Polytope of Type {96,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {96,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,34514)
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
   Self-Petrie
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}*576c
   3-fold quotients : {32,6}*384
   4-fold quotients : {24,6}*288c
   6-fold quotients : {16,6}*192
   8-fold quotients : {12,6}*144c
   9-fold quotients : {32,2}*128
   12-fold quotients : {8,6}*96
   16-fold quotients : {6,6}*72b
   18-fold quotients : {16,2}*64
   24-fold quotients : {4,6}*48a
   32-fold quotients : {6,3}*36
   36-fold quotients : {8,2}*32
   48-fold quotients : {2,6}*24
   72-fold quotients : {4,2}*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 := (  1,289)(  2,294)(  3,296)(  4,292)(  5,297)(  6,290)(  7,295)(  8,291)
(  9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)( 16,304)
( 17,300)( 18,302)( 19,316)( 20,321)( 21,323)( 22,319)( 23,324)( 24,317)
( 25,322)( 26,318)( 27,320)( 28,307)( 29,312)( 30,314)( 31,310)( 32,315)
( 33,308)( 34,313)( 35,309)( 36,311)( 37,343)( 38,348)( 39,350)( 40,346)
( 41,351)( 42,344)( 43,349)( 44,345)( 45,347)( 46,352)( 47,357)( 48,359)
( 49,355)( 50,360)( 51,353)( 52,358)( 53,354)( 54,356)( 55,325)( 56,330)
( 57,332)( 58,328)( 59,333)( 60,326)( 61,331)( 62,327)( 63,329)( 64,334)
( 65,339)( 66,341)( 67,337)( 68,342)( 69,335)( 70,340)( 71,336)( 72,338)
( 73,397)( 74,402)( 75,404)( 76,400)( 77,405)( 78,398)( 79,403)( 80,399)
( 81,401)( 82,406)( 83,411)( 84,413)( 85,409)( 86,414)( 87,407)( 88,412)
( 89,408)( 90,410)( 91,424)( 92,429)( 93,431)( 94,427)( 95,432)( 96,425)
( 97,430)( 98,426)( 99,428)(100,415)(101,420)(102,422)(103,418)(104,423)
(105,416)(106,421)(107,417)(108,419)(109,361)(110,366)(111,368)(112,364)
(113,369)(114,362)(115,367)(116,363)(117,365)(118,370)(119,375)(120,377)
(121,373)(122,378)(123,371)(124,376)(125,372)(126,374)(127,388)(128,393)
(129,395)(130,391)(131,396)(132,389)(133,394)(134,390)(135,392)(136,379)
(137,384)(138,386)(139,382)(140,387)(141,380)(142,385)(143,381)(144,383)
(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)(152,435)
(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)(160,448)
(161,444)(162,446)(163,460)(164,465)(165,467)(166,463)(167,468)(168,461)
(169,466)(170,462)(171,464)(172,451)(173,456)(174,458)(175,454)(176,459)
(177,452)(178,457)(179,453)(180,455)(181,487)(182,492)(183,494)(184,490)
(185,495)(186,488)(187,493)(188,489)(189,491)(190,496)(191,501)(192,503)
(193,499)(194,504)(195,497)(196,502)(197,498)(198,500)(199,469)(200,474)
(201,476)(202,472)(203,477)(204,470)(205,475)(206,471)(207,473)(208,478)
(209,483)(210,485)(211,481)(212,486)(213,479)(214,484)(215,480)(216,482)
(217,541)(218,546)(219,548)(220,544)(221,549)(222,542)(223,547)(224,543)
(225,545)(226,550)(227,555)(228,557)(229,553)(230,558)(231,551)(232,556)
(233,552)(234,554)(235,568)(236,573)(237,575)(238,571)(239,576)(240,569)
(241,574)(242,570)(243,572)(244,559)(245,564)(246,566)(247,562)(248,567)
(249,560)(250,565)(251,561)(252,563)(253,505)(254,510)(255,512)(256,508)
(257,513)(258,506)(259,511)(260,507)(261,509)(262,514)(263,519)(264,521)
(265,517)(266,522)(267,515)(268,520)(269,516)(270,518)(271,532)(272,537)
(273,539)(274,535)(275,540)(276,533)(277,538)(278,534)(279,536)(280,523)
(281,528)(282,530)(283,526)(284,531)(285,524)(286,529)(287,525)(288,527);;
