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# Polytope of Type {12,24}

Atlas Canonical Name : {12,24}*1152p
if this polytope has a name.
Group : SmallGroup(1152,155800)
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}*384c
4-fold quotients : {6,24}*288b, {12,6}*288b
6-fold quotients : {4,24}*192c, {4,24}*192d, {4,12}*192b
8-fold quotients : {6,12}*144b, {12,3}*144
12-fold quotients : {2,24}*96, {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
36-fold quotients : {2,8}*32
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)
(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,159)(158,160)
(161,167)(162,168)(163,165)(164,166)(169,171)(170,172)(173,179)(174,180)
(175,177)(176,178)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)
(193,195)(194,196)(197,203)(198,204)(199,201)(200,202)(205,207)(206,208)
(209,215)(210,216)(211,213)(212,214)(217,219)(218,220)(221,227)(222,228)
(223,225)(224,226)(229,231)(230,232)(233,239)(234,240)(235,237)(236,238)
(241,243)(242,244)(245,251)(246,252)(247,249)(248,250)(253,255)(254,256)
(257,263)(258,264)(259,261)(260,262)(265,267)(266,268)(269,275)(270,276)
(271,273)(272,274)(277,279)(278,280)(281,287)(282,288)(283,285)(284,286);;
s1 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)( 11, 12)( 13, 29)( 14, 30)( 15, 32)
( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)( 23, 36)
( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)( 50, 66)
( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)( 58, 70)
( 59, 72)( 60, 71)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)( 78,110)
( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)( 86,138)
( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)( 94,142)
( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)(102,122)
(103,124)(104,123)(105,129)(106,130)(107,132)(108,131)(145,221)(146,222)
(147,224)(148,223)(149,217)(150,218)(151,220)(152,219)(153,225)(154,226)
(155,228)(156,227)(157,245)(158,246)(159,248)(160,247)(161,241)(162,242)
(163,244)(164,243)(165,249)(166,250)(167,252)(168,251)(169,233)(170,234)
(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,237)(178,238)
(179,240)(180,239)(181,257)(182,258)(183,260)(184,259)(185,253)(186,254)
(187,256)(188,255)(189,261)(190,262)(191,264)(192,263)(193,281)(194,282)
(195,284)(196,283)(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)
(203,288)(204,287)(205,269)(206,270)(207,272)(208,271)(209,265)(210,266)
(211,268)(212,267)(213,273)(214,274)(215,276)(216,275);;
s2 := (  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)
( 73,265)( 74,268)( 75,267)( 76,266)( 77,273)( 78,276)( 79,275)( 80,274)
( 81,269)( 82,272)( 83,271)( 84,270)( 85,253)( 86,256)( 87,255)( 88,254)
( 89,261)( 90,264)( 91,263)( 92,262)( 93,257)( 94,260)( 95,259)( 96,258)
( 97,277)( 98,280)( 99,279)(100,278)(101,285)(102,288)(103,287)(104,286)
(105,281)(106,284)(107,283)(108,282)(109,229)(110,232)(111,231)(112,230)
(113,237)(114,240)(115,239)(116,238)(117,233)(118,236)(119,235)(120,234)
(121,217)(122,220)(123,219)(124,218)(125,225)(126,228)(127,227)(128,226)
(129,221)(130,224)(131,223)(132,222)(133,241)(134,244)(135,243)(136,242)
(137,249)(138,252)(139,251)(140,250)(141,245)(142,248)(143,247)(144,246);;
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*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*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)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,159)
(158,160)(161,167)(162,168)(163,165)(164,166)(169,171)(170,172)(173,179)
(174,180)(175,177)(176,178)(181,183)(182,184)(185,191)(186,192)(187,189)
(188,190)(193,195)(194,196)(197,203)(198,204)(199,201)(200,202)(205,207)
(206,208)(209,215)(210,216)(211,213)(212,214)(217,219)(218,220)(221,227)
(222,228)(223,225)(224,226)(229,231)(230,232)(233,239)(234,240)(235,237)
(236,238)(241,243)(242,244)(245,251)(246,252)(247,249)(248,250)(253,255)
(254,256)(257,263)(258,264)(259,261)(260,262)(265,267)(266,268)(269,275)
(270,276)(271,273)(272,274)(277,279)(278,280)(281,287)(282,288)(283,285)
(284,286);
s1 := Sym(288)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)( 11, 12)( 13, 29)( 14, 30)
( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)
( 23, 36)( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)
( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)
( 58, 70)( 59, 72)( 60, 71)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)
( 78,110)( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)
( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)
( 94,142)( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)
(102,122)(103,124)(104,123)(105,129)(106,130)(107,132)(108,131)(145,221)
(146,222)(147,224)(148,223)(149,217)(150,218)(151,220)(152,219)(153,225)
(154,226)(155,228)(156,227)(157,245)(158,246)(159,248)(160,247)(161,241)
(162,242)(163,244)(164,243)(165,249)(166,250)(167,252)(168,251)(169,233)
(170,234)(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,237)
(178,238)(179,240)(180,239)(181,257)(182,258)(183,260)(184,259)(185,253)
(186,254)(187,256)(188,255)(189,261)(190,262)(191,264)(192,263)(193,281)
(194,282)(195,284)(196,283)(197,277)(198,278)(199,280)(200,279)(201,285)
(202,286)(203,288)(204,287)(205,269)(206,270)(207,272)(208,271)(209,265)
(210,266)(211,268)(212,267)(213,273)(214,274)(215,276)(216,275);
s2 := 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)( 73,265)( 74,268)( 75,267)( 76,266)( 77,273)( 78,276)( 79,275)
( 80,274)( 81,269)( 82,272)( 83,271)( 84,270)( 85,253)( 86,256)( 87,255)
( 88,254)( 89,261)( 90,264)( 91,263)( 92,262)( 93,257)( 94,260)( 95,259)
( 96,258)( 97,277)( 98,280)( 99,279)(100,278)(101,285)(102,288)(103,287)
(104,286)(105,281)(106,284)(107,283)(108,282)(109,229)(110,232)(111,231)
(112,230)(113,237)(114,240)(115,239)(116,238)(117,233)(118,236)(119,235)
(120,234)(121,217)(122,220)(123,219)(124,218)(125,225)(126,228)(127,227)
(128,226)(129,221)(130,224)(131,223)(132,222)(133,241)(134,244)(135,243)
(136,242)(137,249)(138,252)(139,251)(140,250)(141,245)(142,248)(143,247)
(144,246);
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*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*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