Polytope of Type {32,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,34520)
Rank : 3
Schlafli Type : {32,6}
Number of vertices, edges, etc : 96, 288, 18
Order of s₀s₁s₂ : 32
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   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 : {16,6}*576
   4-fold quotients : {8,6}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {32,2}*128
   16-fold quotients : {4,6}*72
   18-fold quotients : {16,2}*64
   36-fold quotients : {8,2}*32
   72-fold quotients : {4,2}*16
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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