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# Polytope of Type {24,12}

Atlas Canonical Name : {24,12}*1152p
if this polytope has a name.
Group : SmallGroup(1152,155800)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 48, 288, 24
Order of s0s1s2 : 24
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
3-fold quotients : {24,4}*384c
4-fold quotients : {24,6}*288b, {6,12}*288b
6-fold quotients : {24,4}*192c, {24,4}*192d, {12,4}*192b
8-fold quotients : {12,6}*144b, {3,12}*144
12-fold quotients : {24,2}*96, {12,4}*96b, {12,4}*96c, {6,4}*96
16-fold quotients : {6,6}*72c
24-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
32-fold quotients : {3,6}*36
36-fold quotients : {8,2}*32
48-fold quotients : {3,4}*24, {6,2}*24
72-fold quotients : {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)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)( 78,118)
( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,133)( 86,134)
( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)
( 95,140)( 96,139)( 97,121)( 98,122)( 99,124)(100,123)(101,129)(102,130)
(103,132)(104,131)(105,125)(106,126)(107,128)(108,127)(145,217)(146,218)
(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)(154,222)
(155,224)(156,223)(157,241)(158,242)(159,244)(160,243)(161,249)(162,250)
(163,252)(164,251)(165,245)(166,246)(167,248)(168,247)(169,229)(170,230)
(171,232)(172,231)(173,237)(174,238)(175,240)(176,239)(177,233)(178,234)
(179,236)(180,235)(181,253)(182,254)(183,256)(184,255)(185,261)(186,262)
(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,277)(194,278)
(195,280)(196,279)(197,285)(198,286)(199,288)(200,287)(201,281)(202,282)
(203,284)(204,283)(205,265)(206,266)(207,268)(208,267)(209,273)(210,274)
(211,276)(212,275)(213,269)(214,270)(215,272)(216,271);;
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)
( 73,269)( 74,272)( 75,271)( 76,270)( 77,265)( 78,268)( 79,267)( 80,266)
( 81,273)( 82,276)( 83,275)( 84,274)( 85,257)( 86,260)( 87,259)( 88,258)
( 89,253)( 90,256)( 91,255)( 92,254)( 93,261)( 94,264)( 95,263)( 96,262)
( 97,281)( 98,284)( 99,283)(100,282)(101,277)(102,280)(103,279)(104,278)
(105,285)(106,288)(107,287)(108,286)(109,233)(110,236)(111,235)(112,234)
(113,229)(114,232)(115,231)(116,230)(117,237)(118,240)(119,239)(120,238)
(121,221)(122,224)(123,223)(124,222)(125,217)(126,220)(127,219)(128,218)
(129,225)(130,228)(131,227)(132,226)(133,245)(134,248)(135,247)(136,246)
(137,241)(138,244)(139,243)(140,242)(141,249)(142,252)(143,251)(144,250);;
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)
(145,146)(147,148)(149,154)(150,153)(151,156)(152,155)(157,158)(159,160)
(161,166)(162,165)(163,168)(164,167)(169,170)(171,172)(173,178)(174,177)
(175,180)(176,179)(181,182)(183,184)(185,190)(186,189)(187,192)(188,191)
(193,194)(195,196)(197,202)(198,201)(199,204)(200,203)(205,206)(207,208)
(209,214)(210,213)(211,216)(212,215)(217,218)(219,220)(221,226)(222,225)
(223,228)(224,227)(229,230)(231,232)(233,238)(234,237)(235,240)(236,239)
(241,242)(243,244)(245,250)(246,249)(247,252)(248,251)(253,254)(255,256)
(257,262)(258,261)(259,264)(260,263)(265,266)(267,268)(269,274)(270,273)
(271,276)(272,275)(277,278)(279,280)(281,286)(282,285)(283,288)(284,287);;
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*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)
( 78,118)( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,133)
( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)
( 94,138)( 95,140)( 96,139)( 97,121)( 98,122)( 99,124)(100,123)(101,129)
(102,130)(103,132)(104,131)(105,125)(106,126)(107,128)(108,127)(145,217)
(146,218)(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)
(154,222)(155,224)(156,223)(157,241)(158,242)(159,244)(160,243)(161,249)
(162,250)(163,252)(164,251)(165,245)(166,246)(167,248)(168,247)(169,229)
(170,230)(171,232)(172,231)(173,237)(174,238)(175,240)(176,239)(177,233)
(178,234)(179,236)(180,235)(181,253)(182,254)(183,256)(184,255)(185,261)
(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,277)
(194,278)(195,280)(196,279)(197,285)(198,286)(199,288)(200,287)(201,281)
(202,282)(203,284)(204,283)(205,265)(206,266)(207,268)(208,267)(209,273)
(210,274)(211,276)(212,275)(213,269)(214,270)(215,272)(216,271);
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)( 73,269)( 74,272)( 75,271)( 76,270)( 77,265)( 78,268)( 79,267)
( 80,266)( 81,273)( 82,276)( 83,275)( 84,274)( 85,257)( 86,260)( 87,259)
( 88,258)( 89,253)( 90,256)( 91,255)( 92,254)( 93,261)( 94,264)( 95,263)
( 96,262)( 97,281)( 98,284)( 99,283)(100,282)(101,277)(102,280)(103,279)
(104,278)(105,285)(106,288)(107,287)(108,286)(109,233)(110,236)(111,235)
(112,234)(113,229)(114,232)(115,231)(116,230)(117,237)(118,240)(119,239)
(120,238)(121,221)(122,224)(123,223)(124,222)(125,217)(126,220)(127,219)
(128,218)(129,225)(130,228)(131,227)(132,226)(133,245)(134,248)(135,247)
(136,246)(137,241)(138,244)(139,243)(140,242)(141,249)(142,252)(143,251)
(144,250);
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)(145,146)(147,148)(149,154)(150,153)(151,156)(152,155)(157,158)
(159,160)(161,166)(162,165)(163,168)(164,167)(169,170)(171,172)(173,178)
(174,177)(175,180)(176,179)(181,182)(183,184)(185,190)(186,189)(187,192)
(188,191)(193,194)(195,196)(197,202)(198,201)(199,204)(200,203)(205,206)
(207,208)(209,214)(210,213)(211,216)(212,215)(217,218)(219,220)(221,226)
(222,225)(223,228)(224,227)(229,230)(231,232)(233,238)(234,237)(235,240)
(236,239)(241,242)(243,244)(245,250)(246,249)(247,252)(248,251)(253,254)
(255,256)(257,262)(258,261)(259,264)(260,263)(265,266)(267,268)(269,274)
(270,273)(271,276)(272,275)(277,278)(279,280)(281,286)(282,285)(283,288)
(284,287);
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*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope