Questions?
See the FAQ
or other info.

# Polytope of Type {12,24}

Atlas Canonical Name : {12,24}*1152r
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 : 12
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}*576g
3-fold quotients : {4,24}*384d
4-fold quotients : {12,6}*288b
6-fold quotients : {4,12}*192b
8-fold quotients : {6,12}*144b, {12,3}*144
12-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
16-fold quotients : {6,6}*72b
24-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
32-fold quotients : {6,3}*36
48-fold quotients : {4,3}*24, {2,6}*24
72-fold quotients : {2,4}*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)
( 73,257)( 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, 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)( 73,121)( 74,124)( 75,123)( 76,122)( 77,129)( 78,132)
( 79,131)( 80,130)( 81,125)( 82,128)( 83,127)( 84,126)( 85,109)( 86,112)
( 87,111)( 88,110)( 89,117)( 90,120)( 91,119)( 92,118)( 93,113)( 94,116)
( 95,115)( 96,114)( 97,133)( 98,136)( 99,135)(100,134)(101,141)(102,144)
(103,143)(104,142)(105,137)(106,140)(107,139)(108,138)(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,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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, 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)( 73,121)( 74,124)( 75,123)( 76,122)( 77,129)
( 78,132)( 79,131)( 80,130)( 81,125)( 82,128)( 83,127)( 84,126)( 85,109)
( 86,112)( 87,111)( 88,110)( 89,117)( 90,120)( 91,119)( 92,118)( 93,113)
( 94,116)( 95,115)( 96,114)( 97,133)( 98,136)( 99,135)(100,134)(101,141)
(102,144)(103,143)(104,142)(105,137)(106,140)(107,139)(108,138)(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,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;

```
References : None.
to this polytope