ
or other info.

# Polytope of Type {12,12}

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

```
Permutation Representation (Magma) :
```s0 := Sym(288)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 25)( 14, 26)
( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)
( 23, 32)( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)
( 50, 62)( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)
( 58, 66)( 59, 68)( 60, 67)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)
( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,105)( 90,106)( 91,108)( 92,107)
( 93,101)( 94,102)( 95,104)( 96,103)(111,112)(113,117)(114,118)(115,120)
(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)(127,144)
(128,143)(129,137)(130,138)(131,140)(132,139)(145,253)(146,254)(147,256)
(148,255)(149,261)(150,262)(151,264)(152,263)(153,257)(154,258)(155,260)
(156,259)(157,277)(158,278)(159,280)(160,279)(161,285)(162,286)(163,288)
(164,287)(165,281)(166,282)(167,284)(168,283)(169,265)(170,266)(171,268)
(172,267)(173,273)(174,274)(175,276)(176,275)(177,269)(178,270)(179,272)
(180,271)(181,217)(182,218)(183,220)(184,219)(185,225)(186,226)(187,228)
(188,227)(189,221)(190,222)(191,224)(192,223)(193,241)(194,242)(195,244)
(196,243)(197,249)(198,250)(199,252)(200,251)(201,245)(202,246)(203,248)
(204,247)(205,229)(206,230)(207,232)(208,231)(209,237)(210,238)(211,240)
(212,239)(213,233)(214,234)(215,236)(216,235);
s1 := Sym(288)!(  1,161)(  2,164)(  3,163)(  4,162)(  5,157)(  6,160)(  7,159)
(  8,158)(  9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)
( 16,150)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)
( 24,154)( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)
( 32,170)( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)
( 40,198)( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)
( 48,202)( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)
( 56,182)( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)
( 64,210)( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)
( 80,230)( 81,237)( 82,240)( 83,239)( 84,238)( 85,221)( 86,224)( 87,223)
( 88,222)( 89,217)( 90,220)( 91,219)( 92,218)( 93,225)( 94,228)( 95,227)
( 96,226)( 97,245)( 98,248)( 99,247)(100,246)(101,241)(102,244)(103,243)
(104,242)(105,249)(106,252)(107,251)(108,250)(109,269)(110,272)(111,271)
(112,270)(113,265)(114,268)(115,267)(116,266)(117,273)(118,276)(119,275)
(120,274)(121,257)(122,260)(123,259)(124,258)(125,253)(126,256)(127,255)
(128,254)(129,261)(130,264)(131,263)(132,262)(133,281)(134,284)(135,283)
(136,282)(137,277)(138,280)(139,279)(140,278)(141,285)(142,288)(143,287)
(144,286);
s2 := Sym(288)!(  1,  2)(  3,  4)(  5, 10)(  6,  9)(  7, 12)(  8, 11)( 13, 14)
( 15, 16)( 17, 22)( 18, 21)( 19, 24)( 20, 23)( 25, 26)( 27, 28)( 29, 34)
( 30, 33)( 31, 36)( 32, 35)( 37, 38)( 39, 40)( 41, 46)( 42, 45)( 43, 48)
( 44, 47)( 49, 50)( 51, 52)( 53, 58)( 54, 57)( 55, 60)( 56, 59)( 61, 62)
( 63, 64)( 65, 70)( 66, 69)( 67, 72)( 68, 71)( 73, 74)( 75, 76)( 77, 82)
( 78, 81)( 79, 84)( 80, 83)( 85, 86)( 87, 88)( 89, 94)( 90, 93)( 91, 96)
( 92, 95)( 97, 98)( 99,100)(101,106)(102,105)(103,108)(104,107)(109,110)
(111,112)(113,118)(114,117)(115,120)(116,119)(121,122)(123,124)(125,130)
(126,129)(127,132)(128,131)(133,134)(135,136)(137,142)(138,141)(139,144)
(140,143)(145,182)(146,181)(147,184)(148,183)(149,190)(150,189)(151,192)
(152,191)(153,186)(154,185)(155,188)(156,187)(157,194)(158,193)(159,196)
(160,195)(161,202)(162,201)(163,204)(164,203)(165,198)(166,197)(167,200)
(168,199)(169,206)(170,205)(171,208)(172,207)(173,214)(174,213)(175,216)
(176,215)(177,210)(178,209)(179,212)(180,211)(217,254)(218,253)(219,256)
(220,255)(221,262)(222,261)(223,264)(224,263)(225,258)(226,257)(227,260)
(228,259)(229,266)(230,265)(231,268)(232,267)(233,274)(234,273)(235,276)
(236,275)(237,270)(238,269)(239,272)(240,271)(241,278)(242,277)(243,280)
(244,279)(245,286)(246,285)(247,288)(248,287)(249,282)(250,281)(251,284)
(252,283);
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*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope