Polytope of Type {8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8}*1152d
if this polytope has a name.
Group : SmallGroup(1152,14487)
Rank : 3
Schlafli Type : {8,8}
Number of vertices, edges, etc : 72, 288, 72
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
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 : {4,8}*576b, {8,4}*576b
   4-fold quotients : {4,4}*288
   8-fold quotients : {4,4}*144
   9-fold quotients : {8,8}*128d
   16-fold quotients : {4,4}*72
   18-fold quotients : {4,8}*64b, {8,4}*64b
   36-fold quotients : {4,4}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope