Polytope of Type {8,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98808)
Rank : 4
Schlafli Type : {8,4,6}
Number of vertices, edges, etc : 8, 48, 36, 18
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {4,4,6}*576
4-fold quotients : {4,4,6}*288, {2,4,6}*288
8-fold quotients : {2,4,6}*144
9-fold quotients : {8,4,2}*128b
18-fold quotients : {4,4,2}*64
36-fold quotients : {2,4,2}*32, {4,2,2}*32
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)
( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)
( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)
( 33,312)( 34,313)( 35,314)( 36,315)( 37,334)( 38,335)( 39,336)( 40,337)
( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)
( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,343)( 56,344)
( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)( 64,352)
( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)( 72,360)
( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)( 80,368)
( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)( 88,376)
( 89,377)( 90,378)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)( 96,393)
( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)(104,383)
(105,384)(106,385)(107,386)(108,387)(109,406)(110,407)(111,408)(112,409)
(113,410)(114,411)(115,412)(116,413)(117,414)(118,397)(119,398)(120,399)
(121,400)(122,401)(123,402)(124,403)(125,404)(126,405)(127,415)(128,416)
(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)(136,424)
(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)(144,432)
(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)
(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)
(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)
(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)
(177,456)(178,457)(179,458)(180,459)(181,478)(182,479)(183,480)(184,481)
(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)
(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,487)(200,488)
(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)(208,496)
(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)(216,504)
(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)(224,512)
(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)(232,520)
(233,521)(234,522)(235,532)(236,533)(237,534)(238,535)(239,536)(240,537)
(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)(248,527)
(249,528)(250,529)(251,530)(252,531)(253,550)(254,551)(255,552)(256,553)
(257,554)(258,555)(259,556)(260,557)(261,558)(262,541)(263,542)(264,543)
(265,544)(266,545)(267,546)(268,547)(269,548)(270,549)(271,559)(272,560)
(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)(280,568)
(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)(288,576);;
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, 46)( 38, 51)( 39, 53)( 40, 49)
( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)( 57, 71)
( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 74, 78)( 75, 80)
( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)(101,105)
(102,107)(104,108)(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)(145,163)(146,168)(147,170)(148,166)
(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)(156,179)
(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,208)(182,213)
(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)(190,199)
(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)(198,203)
(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)(224,237)
(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)(232,250)
(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)(258,281)
(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)(266,279)
(267,272)(268,277)(269,273)(270,275)(289,325)(290,330)(291,332)(292,328)
(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)(300,341)
(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)(308,348)
(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)(316,352)
(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)(324,356)
(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)(368,399)
(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)(376,412)
(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)(384,416)
(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)(392,432)
(393,425)(394,430)(395,426)(396,428)(433,496)(434,501)(435,503)(436,499)
(437,504)(438,497)(439,502)(440,498)(441,500)(442,487)(443,492)(444,494)
(445,490)(446,495)(447,488)(448,493)(449,489)(450,491)(451,478)(452,483)
(453,485)(454,481)(455,486)(456,479)(457,484)(458,480)(459,482)(460,469)
(461,474)(462,476)(463,472)(464,477)(465,470)(466,475)(467,471)(468,473)
(505,568)(506,573)(507,575)(508,571)(509,576)(510,569)(511,574)(512,570)
(513,572)(514,559)(515,564)(516,566)(517,562)(518,567)(519,560)(520,565)
(521,561)(522,563)(523,550)(524,555)(525,557)(526,553)(527,558)(528,551)
(529,556)(530,552)(531,554)(532,541)(533,546)(534,548)(535,544)(536,549)
(537,542)(538,547)(539,543)(540,545);;
s2 := ( 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)( 37,190)( 38,192)( 39,191)( 40,194)
( 41,193)( 42,195)( 43,198)( 44,197)( 45,196)( 46,181)( 47,183)( 48,182)
( 49,185)( 50,184)( 51,186)( 52,189)( 53,188)( 54,187)( 55,208)( 56,210)
( 57,209)( 58,212)( 59,211)( 60,213)( 61,216)( 62,215)( 63,214)( 64,199)
( 65,201)( 66,200)( 67,203)( 68,202)( 69,204)( 70,207)( 71,206)( 72,205)
( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)( 80,224)
( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)( 88,234)
( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)( 96,240)
( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)(104,247)
(105,249)(106,252)(107,251)(108,250)(109,262)(110,264)(111,263)(112,266)
(113,265)(114,267)(115,270)(116,269)(117,268)(118,253)(119,255)(120,254)
(121,257)(122,256)(123,258)(124,261)(125,260)(126,259)(127,280)(128,282)
(129,281)(130,284)(131,283)(132,285)(133,288)(134,287)(135,286)(136,271)
(137,273)(138,272)(139,275)(140,274)(141,276)(142,279)(143,278)(144,277)
(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)(325,478)(326,480)(327,479)(328,482)
(329,481)(330,483)(331,486)(332,485)(333,484)(334,469)(335,471)(336,470)
(337,473)(338,472)(339,474)(340,477)(341,476)(342,475)(343,496)(344,498)
(345,497)(346,500)(347,499)(348,501)(349,504)(350,503)(351,502)(352,487)
(353,489)(354,488)(355,491)(356,490)(357,492)(358,495)(359,494)(360,493)
(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)(368,512)
(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)(376,522)
(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)(384,528)
(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)(392,535)
(393,537)(394,540)(395,539)(396,538)(397,550)(398,552)(399,551)(400,554)
(401,553)(402,555)(403,558)(404,557)(405,556)(406,541)(407,543)(408,542)
(409,545)(410,544)(411,546)(412,549)(413,548)(414,547)(415,568)(416,570)
(417,569)(418,572)(419,571)(420,573)(421,576)(422,575)(423,574)(424,559)
(425,561)(426,560)(427,563)(428,562)(429,564)(430,567)(431,566)(432,565);;
s3 := ( 1, 76)( 2, 78)( 3, 77)( 4, 73)( 5, 75)( 6, 74)( 7, 79)( 8, 81)
( 9, 80)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 88)
( 17, 90)( 18, 89)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)
( 25, 97)( 26, 99)( 27, 98)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)
( 33,101)( 34,106)( 35,108)( 36,107)( 37,112)( 38,114)( 39,113)( 40,109)
( 41,111)( 42,110)( 43,115)( 44,117)( 45,116)( 46,121)( 47,123)( 48,122)
( 49,118)( 50,120)( 51,119)( 52,124)( 53,126)( 54,125)( 55,130)( 56,132)
( 57,131)( 58,127)( 59,129)( 60,128)( 61,133)( 62,135)( 63,134)( 64,139)
( 65,141)( 66,140)( 67,136)( 68,138)( 69,137)( 70,142)( 71,144)( 72,143)
(145,220)(146,222)(147,221)(148,217)(149,219)(150,218)(151,223)(152,225)
(153,224)(154,229)(155,231)(156,230)(157,226)(158,228)(159,227)(160,232)
(161,234)(162,233)(163,238)(164,240)(165,239)(166,235)(167,237)(168,236)
(169,241)(170,243)(171,242)(172,247)(173,249)(174,248)(175,244)(176,246)
(177,245)(178,250)(179,252)(180,251)(181,256)(182,258)(183,257)(184,253)
(185,255)(186,254)(187,259)(188,261)(189,260)(190,265)(191,267)(192,266)
(193,262)(194,264)(195,263)(196,268)(197,270)(198,269)(199,274)(200,276)
(201,275)(202,271)(203,273)(204,272)(205,277)(206,279)(207,278)(208,283)
(209,285)(210,284)(211,280)(212,282)(213,281)(214,286)(215,288)(216,287)
(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)
(297,368)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,376)
(305,378)(306,377)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)
(313,385)(314,387)(315,386)(316,391)(317,393)(318,392)(319,388)(320,390)
(321,389)(322,394)(323,396)(324,395)(325,400)(326,402)(327,401)(328,397)
(329,399)(330,398)(331,403)(332,405)(333,404)(334,409)(335,411)(336,410)
(337,406)(338,408)(339,407)(340,412)(341,414)(342,413)(343,418)(344,420)
(345,419)(346,415)(347,417)(348,416)(349,421)(350,423)(351,422)(352,427)
(353,429)(354,428)(355,424)(356,426)(357,425)(358,430)(359,432)(360,431)
(433,508)(434,510)(435,509)(436,505)(437,507)(438,506)(439,511)(440,513)
(441,512)(442,517)(443,519)(444,518)(445,514)(446,516)(447,515)(448,520)
(449,522)(450,521)(451,526)(452,528)(453,527)(454,523)(455,525)(456,524)
(457,529)(458,531)(459,530)(460,535)(461,537)(462,536)(463,532)(464,534)
(465,533)(466,538)(467,540)(468,539)(469,544)(470,546)(471,545)(472,541)
(473,543)(474,542)(475,547)(476,549)(477,548)(478,553)(479,555)(480,554)
(481,550)(482,552)(483,551)(484,556)(485,558)(486,557)(487,562)(488,564)