s1 := (  1,146)(  2,145)(  3,147)(  4,152)(  5,151)(  6,153)(  7,149)(  8,148)
(  9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)( 16,158)
( 17,157)( 18,159)( 19,173)( 20,172)( 21,174)( 22,179)( 23,178)( 24,180)
( 25,176)( 26,175)( 27,177)( 28,164)( 29,163)( 30,165)( 31,170)( 32,169)
( 33,171)( 34,167)( 35,166)( 36,168)( 37,200)( 38,199)( 39,201)( 40,206)
( 41,205)( 42,207)( 43,203)( 44,202)( 45,204)( 46,209)( 47,208)( 48,210)
( 49,215)( 50,214)( 51,216)( 52,212)( 53,211)( 54,213)( 55,182)( 56,181)
( 57,183)( 58,188)( 59,187)( 60,189)( 61,185)( 62,184)( 63,186)( 64,191)
( 65,190)( 66,192)( 67,197)( 68,196)( 69,198)( 70,194)( 71,193)( 72,195)
( 73,254)( 74,253)( 75,255)( 76,260)( 77,259)( 78,261)( 79,257)( 80,256)
( 81,258)( 82,263)( 83,262)( 84,264)( 85,269)( 86,268)( 87,270)( 88,266)
( 89,265)( 90,267)( 91,281)( 92,280)( 93,282)( 94,287)( 95,286)( 96,288)
( 97,284)( 98,283)( 99,285)(100,272)(101,271)(102,273)(103,278)(104,277)
(105,279)(106,275)(107,274)(108,276)(109,218)(110,217)(111,219)(112,224)
(113,223)(114,225)(115,221)(116,220)(117,222)(118,227)(119,226)(120,228)
(121,233)(122,232)(123,234)(124,230)(125,229)(126,231)(127,245)(128,244)
(129,246)(130,251)(131,250)(132,252)(133,248)(134,247)(135,249)(136,236)
(137,235)(138,237)(139,242)(140,241)(141,243)(142,239)(143,238)(144,240)
(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)(296,508)
(297,510)(298,515)(299,514)(300,516)(301,521)(302,520)(303,522)(304,518)
(305,517)(306,519)(307,533)(308,532)(309,534)(310,539)(311,538)(312,540)
(313,536)(314,535)(315,537)(316,524)(317,523)(318,525)(319,530)(320,529)
(321,531)(322,527)(323,526)(324,528)(325,560)(326,559)(327,561)(328,566)
(329,565)(330,567)(331,563)(332,562)(333,564)(334,569)(335,568)(336,570)
(337,575)(338,574)(339,576)(340,572)(341,571)(342,573)(343,542)(344,541)
(345,543)(346,548)(347,547)(348,549)(349,545)(350,544)(351,546)(352,551)
(353,550)(354,552)(355,557)(356,556)(357,558)(358,554)(359,553)(360,555)
(361,434)(362,433)(363,435)(364,440)(365,439)(366,441)(367,437)(368,436)
(369,438)(370,443)(371,442)(372,444)(373,449)(374,448)(375,450)(376,446)
(377,445)(378,447)(379,461)(380,460)(381,462)(382,467)(383,466)(384,468)
(385,464)(386,463)(387,465)(388,452)(389,451)(390,453)(391,458)(392,457)
(393,459)(394,455)(395,454)(396,456)(397,488)(398,487)(399,489)(400,494)
(401,493)(402,495)(403,491)(404,490)(405,492)(406,497)(407,496)(408,498)
(409,503)(410,502)(411,504)(412,500)(413,499)(414,501)(415,470)(416,469)
(417,471)(418,476)(419,475)(420,477)(421,473)(422,472)(423,474)(424,479)
(425,478)(426,480)(427,485)(428,484)(429,486)(430,482)(431,481)(432,483);;
s2 := (  1,145)(  2,147)(  3,146)(  4,151)(  5,153)(  6,152)(  7,148)(  8,150)
(  9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)( 16,157)
( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)( 24,170)
( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)( 32,180)
( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)( 40,187)
( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,190)( 47,192)( 48,191)
( 49,196)( 50,198)( 51,197)( 52,193)( 53,195)( 54,194)( 55,199)( 56,201)
( 57,200)( 58,205)( 59,207)( 60,206)( 61,202)( 62,204)( 63,203)( 64,208)
( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)( 72,212)
