Polytope of Type {4,9,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,9,8}*1152
if this polytope has a name.
Group : SmallGroup(1152,155437)
Rank : 4
Schlafli Type : {4,9,8}
Number of vertices, edges, etc : 4, 36, 72, 16
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,9,4}*576a
3-fold quotients : {4,3,8}*384
4-fold quotients : {4,9,4}*288
6-fold quotients : {4,3,4}*192a
8-fold quotients : {4,9,2}*144
12-fold quotients : {4,3,4}*96
24-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 17)( 2, 18)( 3, 19)( 4, 20)( 5, 21)( 6, 22)( 7, 23)( 8, 24)
( 9, 25)( 10, 26)( 11, 27)( 12, 28)( 13, 29)( 14, 30)( 15, 31)( 16, 32)
( 33, 49)( 34, 50)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)
( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)
( 65, 81)( 66, 82)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)
( 73, 89)( 74, 90)( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)( 80, 96)
( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)
(105,121)(106,122)(107,123)(108,124)(109,125)(110,126)(111,127)(112,128)
(129,145)(130,146)(131,147)(132,148)(133,149)(134,150)(135,151)(136,152)
(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)
(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)
(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)(176,192)
(193,209)(194,210)(195,211)(196,212)(197,213)(198,214)(199,215)(200,216)
(201,217)(202,218)(203,219)(204,220)(205,221)(206,222)(207,223)(208,224)
(225,241)(226,242)(227,243)(228,244)(229,245)(230,246)(231,247)(232,248)
(233,249)(234,250)(235,251)(236,252)(237,253)(238,254)(239,255)(240,256)
(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)(264,280)
(265,281)(266,282)(267,283)(268,284)(269,285)(270,286)(271,287)(272,288)
(289,305)(290,306)(291,307)(292,308)(293,309)(294,310)(295,311)(296,312)
(297,313)(298,314)(299,315)(300,316)(301,317)(302,318)(303,319)(304,320)
(321,337)(322,338)(323,339)(324,340)(325,341)(326,342)(327,343)(328,344)
(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)(336,352)
(353,369)(354,370)(355,371)(356,372)(357,373)(358,374)(359,375)(360,376)
(361,377)(362,378)(363,379)(364,380)(365,381)(366,382)(367,383)(368,384)
(385,401)(386,402)(387,403)(388,404)(389,405)(390,406)(391,407)(392,408)
(393,409)(394,410)(395,411)(396,412)(397,413)(398,414)(399,415)(400,416)
(417,433)(418,434)(419,435)(420,436)(421,437)(422,438)(423,439)(424,440)
(425,441)(426,442)(427,443)(428,444)(429,445)(430,446)(431,447)(432,448)
(449,465)(450,466)(451,467)(452,468)(453,469)(454,470)(455,471)(456,472)
(457,473)(458,474)(459,475)(460,476)(461,477)(462,478)(463,479)(464,480)
(481,497)(482,498)(483,499)(484,500)(485,501)(486,502)(487,503)(488,504)
(489,505)(490,506)(491,507)(492,508)(493,509)(494,510)(495,511)(496,512)
(513,529)(514,530)(515,531)(516,532)(517,533)(518,534)(519,535)(520,536)
(521,537)(522,538)(523,539)(524,540)(525,541)(526,542)(527,543)(528,544)
(545,561)(546,562)(547,563)(548,564)(549,565)(550,566)(551,567)(552,568)
(553,569)(554,570)(555,571)(556,572)(557,573)(558,574)(559,575)(560,576);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 17, 25)( 18, 26)
( 19, 28)( 20, 27)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)
( 35, 68)( 36, 67)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)
( 43, 76)( 44, 75)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)
( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)
( 59, 84)( 60, 83)( 61, 87)( 62, 88)( 63, 85)( 64, 86)( 97,257)( 98,258)
( 99,260)(100,259)(101,263)(102,264)(103,261)(104,262)(105,265)(106,266)
(107,268)(108,267)(109,271)(110,272)(111,269)(112,270)(113,281)(114,282)
(115,284)(116,283)(117,287)(118,288)(119,285)(120,286)(121,273)(122,274)
(123,276)(124,275)(125,279)(126,280)(127,277)(128,278)(129,225)(130,226)
(131,228)(132,227)(133,231)(134,232)(135,229)(136,230)(137,233)(138,234)
(139,236)(140,235)(141,239)(142,240)(143,237)(144,238)(145,249)(146,250)
(147,252)(148,251)(149,255)(150,256)(151,253)(152,254)(153,241)(154,242)
(155,244)(156,243)(157,247)(158,248)(159,245)(160,246)(161,193)(162,194)
(163,196)(164,195)(165,199)(166,200)(167,197)(168,198)(169,201)(170,202)
(171,204)(172,203)(173,207)(174,208)(175,205)(176,206)(177,217)(178,218)
(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,209)(186,210)
(187,212)(188,211)(189,215)(190,216)(191,213)(192,214)(289,290)(293,296)
(294,295)(297,298)(301,304)(302,303)(305,314)(306,313)(307,315)(308,316)
(309,320)(310,319)(311,318)(312,317)(321,354)(322,353)(323,355)(324,356)
(325,360)(326,359)(327,358)(328,357)(329,362)(330,361)(331,363)(332,364)
(333,368)(334,367)(335,366)(336,365)(337,378)(338,377)(339,379)(340,380)
(341,384)(342,383)(343,382)(344,381)(345,370)(346,369)(347,371)(348,372)
(349,376)(350,375)(351,374)(352,373)(385,546)(386,545)(387,547)(388,548)
(389,552)(390,551)(391,550)(392,549)(393,554)(394,553)(395,555)(396,556)
(397,560)(398,559)(399,558)(400,557)(401,570)(402,569)(403,571)(404,572)
(405,576)(406,575)(407,574)(408,573)(409,562)(410,561)(411,563)(412,564)
(413,568)(414,567)(415,566)(416,565)(417,514)(418,513)(419,515)(420,516)
(421,520)(422,519)(423,518)(424,517)(425,522)(426,521)(427,523)(428,524)
(429,528)(430,527)(431,526)(432,525)(433,538)(434,537)(435,539)(436,540)
(437,544)(438,543)(439,542)(440,541)(441,530)(442,529)(443,531)(444,532)
(445,536)(446,535)(447,534)(448,533)(449,482)(450,481)(451,483)(452,484)
(453,488)(454,487)(455,486)(456,485)(457,490)(458,489)(459,491)(460,492)
(461,496)(462,495)(463,494)(464,493)(465,506)(466,505)(467,507)(468,508)
(469,512)(470,511)(471,510)(472,509)(473,498)(474,497)(475,499)(476,500)
(477,504)(478,503)(479,502)(480,501);;
s2 := ( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)( 8,100)
( 9,121)( 10,122)( 11,127)( 12,128)( 13,126)( 14,125)( 15,123)( 16,124)
( 17,113)( 18,114)( 19,119)( 20,120)( 21,118)( 22,117)( 23,115)( 24,116)
( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)( 32,108)
( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)( 40,164)
( 41,185)( 42,186)( 43,191)( 44,192)( 45,190)( 46,189)( 47,187)( 48,188)
( 49,177)( 50,178)( 51,183)( 52,184)( 53,182)( 54,181)( 55,179)( 56,180)
( 57,169)( 58,170)( 59,175)( 60,176)( 61,174)( 62,173)( 63,171)( 64,172)
( 65,129)( 66,130)( 67,135)( 68,136)( 69,134)( 70,133)( 71,131)( 72,132)
( 73,153)( 74,154)( 75,159)( 76,160)( 77,158)( 78,157)( 79,155)( 80,156)
( 81,145)( 82,146)( 83,151)( 84,152)( 85,150)( 86,149)( 87,147)( 88,148)
( 89,137)( 90,138)( 91,143)( 92,144)( 93,142)( 94,141)( 95,139)( 96,140)
(193,257)(194,258)(195,263)(196,264)(197,262)(198,261)(199,259)(200,260)
(201,281)(202,282)(203,287)(204,288)(205,286)(206,285)(207,283)(208,284)
(209,273)(210,274)(211,279)(212,280)(213,278)(214,277)(215,275)(216,276)
(217,265)(218,266)(219,271)(220,272)(221,270)(222,269)(223,267)(224,268)
(227,231)(228,232)(229,230)(233,249)(234,250)(235,255)(236,256)(237,254)
(238,253)(239,251)(240,252)(243,247)(244,248)(245,246)(289,386)(290,385)
(291,392)(292,391)(293,389)(294,390)(295,388)(296,387)(297,410)(298,409)
(299,416)(300,415)(301,413)(302,414)(303,412)(304,411)(305,402)(306,401)
(307,408)(308,407)(309,405)(310,406)(311,404)(312,403)(313,394)(314,393)
(315,400)(316,399)(317,397)(318,398)(319,396)(320,395)(321,450)(322,449)
(323,456)(324,455)(325,453)(326,454)(327,452)(328,451)(329,474)(330,473)
(331,480)(332,479)(333,477)(334,478)(335,476)(336,475)(337,466)(338,465)
(339,472)(340,471)(341,469)(342,470)(343,468)(344,467)(345,458)(346,457)
(347,464)(348,463)(349,461)(350,462)(351,460)(352,459)(353,418)(354,417)
(355,424)(356,423)(357,421)(358,422)(359,420)(360,419)(361,442)(362,441)
(363,448)(364,447)(365,445)(366,446)(367,444)(368,443)(369,434)(370,433)
(371,440)(372,439)(373,437)(374,438)(375,436)(376,435)(377,426)(378,425)
(379,432)(380,431)(381,429)(382,430)(383,428)(384,427)(481,546)(482,545)
(483,552)(484,551)(485,549)(486,550)(487,548)(488,547)(489,570)(490,569)
(491,576)(492,575)(493,573)(494,574)(495,572)(496,571)(497,562)(498,561)
(499,568)(500,567)(501,565)(502,566)(503,564)(504,563)(505,554)(506,553)
(507,560)(508,559)(509,557)(510,558)(511,556)(512,555)(513,514)(515,520)
(516,519)(521,538)(522,537)(523,544)(524,543)(525,541)(526,542)(527,540)
(528,539)(529,530)(531,536)(532,535);;
s3 := ( 1,291)( 2,292)( 3,290)( 4,289)( 5,295)( 6,296)( 7,294)( 8,293)
( 9,299)( 10,300)( 11,298)( 12,297)( 13,303)( 14,304)( 15,302)( 16,301)
( 17,307)( 18,308)( 19,306)( 20,305)( 21,311)( 22,312)( 23,310)( 24,309)
( 25,315)( 26,316)( 27,314)( 28,313)( 29,319)( 30,320)( 31,318)( 32,317)
( 33,323)( 34,324)( 35,322)( 36,321)( 37,327)( 38,328)( 39,326)( 40,325)
( 41,331)( 42,332)( 43,330)( 44,329)( 45,335)( 46,336)( 47,334)( 48,333)
( 49,339)( 50,340)( 51,338)( 52,337)( 53,343)( 54,344)( 55,342)( 56,341)
( 57,347)( 58,348)( 59,346)( 60,345)( 61,351)( 62,352)( 63,350)( 64,349)
( 65,355)( 66,356)( 67,354)( 68,353)( 69,359)( 70,360)( 71,358)( 72,357)
( 73,363)( 74,364)( 75,362)( 76,361)( 77,367)( 78,368)( 79,366)( 80,365)
( 81,371)( 82,372)( 83,370)( 84,369)( 85,375)( 86,376)( 87,374)( 88,373)
( 89,379)( 90,380)( 91,378)( 92,377)( 93,383)( 94,384)( 95,382)( 96,381)
( 97,387)( 98,388)( 99,386)(100,385)(101,391)(102,392)(103,390)(104,389)