(489,563)(490,559)(491,561)(492,560)(493,565)(494,567)(495,566)(496,571)
(497,573)(498,572)(499,568)(500,570)(501,569)(502,574)(503,576)(504,575);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)
( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)
( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)
( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 37,334)( 38,335)( 39,336)
( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)
( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,343)
( 56,344)( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)
( 64,352)( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)
( 72,360)( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)
( 80,368)( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)
( 88,376)( 89,377)( 90,378)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)
( 96,393)( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)
(104,383)(105,384)(106,385)(107,386)(108,387)(109,406)(110,407)(111,408)
(112,409)(113,410)(114,411)(115,412)(116,413)(117,414)(118,397)(119,398)
(120,399)(121,400)(122,401)(123,402)(124,403)(125,404)(126,405)(127,415)
(128,416)(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)
(136,424)(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)
(144,432)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)
(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)
(160,448)(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)
(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)
(176,455)(177,456)(178,457)(179,458)(180,459)(181,478)(182,479)(183,480)
(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)
(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,487)
(200,488)(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)
(208,496)(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)
(216,504)(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)
(224,512)(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)
(232,520)(233,521)(234,522)(235,532)(236,533)(237,534)(238,535)(239,536)
(240,537)(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)
(248,527)(249,528)(250,529)(251,530)(252,531)(253,550)(254,551)(255,552)
(256,553)(257,554)(258,555)(259,556)(260,557)(261,558)(262,541)(263,542)
(264,543)(265,544)(266,545)(267,546)(268,547)(269,548)(270,549)(271,559)
(272,560)(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)
(280,568)(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)
(288,576);
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, 46)( 38, 51)( 39, 53)
( 40, 49)( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)
( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 74, 78)
( 75, 80)( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)
(101,105)(102,107)(104,108)(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)(145,163)(146,168)(147,170)
(148,166)(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)
(156,179)(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,208)
(182,213)(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)
(190,199)(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)
(198,203)(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)
(224,237)(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)
(232,250)(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)
(258,281)(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)
(266,279)(267,272)(268,277)(269,273)(270,275)(289,325)(290,330)(291,332)
(292,328)(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)
(300,341)(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)
(308,348)(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)
(316,352)(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)
(324,356)(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)
(368,399)(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)
(376,412)(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)
(384,416)(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)
(392,432)(393,425)(394,430)(395,426)(396,428)(433,496)(434,501)(435,503)
(436,499)(437,504)(438,497)(439,502)(440,498)(441,500)(442,487)(443,492)
(444,494)(445,490)(446,495)(447,488)(448,493)(449,489)(450,491)(451,478)
(452,483)(453,485)(454,481)(455,486)(456,479)(457,484)(458,480)(459,482)
(460,469)(461,474)(462,476)(463,472)(464,477)(465,470)(466,475)(467,471)
(468,473)(505,568)(506,573)(507,575)(508,571)(509,576)(510,569)(511,574)
(512,570)(513,572)(514,559)(515,564)(516,566)(517,562)(518,567)(519,560)
(520,565)(521,561)(522,563)(523,550)(524,555)(525,557)(526,553)(527,558)
(528,551)(529,556)(530,552)(531,554)(532,541)(533,546)(534,548)(535,544)
(536,549)(537,542)(538,547)(539,543)(540,545);
s2 := 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)( 37,190)( 38,192)( 39,191)
( 40,194)( 41,193)( 42,195)( 43,198)( 44,197)( 45,196)( 46,181)( 47,183)
( 48,182)( 49,185)( 50,184)( 51,186)( 52,189)( 53,188)( 54,187)( 55,208)
( 56,210)( 57,209)( 58,212)( 59,211)( 60,213)( 61,216)( 62,215)( 63,214)
( 64,199)( 65,201)( 66,200)( 67,203)( 68,202)( 69,204)( 70,207)( 71,206)
( 72,205)( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)
( 80,224)( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)
( 88,234)( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)
( 96,240)( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)
(104,247)(105,249)(106,252)(107,251)(108,250)(109,262)(110,264)(111,263)
(112,266)(113,265)(114,267)(115,270)(116,269)(117,268)(118,253)(119,255)
(120,254)(121,257)(122,256)(123,258)(124,261)(125,260)(126,259)(127,280)
(128,282)(129,281)(130,284)(131,283)(132,285)(133,288)(134,287)(135,286)
(136,271)(137,273)(138,272)(139,275)(140,274)(141,276)(142,279)(143,278)
(144,277)(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)(325,478)(326,480)(327,479)
(328,482)(329,481)(330,483)(331,486)(332,485)(333,484)(334,469)(335,471)
(336,470)(337,473)(338,472)(339,474)(340,477)(341,476)(342,475)(343,496)
(344,498)(345,497)(346,500)(347,499)(348,501)(349,504)(350,503)(351,502)
(352,487)(353,489)(354,488)(355,491)(356,490)(357,492)(358,495)(359,494)
(360,493)(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)
(368,512)(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)
(376,522)(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)
(384,528)(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)
(392,535)(393,537)(394,540)(395,539)(396,538)(397,550)(398,552)(399,551)
(400,554)(401,553)(402,555)(403,558)(404,557)(405,556)(406,541)(407,543)
(408,542)(409,545)(410,544)(411,546)(412,549)(413,548)(414,547)(415,568)
(416,570)(417,569)(418,572)(419,571)(420,573)(421,576)(422,575)(423,574)
(424,559)(425,561)(426,560)(427,563)(428,562)(429,564)(430,567)(431,566)
(432,565);
s3 := Sym(576)!( 1, 76)( 2, 78)( 3, 77)( 4, 73)( 5, 75)( 6, 74)( 7, 79)
( 8, 81)( 9, 80)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)
( 16, 88)( 17, 90)( 18, 89)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)
( 24, 92)( 25, 97)( 26, 99)( 27, 98)( 28,103)( 29,105)( 30,104)( 31,100)
( 32,102)( 33,101)( 34,106)( 35,108)( 36,107)( 37,112)( 38,114)( 39,113)
( 40,109)( 41,111)( 42,110)( 43,115)( 44,117)( 45,116)( 46,121)( 47,123)
( 48,122)( 49,118)( 50,120)( 51,119)( 52,124)( 53,126)( 54,125)( 55,130)
( 56,132)( 57,131)( 58,127)( 59,129)( 60,128)( 61,133)( 62,135)( 63,134)
( 64,139)( 65,141)( 66,140)( 67,136)( 68,138)( 69,137)( 70,142)( 71,144)
( 72,143)(145,220)(146,222)(147,221)(148,217)(149,219)(150,218)(151,223)
(152,225)(153,224)(154,229)(155,231)(156,230)(157,226)(158,228)(159,227)
(160,232)(161,234)(162,233)(163,238)(164,240)(165,239)(166,235)(167,237)
(168,236)(169,241)(170,243)(171,242)(172,247)(173,249)(174,248)(175,244)
(176,246)(177,245)(178,250)(179,252)(180,251)(181,256)(182,258)(183,257)
(184,253)(185,255)(186,254)(187,259)(188,261)(189,260)(190,265)(191,267)
(192,266)(193,262)(194,264)(195,263)(196,268)(197,270)(198,269)(199,274)
(200,276)(201,275)(202,271)(203,273)(204,272)(205,277)(206,279)(207,278)
(208,283)(209,285)(210,284)(211,280)(212,282)(213,281)(214,286)(215,288)
(216,287)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)
(296,369)(297,368)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)
(304,376)(305,378)(306,377)(307,382)(308,384)(309,383)(310,379)(311,381)
(312,380)(313,385)(314,387)(315,386)(316,391)(317,393)(318,392)(319,388)
(320,390)(321,389)(322,394)(323,396)(324,395)(325,400)(326,402)(327,401)
(328,397)(329,399)(330,398)(331,403)(332,405)(333,404)(334,409)(335,411)
(336,410)(337,406)(338,408)(339,407)(340,412)(341,414)(342,413)(343,418)
(344,420)(345,419)(346,415)(347,417)(348,416)(349,421)(350,423)(351,422)
(352,427)(353,429)(354,428)(355,424)(356,426)(357,425)(358,430)(359,432)
(360,431)(433,508)(434,510)(435,509)(436,505)(437,507)(438,506)(439,511)
(440,513)(441,512)(442,517)(443,519)(444,518)(445,514)(446,516)(447,515)
(448,520)(449,522)(450,521)(451,526)(452,528)(453,527)(454,523)(455,525)
(456,524)(457,529)(458,531)(459,530)(460,535)(461,537)(462,536)(463,532)
(464,534)(465,533)(466,538)(467,540)(468,539)(469,544)(470,546)(471,545)
(472,541)(473,543)(474,542)(475,547)(476,549)(477,548)(478,553)(479,555)
(480,554)(481,550)(482,552)(483,551)(484,556)(485,558)(486,557)(487,562)
(488,564)(489,563)(490,559)(491,561)(492,560)(493,565)(494,567)(495,566)
(496,571)(497,573)(498,572)(499,568)(500,570)(501,569)(502,574)(503,576)
(504,575);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope