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# Polytope of Type {12,12}

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