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# Polytope of Type {12,24}

Atlas Canonical Name : {12,24}*1152q
if this polytope has a name.
Group : SmallGroup(1152,155801)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 24, 288, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,12}*576f
3-fold quotients : {4,24}*384d
4-fold quotients : {12,6}*288a
6-fold quotients : {4,12}*192b
8-fold quotients : {6,12}*144a, {12,6}*144d
12-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
16-fold quotients : {6,6}*72a
24-fold quotients : {2,12}*48, {6,4}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
48-fold quotients : {4,3}*24, {2,6}*24, {6,2}*24
72-fold quotients : {2,4}*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 := (  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)
( 73,257)( 74,258)( 75,260)( 76,259)( 77,253)( 78,254)( 79,256)( 80,255)
( 81,261)( 82,262)( 83,264)( 84,263)( 85,281)( 86,282)( 87,284)( 88,283)
( 89,277)( 90,278)( 91,280)( 92,279)( 93,285)( 94,286)( 95,288)( 96,287)
( 97,269)( 98,270)( 99,272)(100,271)(101,265)(102,266)(103,268)(104,267)
(105,273)(106,274)(107,276)(108,275)(109,221)(110,222)(111,224)(112,223)
(113,217)(114,218)(115,220)(116,219)(117,225)(118,226)(119,228)(120,227)
(121,245)(122,246)(123,248)(124,247)(125,241)(126,242)(127,244)(128,243)
(129,249)(130,250)(131,252)(132,251)(133,233)(134,234)(135,236)(136,235)
(137,229)(138,230)(139,232)(140,231)(141,237)(142,238)(143,240)(144,239);;
s2 := (  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 17)(  6, 20)(  7, 19)(  8, 18)
(  9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)( 37, 49)
( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 45, 57)
( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73,121)( 74,124)
( 75,123)( 76,122)( 77,125)( 78,128)( 79,127)( 80,126)( 81,129)( 82,132)
( 83,131)( 84,130)( 85,109)( 86,112)( 87,111)( 88,110)( 89,113)( 90,116)
( 91,115)( 92,114)( 93,117)( 94,120)( 95,119)( 96,118)( 97,133)( 98,136)
( 99,135)(100,134)(101,137)(102,140)(103,139)(104,138)(105,141)(106,144)
(107,143)(108,142)(145,229)(146,232)(147,231)(148,230)(149,233)(150,236)
(151,235)(152,234)(153,237)(154,240)(155,239)(156,238)(157,217)(158,220)
(159,219)(160,218)(161,221)(162,224)(163,223)(164,222)(165,225)(166,228)
(167,227)(168,226)(169,241)(170,244)(171,243)(172,242)(173,245)(174,248)
(175,247)(176,246)(177,249)(178,252)(179,251)(180,250)(181,265)(182,268)
(183,267)(184,266)(185,269)(186,272)(187,271)(188,270)(189,273)(190,276)
(191,275)(192,274)(193,253)(194,256)(195,255)(196,254)(197,257)(198,260)
(199,259)(200,258)(201,261)(202,264)(203,263)(204,262)(205,277)(206,280)
(207,279)(208,278)(209,281)(210,284)(211,283)(212,282)(213,285)(214,288)
(215,287)(216,286);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*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*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
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)( 73,257)( 74,258)( 75,260)( 76,259)( 77,253)( 78,254)( 79,256)
( 80,255)( 81,261)( 82,262)( 83,264)( 84,263)( 85,281)( 86,282)( 87,284)
( 88,283)( 89,277)( 90,278)( 91,280)( 92,279)( 93,285)( 94,286)( 95,288)
( 96,287)( 97,269)( 98,270)( 99,272)(100,271)(101,265)(102,266)(103,268)
(104,267)(105,273)(106,274)(107,276)(108,275)(109,221)(110,222)(111,224)
(112,223)(113,217)(114,218)(115,220)(116,219)(117,225)(118,226)(119,228)
(120,227)(121,245)(122,246)(123,248)(124,247)(125,241)(126,242)(127,244)
(128,243)(129,249)(130,250)(131,252)(132,251)(133,233)(134,234)(135,236)
(136,235)(137,229)(138,230)(139,232)(140,231)(141,237)(142,238)(143,240)
(144,239);
s2 := Sym(288)!(  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 17)(  6, 20)(  7, 19)
(  8, 18)(  9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)
( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)
( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73,121)
( 74,124)( 75,123)( 76,122)( 77,125)( 78,128)( 79,127)( 80,126)( 81,129)
( 82,132)( 83,131)( 84,130)( 85,109)( 86,112)( 87,111)( 88,110)( 89,113)
( 90,116)( 91,115)( 92,114)( 93,117)( 94,120)( 95,119)( 96,118)( 97,133)
( 98,136)( 99,135)(100,134)(101,137)(102,140)(103,139)(104,138)(105,141)
(106,144)(107,143)(108,142)(145,229)(146,232)(147,231)(148,230)(149,233)
(150,236)(151,235)(152,234)(153,237)(154,240)(155,239)(156,238)(157,217)
(158,220)(159,219)(160,218)(161,221)(162,224)(163,223)(164,222)(165,225)
(166,228)(167,227)(168,226)(169,241)(170,244)(171,243)(172,242)(173,245)
(174,248)(175,247)(176,246)(177,249)(178,252)(179,251)(180,250)(181,265)
(182,268)(183,267)(184,266)(185,269)(186,272)(187,271)(188,270)(189,273)
(190,276)(191,275)(192,274)(193,253)(194,256)(195,255)(196,254)(197,257)
(198,260)(199,259)(200,258)(201,261)(202,264)(203,263)(204,262)(205,277)
(206,280)(207,279)(208,278)(209,281)(210,284)(211,283)(212,282)(213,285)
(214,288)(215,287)(216,286);
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*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*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

```
References : None.
to this polytope