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Polytope of Type {96,6}

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