( 73,217)( 74,219)( 75,218)( 76,223)( 77,225)( 78,224)( 79,220)( 80,222)
( 81,221)( 82,226)( 83,228)( 84,227)( 85,232)( 86,234)( 87,233)( 88,229)
( 89,231)( 90,230)( 91,235)( 92,237)( 93,236)( 94,241)( 95,243)( 96,242)
( 97,238)( 98,240)( 99,239)(100,244)(101,246)(102,245)(103,250)(104,252)
(105,251)(106,247)(107,249)(108,248)(109,253)(110,255)(111,254)(112,259)
(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)(120,263)
(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)(128,273)
(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)(136,280)
(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)(144,284)
(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)(296,438)
(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)(304,445)
(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)(312,458)
(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)(320,468)
(321,467)(322,463)(323,465)(324,464)(325,469)(326,471)(327,470)(328,475)
(329,477)(330,476)(331,472)(332,474)(333,473)(334,478)(335,480)(336,479)
(337,484)(338,486)(339,485)(340,481)(341,483)(342,482)(343,487)(344,489)
(345,488)(346,493)(347,495)(348,494)(349,490)(350,492)(351,491)(352,496)
(353,498)(354,497)(355,502)(356,504)(357,503)(358,499)(359,501)(360,500)
(361,505)(362,507)(363,506)(364,511)(365,513)(366,512)(367,508)(368,510)
(369,509)(370,514)(371,516)(372,515)(373,520)(374,522)(375,521)(376,517)
(377,519)(378,518)(379,523)(380,525)(381,524)(382,529)(383,531)(384,530)
(385,526)(386,528)(387,527)(388,532)(389,534)(390,533)(391,538)(392,540)
(393,539)(394,535)(395,537)(396,536)(397,541)(398,543)(399,542)(400,547)
(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)(408,551)
(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)(416,561)
(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)(424,568)
(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*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*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*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)!(  1,289)(  2,294)(  3,296)(  4,292)(  5,297)(  6,290)(  7,295)
(  8,291)(  9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)
( 16,304)( 17,300)( 18,302)( 19,316)( 20,321)( 21,323)( 22,319)( 23,324)
( 24,317)( 25,322)( 26,318)( 27,320)( 28,307)( 29,312)( 30,314)( 31,310)
( 32,315)( 33,308)( 34,313)( 35,309)( 36,311)( 37,343)( 38,348)( 39,350)
( 40,346)( 41,351)( 42,344)( 43,349)( 44,345)( 45,347)( 46,352)( 47,357)
( 48,359)( 49,355)( 50,360)( 51,353)( 52,358)( 53,354)( 54,356)( 55,325)
( 56,330)( 57,332)( 58,328)( 59,333)( 60,326)( 61,331)( 62,327)( 63,329)
( 64,334)( 65,339)( 66,341)( 67,337)( 68,342)( 69,335)( 70,340)( 71,336)
( 72,338)( 73,397)( 74,402)( 75,404)( 76,400)( 77,405)( 78,398)( 79,403)
( 80,399)( 81,401)( 82,406)( 83,411)( 84,413)( 85,409)( 86,414)( 87,407)
( 88,412)( 89,408)( 90,410)( 91,424)( 92,429)( 93,431)( 94,427)( 95,432)
( 96,425)( 97,430)( 98,426)( 99,428)(100,415)(101,420)(102,422)(103,418)
(104,423)(105,416)(106,421)(107,417)(108,419)(109,361)(110,366)(111,368)
(112,364)(113,369)(114,362)(115,367)(116,363)(117,365)(118,370)(119,375)
(120,377)(121,373)(122,378)(123,371)(124,376)(125,372)(126,374)(127,388)
(128,393)(129,395)(130,391)(131,396)(132,389)(133,394)(134,390)(135,392)
(136,379)(137,384)(138,386)(139,382)(140,387)(141,380)(142,385)(143,381)
(144,383)(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)
(152,435)(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)
(160,448)(161,444)(162,446)(163,460)(164,465)(165,467)(166,463)(167,468)
(168,461)(169,466)(170,462)(171,464)(172,451)(173,456)(174,458)(175,454)
(176,459)(177,452)(178,457)(179,453)(180,455)(181,487)(182,492)(183,494)
(184,490)(185,495)(186,488)(187,493)(188,489)(189,491)(190,496)(191,501)
(192,503)(193,499)(194,504)(195,497)(196,502)(197,498)(198,500)(199,469)
(200,474)(201,476)(202,472)(203,477)(204,470)(205,475)(206,471)(207,473)
(208,478)(209,483)(210,485)(211,481)(212,486)(213,479)(214,484)(215,480)
(216,482)(217,541)(218,546)(219,548)(220,544)(221,549)(222,542)(223,547)
(224,543)(225,545)(226,550)(227,555)(228,557)(229,553)(230,558)(231,551)
(232,556)(233,552)(234,554)(235,568)(236,573)(237,575)(238,571)(239,576)
(240,569)(241,574)(242,570)(243,572)(244,559)(245,564)(246,566)(247,562)
(248,567)(249,560)(250,565)(251,561)(252,563)(253,505)(254,510)(255,512)
(256,508)(257,513)(258,506)(259,511)(260,507)(261,509)(262,514)(263,519)
(264,521)(265,517)(266,522)(267,515)(268,520)(269,516)(270,518)(271,532)
(272,537)(273,539)(274,535)(275,540)(276,533)(277,538)(278,534)(279,536)
(280,523)(281,528)(282,530)(283,526)(284,531)(285,524)(286,529)(287,525)
(288,527);
s1 := Sym(576)!(  1,146)(  2,145)(  3,147)(  4,152)(  5,151)(  6,153)(  7,149)
(  8,148)(  9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)
( 16,158)( 17,157)( 18,159)( 19,173)( 20,172)( 21,174)( 22,179)( 23,178)
( 24,180)( 25,176)( 26,175)( 27,177)( 28,164)( 29,163)( 30,165)( 31,170)
( 32,169)( 33,171)( 34,167)( 35,166)( 36,168)( 37,200)( 38,199)( 39,201)
( 40,206)( 41,205)( 42,207)( 43,203)( 44,202)( 45,204)( 46,209)( 47,208)
( 48,210)( 49,215)( 50,214)( 51,216)( 52,212)( 53,211)( 54,213)( 55,182)
( 56,181)( 57,183)( 58,188)( 59,187)( 60,189)( 61,185)( 62,184)( 63,186)
( 64,191)( 65,190)( 66,192)( 67,197)( 68,196)( 69,198)( 70,194)( 71,193)
( 72,195)( 73,254)( 74,253)( 75,255)( 76,260)( 77,259)( 78,261)( 79,257)
( 80,256)( 81,258)( 82,263)( 83,262)( 84,264)( 85,269)( 86,268)( 87,270)
( 88,266)( 89,265)( 90,267)( 91,281)( 92,280)( 93,282)( 94,287)( 95,286)
( 96,288)( 97,284)( 98,283)( 99,285)(100,272)(101,271)(102,273)(103,278)
(104,277)(105,279)(106,275)(107,274)(108,276)(109,218)(110,217)(111,219)
(112,224)(113,223)(114,225)(115,221)(116,220)(117,222)(118,227)(119,226)
(120,228)(121,233)(122,232)(123,234)(124,230)(125,229)(126,231)(127,245)
(128,244)(129,246)(130,251)(131,250)(132,252)(133,248)(134,247)(135,249)
(136,236)(137,235)(138,237)(139,242)(140,241)(141,243)(142,239)(143,238)
(144,240)(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)
(296,508)(297,510)(298,515)(299,514)(300,516)(301,521)(302,520)(303,522)
(304,518)(305,517)(306,519)(307,533)(308,532)(309,534)(310,539)(311,538)
(312,540)(313,536)(314,535)(315,537)(316,524)(317,523)(318,525)(319,530)
(320,529)(321,531)(322,527)(323,526)(324,528)(325,560)(326,559)(327,561)
(328,566)(329,565)(330,567)(331,563)(332,562)(333,564)(334,569)(335,568)
(336,570)(337,575)(338,574)(339,576)(340,572)(341,571)(342,573)(343,542)
(344,541)(345,543)(346,548)(347,547)(348,549)(349,545)(350,544)(351,546)
(352,551)(353,550)(354,552)(355,557)(356,556)(357,558)(358,554)(359,553)
(360,555)(361,434)(362,433)(363,435)(364,440)(365,439)(366,441)(367,437)
(368,436)(369,438)(370,443)(371,442)(372,444)(373,449)(374,448)(375,450)
(376,446)(377,445)(378,447)(379,461)(380,460)(381,462)(382,467)(383,466)
(384,468)(385,464)(386,463)(387,465)(388,452)(389,451)(390,453)(391,458)
(392,457)(393,459)(394,455)(395,454)(396,456)(397,488)(398,487)(399,489)
(400,494)(401,493)(402,495)(403,491)(404,490)(405,492)(406,497)(407,496)
(408,498)(409,503)(410,502)(411,504)(412,500)(413,499)(414,501)(415,470)
(416,469)(417,471)(418,476)(419,475)(420,477)(421,473)(422,472)(423,474)
(424,479)(425,478)(426,480)(427,485)(428,484)(429,486)(430,482)(431,481)
(432,483);
s2 := Sym(576)!(  1,145)(  2,147)(  3,146)(  4,151)(  5,153)(  6,152)(  7,148)
(  8,150)(  9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)
( 16,157)( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)
( 24,170)( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)
( 32,180)( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)
( 40,187)( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,190)( 47,192)
( 48,191)( 49,196)( 50,198)( 51,197)( 52,193)( 53,195)( 54,194)( 55,199)
( 56,201)( 57,200)( 58,205)( 59,207)( 60,206)( 61,202)( 62,204)( 63,203)
( 64,208)( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)
( 72,212)( 73,217)( 74,219)( 75,218)( 76,223)( 77,225)( 78,224)( 79,220)
( 80,222)( 81,221)( 82,226)( 83,228)( 84,227)( 85,232)( 86,234)( 87,233)
( 88,229)( 89,231)( 90,230)( 91,235)( 92,237)( 93,236)( 94,241)( 95,243)
( 96,242)( 97,238)( 98,240)( 99,239)(100,244)(101,246)(102,245)(103,250)
(104,252)(105,251)(106,247)(107,249)(108,248)(109,253)(110,255)(111,254)
(112,259)(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)
(120,263)(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)
(128,273)(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)
(136,280)(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)
(144,284)(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)
(296,438)(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)
(304,445)(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)
(312,458)(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)
(320,468)(321,467)(322,463)(323,465)(324,464)(325,469)(326,471)(327,470)
(328,475)(329,477)(330,476)(331,472)(332,474)(333,473)(334,478)(335,480)
(336,479)(337,484)(338,486)(339,485)(340,481)(341,483)(342,482)(343,487)
(344,489)(345,488)(346,493)(347,495)(348,494)(349,490)(350,492)(351,491)
(352,496)(353,498)(354,497)(355,502)(356,504)(357,503)(358,499)(359,501)
(360,500)(361,505)(362,507)(363,506)(364,511)(365,513)(366,512)(367,508)
(368,510)(369,509)(370,514)(371,516)(372,515)(373,520)(374,522)(375,521)
(376,517)(377,519)(378,518)(379,523)(380,525)(381,524)(382,529)(383,531)
(384,530)(385,526)(386,528)(387,527)(388,532)(389,534)(390,533)(391,538)
(392,540)(393,539)(394,535)(395,537)(396,536)(397,541)(398,543)(399,542)
(400,547)(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)
(408,551)(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)
(416,561)(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)
(424,568)(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)
(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*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*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*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