Polytope of Type {96,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {96,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,34517)
Rank : 3
Schlafli Type : {96,6}
Number of vertices, edges, etc : 96, 288, 6
Order of s₀s₁s₂ : 96
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {48,6}*576b
   3-fold quotients : {96,2}*384
   4-fold quotients : {24,6}*288b
   6-fold quotients : {48,2}*192
   8-fold quotients : {12,6}*144b
   9-fold quotients : {32,2}*128
   12-fold quotients : {24,2}*96
   16-fold quotients : {6,6}*72c
   18-fold quotients : {16,2}*64
   24-fold quotients : {12,2}*48
   32-fold quotients : {3,6}*36
   36-fold quotients : {8,2}*32
   48-fold quotients : {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 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)
( 27, 32)( 37, 55)( 38, 57)( 39, 56)( 40, 61)( 41, 63)( 42, 62)( 43, 58)
( 44, 60)( 45, 59)( 46, 64)( 47, 66)( 48, 65)( 49, 70)( 50, 72)( 51, 71)
( 52, 67)( 53, 69)( 54, 68)( 73,109)( 74,111)( 75,110)( 76,115)( 77,117)
( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)( 84,119)( 85,124)
( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,136)( 92,138)( 93,137)
( 94,142)( 95,144)( 96,143)( 97,139)( 98,141)( 99,140)(100,127)(101,129)
(102,128)(103,133)(104,135)(105,134)(106,130)(107,132)(108,131)(146,147)
(148,151)(149,153)(150,152)(155,156)(157,160)(158,162)(159,161)(163,172)
(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)(170,177)(171,176)
(181,199)(182,201)(183,200)(184,205)(185,207)(186,206)(187,202)(188,204)
(189,203)(190,208)(191,210)(192,209)(193,214)(194,216)(195,215)(196,211)
(197,213)(198,212)(217,253)(218,255)(219,254)(220,259)(221,261)(222,260)
(223,256)(224,258)(225,257)(226,262)(227,264)(228,263)(229,268)(230,270)
(231,269)(232,265)(233,267)(234,266)(235,280)(236,282)(237,281)(238,286)
(239,288)(240,287)(241,283)(242,285)(243,284)(244,271)(245,273)(246,272)
(247,277)(248,279)(249,278)(250,274)(251,276)(252,275)(289,361)(290,363)
(291,362)(292,367)(293,369)(294,368)(295,364)(296,366)(297,365)(298,370)
(299,372)(300,371)(301,376)(302,378)(303,377)(304,373)(305,375)(306,374)
(307,388)(308,390)(309,389)(310,394)(311,396)(312,395)(313,391)(314,393)
(315,392)(316,379)(317,381)(318,380)(319,385)(320,387)(321,386)(322,382)
(323,384)(324,383)(325,415)(326,417)(327,416)(328,421)(329,423)(330,422)
(331,418)(332,420)(333,419)(334,424)(335,426)(336,425)(337,430)(338,432)
(339,431)(340,427)(341,429)(342,428)(343,397)(344,399)(345,398)(346,403)
(347,405)(348,404)(349,400)(350,402)(351,401)(352,406)(353,408)(354,407)
(355,412)(356,414)(357,413)(358,409)(359,411)(360,410)(433,505)(434,507)
(435,506)(436,511)(437,513)(438,512)(439,508)(440,510)(441,509)(442,514)
(443,516)(444,515)(445,520)(446,522)(447,521)(448,517)(449,519)(450,518)
(451,532)(452,534)(453,533)(454,538)(455,540)(456,539)(457,535)(458,537)
(459,536)(460,523)(461,525)(462,524)(463,529)(464,531)(465,530)(466,526)
(467,528)(468,527)(469,559)(470,561)(471,560)(472,565)(473,567)(474,566)
(475,562)(476,564)(477,563)(478,568)(479,570)(480,569)(481,574)(482,576)
(483,575)(484,571)(485,573)(486,572)(487,541)(488,543)(489,542)(490,547)
(491,549)(492,548)(493,544)(494,546)(495,545)(496,550)(497,552)(498,551)
(499,556)(500,558)(501,557)(502,553)(503,555)(504,554);;
s1 := (  1,290)(  2,289)(  3,291)(  4,296)(  5,295)(  6,297)(  7,293)(  8,292)
(  9,294)( 10,299)( 11,298)( 12,300)( 13,305)( 14,304)( 15,306)( 16,302)
( 17,301)( 18,303)( 19,317)( 20,316)( 21,318)( 22,323)( 23,322)( 24,324)
( 25,320)( 26,319)( 27,321)( 28,308)( 29,307)( 30,309)( 31,314)( 32,313)
( 33,315)( 34,311)( 35,310)( 36,312)( 37,344)( 38,343)( 39,345)( 40,350)
( 41,349)( 42,351)( 43,347)( 44,346)( 45,348)( 46,353)( 47,352)( 48,354)
( 49,359)( 50,358)( 51,360)( 52,356)( 53,355)( 54,357)( 55,326)( 56,325)
( 57,327)( 58,332)( 59,331)( 60,333)( 61,329)( 62,328)( 63,330)( 64,335)
( 65,334)( 66,336)( 67,341)( 68,340)( 69,342)( 70,338)( 71,337)( 72,339)
( 73,398)( 74,397)( 75,399)( 76,404)( 77,403)( 78,405)( 79,401)( 80,400)
( 81,402)( 82,407)( 83,406)( 84,408)( 85,413)( 86,412)( 87,414)( 88,410)
( 89,409)( 90,411)( 91,425)( 92,424)( 93,426)( 94,431)( 95,430)( 96,432)
( 97,428)( 98,427)( 99,429)(100,416)(101,415)(102,417)(103,422)(104,421)
(105,423)(106,419)(107,418)(108,420)(109,362)(110,361)(111,363)(112,368)
(113,367)(114,369)(115,365)(116,364)(117,366)(118,371)(119,370)(120,372)
(121,377)(122,376)(123,378)(124,374)(125,373)(126,375)(127,389)(128,388)
(129,390)(130,395)(131,394)(132,396)(133,392)(134,391)(135,393)(136,380)
(137,379)(138,381)(139,386)(140,385)(141,387)(142,383)(143,382)(144,384)
(145,434)(146,433)(147,435)(148,440)(149,439)(150,441)(151,437)(152,436)
(153,438)(154,443)(155,442)(156,444)(157,449)(158,448)(159,450)(160,446)
(161,445)(162,447)(163,461)(164,460)(165,462)(166,467)(167,466)(168,468)
(169,464)(170,463)(171,465)(172,452)(173,451)(174,453)(175,458)(176,457)
(177,459)(178,455)(179,454)(180,456)(181,488)(182,487)(183,489)(184,494)
(185,493)(186,495)(187,491)(188,490)(189,492)(190,497)(191,496)(192,498)
(193,503)(194,502)(195,504)(196,500)(197,499)(198,501)(199,470)(200,469)
(201,471)(202,476)(203,475)(204,477)(205,473)(206,472)(207,474)(208,479)
(209,478)(210,480)(211,485)(212,484)(213,486)(214,482)(215,481)(216,483)
(217,542)(218,541)(219,543)(220,548)(221,547)(222,549)(223,545)(224,544)
(225,546)(226,551)(227,550)(228,552)(229,557)(230,556)(231,558)(232,554)
(233,553)(234,555)(235,569)(236,568)(237,570)(238,575)(239,574)(240,576)
(241,572)(242,571)(243,573)(244,560)(245,559)(246,561)(247,566)(248,565)
(249,567)(250,563)(251,562)(252,564)(253,506)(254,505)(255,507)(256,512)
(257,511)(258,513)(259,509)(260,508)(261,510)(262,515)(263,514)(264,516)
(265,521)(266,520)(267,522)(268,518)(269,517)(270,519)(271,533)(272,532)
(273,534)(274,539)(275,538)(276,540)(277,536)(278,535)(279,537)(280,524)
(281,523)(282,525)(283,530)(284,529)(285,531)(286,527)(287,526)(288,528);;
s2 := (  1,145)(  2,150)(  3,152)(  4,148)(  5,153)(  6,146)(  7,151)(  8,147)
(  9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)
( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)
( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)
( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)( 40,184)
( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)
( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)
( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)
( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)
( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)( 80,219)
( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)( 88,232)
( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)( 96,236)
( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)(104,252)
(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)(112,256)
(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)
(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)
(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)
(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)
(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)
(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)
(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)
(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)
(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)(328,472)
(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)
(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)
(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)
(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)
(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)(368,507)
(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)(376,520)
(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)(384,524)
(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)(392,540)
(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)(400,544)
(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)
(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)
(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)
(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);;
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*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*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*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*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*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*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(576)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)
( 26, 33)( 27, 32)( 37, 55)( 38, 57)( 39, 56)( 40, 61)( 41, 63)( 42, 62)
( 43, 58)( 44, 60)( 45, 59)( 46, 64)( 47, 66)( 48, 65)( 49, 70)( 50, 72)
( 51, 71)( 52, 67)( 53, 69)( 54, 68)( 73,109)( 74,111)( 75,110)( 76,115)
( 77,117)( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)( 84,119)
( 85,124)( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,136)( 92,138)
( 93,137)( 94,142)( 95,144)( 96,143)( 97,139)( 98,141)( 99,140)(100,127)
(101,129)(102,128)(103,133)(104,135)(105,134)(106,130)(107,132)(108,131)
(146,147)(148,151)(149,153)(150,152)(155,156)(157,160)(158,162)(159,161)
(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)(170,177)
(171,176)(181,199)(182,201)(183,200)(184,205)(185,207)(186,206)(187,202)
(188,204)(189,203)(190,208)(191,210)(192,209)(193,214)(194,216)(195,215)
(196,211)(197,213)(198,212)(217,253)(218,255)(219,254)(220,259)(221,261)
(222,260)(223,256)(224,258)(225,257)(226,262)(227,264)(228,263)(229,268)
(230,270)(231,269)(232,265)(233,267)(234,266)(235,280)(236,282)(237,281)
(238,286)(239,288)(240,287)(241,283)(242,285)(243,284)(244,271)(245,273)
(246,272)(247,277)(248,279)(249,278)(250,274)(251,276)(252,275)(289,361)
(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)(296,366)(297,365)
(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)(304,373)(305,375)
(306,374)(307,388)(308,390)(309,389)(310,394)(311,396)(312,395)(313,391)
(314,393)(315,392)(316,379)(317,381)(318,380)(319,385)(320,387)(321,386)
(322,382)(323,384)(324,383)(325,415)(326,417)(327,416)(328,421)(329,423)
(330,422)(331,418)(332,420)(333,419)(334,424)(335,426)(336,425)(337,430)
(338,432)(339,431)(340,427)(341,429)(342,428)(343,397)(344,399)(345,398)
(346,403)(347,405)(348,404)(349,400)(350,402)(351,401)(352,406)(353,408)
(354,407)(355,412)(356,414)(357,413)(358,409)(359,411)(360,410)(433,505)
(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)(440,510)(441,509)
(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)(448,517)(449,519)
(450,518)(451,532)(452,534)(453,533)(454,538)(455,540)(456,539)(457,535)
(458,537)(459,536)(460,523)(461,525)(462,524)(463,529)(464,531)(465,530)
(466,526)(467,528)(468,527)(469,559)(470,561)(471,560)(472,565)(473,567)
(474,566)(475,562)(476,564)(477,563)(478,568)(479,570)(480,569)(481,574)
(482,576)(483,575)(484,571)(485,573)(486,572)(487,541)(488,543)(489,542)
(490,547)(491,549)(492,548)(493,544)(494,546)(495,545)(496,550)(497,552)
(498,551)(499,556)(500,558)(501,557)(502,553)(503,555)(504,554);
s1 := Sym(576)!(  1,290)(  2,289)(  3,291)(  4,296)(  5,295)(  6,297)(  7,293)
(  8,292)(  9,294)( 10,299)( 11,298)( 12,300)( 13,305)( 14,304)( 15,306)
( 16,302)( 17,301)( 18,303)( 19,317)( 20,316)( 21,318)( 22,323)( 23,322)
( 24,324)( 25,320)( 26,319)( 27,321)( 28,308)( 29,307)( 30,309)( 31,314)
( 32,313)( 33,315)( 34,311)( 35,310)( 36,312)( 37,344)( 38,343)( 39,345)
( 40,350)( 41,349)( 42,351)( 43,347)( 44,346)( 45,348)( 46,353)( 47,352)
( 48,354)( 49,359)( 50,358)( 51,360)( 52,356)( 53,355)( 54,357)( 55,326)
( 56,325)( 57,327)( 58,332)( 59,331)( 60,333)( 61,329)( 62,328)( 63,330)
( 64,335)( 65,334)( 66,336)( 67,341)( 68,340)( 69,342)( 70,338)( 71,337)
( 72,339)( 73,398)( 74,397)( 75,399)( 76,404)( 77,403)( 78,405)( 79,401)
( 80,400)( 81,402)( 82,407)( 83,406)( 84,408)( 85,413)( 86,412)( 87,414)
( 88,410)( 89,409)( 90,411)( 91,425)( 92,424)( 93,426)( 94,431)( 95,430)
( 96,432)( 97,428)( 98,427)( 99,429)(100,416)(101,415)(102,417)(103,422)
(104,421)(105,423)(106,419)(107,418)(108,420)(109,362)(110,361)(111,363)
(112,368)(113,367)(114,369)(115,365)(116,364)(117,366)(118,371)(119,370)
(120,372)(121,377)(122,376)(123,378)(124,374)(125,373)(126,375)(127,389)
(128,388)(129,390)(130,395)(131,394)(132,396)(133,392)(134,391)(135,393)
(136,380)(137,379)(138,381)(139,386)(140,385)(141,387)(142,383)(143,382)
(144,384)(145,434)(146,433)(147,435)(148,440)(149,439)(150,441)(151,437)
(152,436)(153,438)(154,443)(155,442)(156,444)(157,449)(158,448)(159,450)
(160,446)(161,445)(162,447)(163,461)(164,460)(165,462)(166,467)(167,466)
(168,468)(169,464)(170,463)(171,465)(172,452)(173,451)(174,453)(175,458)
(176,457)(177,459)(178,455)(179,454)(180,456)(181,488)(182,487)(183,489)
(184,494)(185,493)(186,495)(187,491)(188,490)(189,492)(190,497)(191,496)
(192,498)(193,503)(194,502)(195,504)(196,500)(197,499)(198,501)(199,470)
(200,469)(201,471)(202,476)(203,475)(204,477)(205,473)(206,472)(207,474)
(208,479)(209,478)(210,480)(211,485)(212,484)(213,486)(214,482)(215,481)
(216,483)(217,542)(218,541)(219,543)(220,548)(221,547)(222,549)(223,545)
(224,544)(225,546)(226,551)(227,550)(228,552)(229,557)(230,556)(231,558)
(232,554)(233,553)(234,555)(235,569)(236,568)(237,570)(238,575)(239,574)
(240,576)(241,572)(242,571)(243,573)(244,560)(245,559)(246,561)(247,566)
(248,565)(249,567)(250,563)(251,562)(252,564)(253,506)(254,505)(255,507)
(256,512)(257,511)(258,513)(259,509)(260,508)(261,510)(262,515)(263,514)
(264,516)(265,521)(266,520)(267,522)(268,518)(269,517)(270,519)(271,533)
(272,532)(273,534)(274,539)(275,538)(276,540)(277,536)(278,535)(279,537)
(280,524)(281,523)(282,525)(283,530)(284,529)(285,531)(286,527)(287,526)
(288,528);
s2 := Sym(576)!(  1,145)(  2,150)(  3,152)(  4,148)(  5,153)(  6,146)(  7,151)
(  8,147)(  9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)
( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)
( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)
( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)
( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)
( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)
( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)
( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)
( 72,212)( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)
( 80,219)( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)
( 88,232)( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)
( 96,236)( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)
(104,252)(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)
(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)
(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)
(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)
(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)
(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)
(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)
(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)
(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)
(320,468)(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)
(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)
(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)
(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)
(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)
(360,500)(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)
(368,507)(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)
(376,520)(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)
(384,524)(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)
(392,540)(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)
(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)
(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)
(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)
(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)
(432,572);
poly := sub<Sym(576)|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*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*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*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*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*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*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