(105,395)(106,396)(107,394)(108,393)(109,399)(110,400)(111,398)(112,397)
(113,403)(114,404)(115,402)(116,401)(117,407)(118,408)(119,406)(120,405)
(121,411)(122,412)(123,410)(124,409)(125,415)(126,416)(127,414)(128,413)
(129,419)(130,420)(131,418)(132,417)(133,423)(134,424)(135,422)(136,421)
(137,427)(138,428)(139,426)(140,425)(141,431)(142,432)(143,430)(144,429)
(145,435)(146,436)(147,434)(148,433)(149,439)(150,440)(151,438)(152,437)
(153,443)(154,444)(155,442)(156,441)(157,447)(158,448)(159,446)(160,445)
(161,451)(162,452)(163,450)(164,449)(165,455)(166,456)(167,454)(168,453)
(169,459)(170,460)(171,458)(172,457)(173,463)(174,464)(175,462)(176,461)
(177,467)(178,468)(179,466)(180,465)(181,471)(182,472)(183,470)(184,469)
(185,475)(186,476)(187,474)(188,473)(189,479)(190,480)(191,478)(192,477)
(193,483)(194,484)(195,482)(196,481)(197,487)(198,488)(199,486)(200,485)
(201,491)(202,492)(203,490)(204,489)(205,495)(206,496)(207,494)(208,493)
(209,499)(210,500)(211,498)(212,497)(213,503)(214,504)(215,502)(216,501)
(217,507)(218,508)(219,506)(220,505)(221,511)(222,512)(223,510)(224,509)
(225,515)(226,516)(227,514)(228,513)(229,519)(230,520)(231,518)(232,517)
(233,523)(234,524)(235,522)(236,521)(237,527)(238,528)(239,526)(240,525)
(241,531)(242,532)(243,530)(244,529)(245,535)(246,536)(247,534)(248,533)
(249,539)(250,540)(251,538)(252,537)(253,543)(254,544)(255,542)(256,541)
(257,547)(258,548)(259,546)(260,545)(261,551)(262,552)(263,550)(264,549)
(265,555)(266,556)(267,554)(268,553)(269,559)(270,560)(271,558)(272,557)
(273,563)(274,564)(275,562)(276,561)(277,567)(278,568)(279,566)(280,565)
(281,571)(282,572)(283,570)(284,569)(285,575)(286,576)(287,574)(288,573);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1, 17)( 2, 18)( 3, 19)( 4, 20)( 5, 21)( 6, 22)( 7, 23)
( 8, 24)( 9, 25)( 10, 26)( 11, 27)( 12, 28)( 13, 29)( 14, 30)( 15, 31)
( 16, 32)( 33, 49)( 34, 50)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)
( 40, 56)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)
( 48, 64)( 65, 81)( 66, 82)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)
( 72, 88)( 73, 89)( 74, 90)( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)
( 80, 96)( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)
(104,120)(105,121)(106,122)(107,123)(108,124)(109,125)(110,126)(111,127)
(112,128)(129,145)(130,146)(131,147)(132,148)(133,149)(134,150)(135,151)
(136,152)(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)
(144,160)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)
(168,184)(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)
(176,192)(193,209)(194,210)(195,211)(196,212)(197,213)(198,214)(199,215)
(200,216)(201,217)(202,218)(203,219)(204,220)(205,221)(206,222)(207,223)
(208,224)(225,241)(226,242)(227,243)(228,244)(229,245)(230,246)(231,247)
(232,248)(233,249)(234,250)(235,251)(236,252)(237,253)(238,254)(239,255)
(240,256)(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)
(264,280)(265,281)(266,282)(267,283)(268,284)(269,285)(270,286)(271,287)
(272,288)(289,305)(290,306)(291,307)(292,308)(293,309)(294,310)(295,311)
(296,312)(297,313)(298,314)(299,315)(300,316)(301,317)(302,318)(303,319)
(304,320)(321,337)(322,338)(323,339)(324,340)(325,341)(326,342)(327,343)
(328,344)(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)
(336,352)(353,369)(354,370)(355,371)(356,372)(357,373)(358,374)(359,375)
(360,376)(361,377)(362,378)(363,379)(364,380)(365,381)(366,382)(367,383)
(368,384)(385,401)(386,402)(387,403)(388,404)(389,405)(390,406)(391,407)
(392,408)(393,409)(394,410)(395,411)(396,412)(397,413)(398,414)(399,415)
(400,416)(417,433)(418,434)(419,435)(420,436)(421,437)(422,438)(423,439)
(424,440)(425,441)(426,442)(427,443)(428,444)(429,445)(430,446)(431,447)
(432,448)(449,465)(450,466)(451,467)(452,468)(453,469)(454,470)(455,471)
(456,472)(457,473)(458,474)(459,475)(460,476)(461,477)(462,478)(463,479)
(464,480)(481,497)(482,498)(483,499)(484,500)(485,501)(486,502)(487,503)
(488,504)(489,505)(490,506)(491,507)(492,508)(493,509)(494,510)(495,511)
(496,512)(513,529)(514,530)(515,531)(516,532)(517,533)(518,534)(519,535)
(520,536)(521,537)(522,538)(523,539)(524,540)(525,541)(526,542)(527,543)
(528,544)(545,561)(546,562)(547,563)(548,564)(549,565)(550,566)(551,567)
(552,568)(553,569)(554,570)(555,571)(556,572)(557,573)(558,574)(559,575)
(560,576);
s1 := Sym(576)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 17, 25)
( 18, 26)( 19, 28)( 20, 27)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)
( 34, 66)( 35, 68)( 36, 67)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)
( 42, 74)( 43, 76)( 44, 75)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)
( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)
( 58, 82)( 59, 84)( 60, 83)( 61, 87)( 62, 88)( 63, 85)( 64, 86)( 97,257)
( 98,258)( 99,260)(100,259)(101,263)(102,264)(103,261)(104,262)(105,265)
(106,266)(107,268)(108,267)(109,271)(110,272)(111,269)(112,270)(113,281)
(114,282)(115,284)(116,283)(117,287)(118,288)(119,285)(120,286)(121,273)
(122,274)(123,276)(124,275)(125,279)(126,280)(127,277)(128,278)(129,225)
(130,226)(131,228)(132,227)(133,231)(134,232)(135,229)(136,230)(137,233)
(138,234)(139,236)(140,235)(141,239)(142,240)(143,237)(144,238)(145,249)
(146,250)(147,252)(148,251)(149,255)(150,256)(151,253)(152,254)(153,241)
(154,242)(155,244)(156,243)(157,247)(158,248)(159,245)(160,246)(161,193)
(162,194)(163,196)(164,195)(165,199)(166,200)(167,197)(168,198)(169,201)
(170,202)(171,204)(172,203)(173,207)(174,208)(175,205)(176,206)(177,217)
(178,218)(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,209)
(186,210)(187,212)(188,211)(189,215)(190,216)(191,213)(192,214)(289,290)
(293,296)(294,295)(297,298)(301,304)(302,303)(305,314)(306,313)(307,315)
(308,316)(309,320)(310,319)(311,318)(312,317)(321,354)(322,353)(323,355)
(324,356)(325,360)(326,359)(327,358)(328,357)(329,362)(330,361)(331,363)
(332,364)(333,368)(334,367)(335,366)(336,365)(337,378)(338,377)(339,379)
(340,380)(341,384)(342,383)(343,382)(344,381)(345,370)(346,369)(347,371)
(348,372)(349,376)(350,375)(351,374)(352,373)(385,546)(386,545)(387,547)
(388,548)(389,552)(390,551)(391,550)(392,549)(393,554)(394,553)(395,555)
(396,556)(397,560)(398,559)(399,558)(400,557)(401,570)(402,569)(403,571)
(404,572)(405,576)(406,575)(407,574)(408,573)(409,562)(410,561)(411,563)
(412,564)(413,568)(414,567)(415,566)(416,565)(417,514)(418,513)(419,515)
(420,516)(421,520)(422,519)(423,518)(424,517)(425,522)(426,521)(427,523)
(428,524)(429,528)(430,527)(431,526)(432,525)(433,538)(434,537)(435,539)
(436,540)(437,544)(438,543)(439,542)(440,541)(441,530)(442,529)(443,531)
(444,532)(445,536)(446,535)(447,534)(448,533)(449,482)(450,481)(451,483)
(452,484)(453,488)(454,487)(455,486)(456,485)(457,490)(458,489)(459,491)
(460,492)(461,496)(462,495)(463,494)(464,493)(465,506)(466,505)(467,507)
(468,508)(469,512)(470,511)(471,510)(472,509)(473,498)(474,497)(475,499)
(476,500)(477,504)(478,503)(479,502)(480,501);
s2 := Sym(576)!( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)
( 8,100)( 9,121)( 10,122)( 11,127)( 12,128)( 13,126)( 14,125)( 15,123)
( 16,124)( 17,113)( 18,114)( 19,119)( 20,120)( 21,118)( 22,117)( 23,115)
( 24,116)( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)
( 32,108)( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)
( 40,164)( 41,185)( 42,186)( 43,191)( 44,192)( 45,190)( 46,189)( 47,187)
( 48,188)( 49,177)( 50,178)( 51,183)( 52,184)( 53,182)( 54,181)( 55,179)
( 56,180)( 57,169)( 58,170)( 59,175)( 60,176)( 61,174)( 62,173)( 63,171)
( 64,172)( 65,129)( 66,130)( 67,135)( 68,136)( 69,134)( 70,133)( 71,131)
( 72,132)( 73,153)( 74,154)( 75,159)( 76,160)( 77,158)( 78,157)( 79,155)
( 80,156)( 81,145)( 82,146)( 83,151)( 84,152)( 85,150)( 86,149)( 87,147)
( 88,148)( 89,137)( 90,138)( 91,143)( 92,144)( 93,142)( 94,141)( 95,139)
( 96,140)(193,257)(194,258)(195,263)(196,264)(197,262)(198,261)(199,259)
(200,260)(201,281)(202,282)(203,287)(204,288)(205,286)(206,285)(207,283)
(208,284)(209,273)(210,274)(211,279)(212,280)(213,278)(214,277)(215,275)
(216,276)(217,265)(218,266)(219,271)(220,272)(221,270)(222,269)(223,267)
(224,268)(227,231)(228,232)(229,230)(233,249)(234,250)(235,255)(236,256)
(237,254)(238,253)(239,251)(240,252)(243,247)(244,248)(245,246)(289,386)
(290,385)(291,392)(292,391)(293,389)(294,390)(295,388)(296,387)(297,410)
(298,409)(299,416)(300,415)(301,413)(302,414)(303,412)(304,411)(305,402)
(306,401)(307,408)(308,407)(309,405)(310,406)(311,404)(312,403)(313,394)
(314,393)(315,400)(316,399)(317,397)(318,398)(319,396)(320,395)(321,450)
(322,449)(323,456)(324,455)(325,453)(326,454)(327,452)(328,451)(329,474)
(330,473)(331,480)(332,479)(333,477)(334,478)(335,476)(336,475)(337,466)
(338,465)(339,472)(340,471)(341,469)(342,470)(343,468)(344,467)(345,458)
(346,457)(347,464)(348,463)(349,461)(350,462)(351,460)(352,459)(353,418)
(354,417)(355,424)(356,423)(357,421)(358,422)(359,420)(360,419)(361,442)
(362,441)(363,448)(364,447)(365,445)(366,446)(367,444)(368,443)(369,434)
(370,433)(371,440)(372,439)(373,437)(374,438)(375,436)(376,435)(377,426)
(378,425)(379,432)(380,431)(381,429)(382,430)(383,428)(384,427)(481,546)
(482,545)(483,552)(484,551)(485,549)(486,550)(487,548)(488,547)(489,570)
(490,569)(491,576)(492,575)(493,573)(494,574)(495,572)(496,571)(497,562)
(498,561)(499,568)(500,567)(501,565)(502,566)(503,564)(504,563)(505,554)
(506,553)(507,560)(508,559)(509,557)(510,558)(511,556)(512,555)(513,514)
(515,520)(516,519)(521,538)(522,537)(523,544)(524,543)(525,541)(526,542)
(527,540)(528,539)(529,530)(531,536)(532,535);
s3 := Sym(576)!( 1,291)( 2,292)( 3,290)( 4,289)( 5,295)( 6,296)( 7,294)
( 8,293)( 9,299)( 10,300)( 11,298)( 12,297)( 13,303)( 14,304)( 15,302)
( 16,301)( 17,307)( 18,308)( 19,306)( 20,305)( 21,311)( 22,312)( 23,310)
( 24,309)( 25,315)( 26,316)( 27,314)( 28,313)( 29,319)( 30,320)( 31,318)
( 32,317)( 33,323)( 34,324)( 35,322)( 36,321)( 37,327)( 38,328)( 39,326)
( 40,325)( 41,331)( 42,332)( 43,330)( 44,329)( 45,335)( 46,336)( 47,334)
( 48,333)( 49,339)( 50,340)( 51,338)( 52,337)( 53,343)( 54,344)( 55,342)
( 56,341)( 57,347)( 58,348)( 59,346)( 60,345)( 61,351)( 62,352)( 63,350)
( 64,349)( 65,355)( 66,356)( 67,354)( 68,353)( 69,359)( 70,360)( 71,358)
( 72,357)( 73,363)( 74,364)( 75,362)( 76,361)( 77,367)( 78,368)( 79,366)
( 80,365)( 81,371)( 82,372)( 83,370)( 84,369)( 85,375)( 86,376)( 87,374)
( 88,373)( 89,379)( 90,380)( 91,378)( 92,377)( 93,383)( 94,384)( 95,382)
( 96,381)( 97,387)( 98,388)( 99,386)(100,385)(101,391)(102,392)(103,390)
(104,389)(105,395)(106,396)(107,394)(108,393)(109,399)(110,400)(111,398)
(112,397)(113,403)(114,404)(115,402)(116,401)(117,407)(118,408)(119,406)
(120,405)(121,411)(122,412)(123,410)(124,409)(125,415)(126,416)(127,414)
(128,413)(129,419)(130,420)(131,418)(132,417)(133,423)(134,424)(135,422)
(136,421)(137,427)(138,428)(139,426)(140,425)(141,431)(142,432)(143,430)
(144,429)(145,435)(146,436)(147,434)(148,433)(149,439)(150,440)(151,438)
(152,437)(153,443)(154,444)(155,442)(156,441)(157,447)(158,448)(159,446)
(160,445)(161,451)(162,452)(163,450)(164,449)(165,455)(166,456)(167,454)
(168,453)(169,459)(170,460)(171,458)(172,457)(173,463)(174,464)(175,462)
(176,461)(177,467)(178,468)(179,466)(180,465)(181,471)(182,472)(183,470)
(184,469)(185,475)(186,476)(187,474)(188,473)(189,479)(190,480)(191,478)
(192,477)(193,483)(194,484)(195,482)(196,481)(197,487)(198,488)(199,486)
(200,485)(201,491)(202,492)(203,490)(204,489)(205,495)(206,496)(207,494)
(208,493)(209,499)(210,500)(211,498)(212,497)(213,503)(214,504)(215,502)
(216,501)(217,507)(218,508)(219,506)(220,505)(221,511)(222,512)(223,510)
(224,509)(225,515)(226,516)(227,514)(228,513)(229,519)(230,520)(231,518)
(232,517)(233,523)(234,524)(235,522)(236,521)(237,527)(238,528)(239,526)
(240,525)(241,531)(242,532)(243,530)(244,529)(245,535)(246,536)(247,534)
(248,533)(249,539)(250,540)(251,538)(252,537)(253,543)(254,544)(255,542)
(256,541)(257,547)(258,548)(259,546)(260,545)(261,551)(262,552)(263,550)
(264,549)(265,555)(266,556)(267,554)(268,553)(269,559)(270,560)(271,558)
(272,557)(273,563)(274,564)(275,562)(276,561)(277,567)(278,568)(279,566)
(280,565)(281,571)(282,572)(283,570)(284,569)(285,575)(286,576)(287,574)
(288,573);
poly := sub<Sym(576)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope