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Polytope of Type {4,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97555)
Rank : 4
Schlafli Type : {4,8,6}
Number of vertices, edges, etc : 4, 48, 72, 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 : {2,8,6}*576, {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 : {4,8,2}*128a
   18-fold quotients : {4,4,2}*64, {2,8,2}*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 := (  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)(  8,152)
(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)
( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)(104,248)
(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)(112,256)
(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)
(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)
(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)
(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)
(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)
(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)
(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)
(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)
(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)(328,472)
(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)
(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)
(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)
(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)
(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)(368,512)
(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)(376,520)
(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)(384,528)
(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)(392,536)
(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)(400,544)
(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)
(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)
(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)
(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
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)(433,487)(434,492)(435,494)(436,490)
(437,495)(438,488)(439,493)(440,489)(441,491)(442,496)(443,501)(444,503)
(445,499)(446,504)(447,497)(448,502)(449,498)(450,500)(451,469)(452,474)
(453,476)(454,472)(455,477)(456,470)(457,475)(458,471)(459,473)(460,478)
(461,483)(462,485)(463,481)(464,486)(465,479)(466,484)(467,480)(468,482)
(505,559)(506,564)(507,566)(508,562)(509,567)(510,560)(511,565)(512,561)
(513,563)(514,568)(515,573)(516,575)(517,571)(518,576)(519,569)(520,574)
(521,570)(522,572)(523,541)(524,546)(525,548)(526,544)(527,549)(528,542)
(529,547)(530,543)(531,545)(532,550)(533,555)(534,557)(535,553)(536,558)
(537,551)(538,556)(539,552)(540,554);;
s2 := (  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)( 19,307)( 20,309)( 21,308)( 22,311)( 23,310)( 24,312)
( 25,315)( 26,314)( 27,313)( 28,316)( 29,318)( 30,317)( 31,320)( 32,319)
( 33,321)( 34,324)( 35,323)( 36,322)( 37,334)( 38,336)( 39,335)( 40,338)
( 41,337)( 42,339)( 43,342)( 44,341)( 45,340)( 46,325)( 47,327)( 48,326)
( 49,329)( 50,328)( 51,330)( 52,333)( 53,332)( 54,331)( 55,352)( 56,354)
( 57,353)( 58,356)( 59,355)( 60,357)( 61,360)( 62,359)( 63,358)( 64,343)
( 65,345)( 66,344)( 67,347)( 68,346)( 69,348)( 70,351)( 71,350)( 72,349)
( 73,361)( 74,363)( 75,362)( 76,365)( 77,364)( 78,366)( 79,369)( 80,368)
( 81,367)( 82,370)( 83,372)( 84,371)( 85,374)( 86,373)( 87,375)( 88,378)
( 89,377)( 90,376)( 91,379)( 92,381)( 93,380)( 94,383)( 95,382)( 96,384)
( 97,387)( 98,386)( 99,385)(100,388)(101,390)(102,389)(103,392)(104,391)
(105,393)(106,396)(107,395)(108,394)(109,406)(110,408)(111,407)(112,410)
(113,409)(114,411)(115,414)(116,413)(117,412)(118,397)(119,399)(120,398)
(121,401)(122,400)(123,402)(124,405)(125,404)(126,403)(127,424)(128,426)
(129,425)(130,428)(131,427)(132,429)(133,432)(134,431)(135,430)(136,415)
(137,417)(138,416)(139,419)(140,418)(141,420)(142,423)(143,422)(144,421)
(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)(163,451)(164,453)(165,452)(166,455)(167,454)(168,456)
(169,459)(170,458)(171,457)(172,460)(173,462)(174,461)(175,464)(176,463)
(177,465)(178,468)(179,467)(180,466)(181,478)(182,480)(183,479)(184,482)
(185,481)(186,483)(187,486)(188,485)(189,484)(190,469)(191,471)(192,470)
(193,473)(194,472)(195,474)(196,477)(197,476)(198,475)(199,496)(200,498)
(201,497)(202,500)(203,499)(204,501)(205,504)(206,503)(207,502)(208,487)
(209,489)(210,488)(211,491)(212,490)(213,492)(214,495)(215,494)(216,493)
(217,505)(218,507)(219,506)(220,509)(221,508)(222,510)(223,513)(224,512)
(225,511)(226,514)(227,516)(228,515)(229,518)(230,517)(231,519)(232,522)
(233,521)(234,520)(235,523)(236,525)(237,524)(238,527)(239,526)(240,528)
(241,531)(242,530)(243,529)(244,532)(245,534)(246,533)(247,536)(248,535)
(249,537)(250,540)(251,539)(252,538)(253,550)(254,552)(255,551)(256,554)
(257,553)(258,555)(259,558)(260,557)(261,556)(262,541)(263,543)(264,542)
(265,545)(266,544)(267,546)(268,549)(269,548)(270,547)(271,568)(272,570)
(273,569)(274,572)(275,571)(276,573)(277,576)(278,575)(279,574)(280,559)
(281,561)(282,560)(283,563)(284,562)(285,564)(286,567)(287,566)(288,565);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*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)!(  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)
(  8,152)(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)
( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)
( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)
( 96,240)( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)
(104,248)(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)
(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)
(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)
(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)
(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)
(144,288)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)
(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)
(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)
(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)
(320,464)(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)
(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)
(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)
(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)
(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)
(360,504)(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)
(368,512)(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)
(376,520)(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)
(384,528)(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)
(392,536)(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)
(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)
(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)
(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)
(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)
(432,576);
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)(433,487)(434,492)(435,494)
(436,490)(437,495)(438,488)(439,493)(440,489)(441,491)(442,496)(443,501)
(444,503)(445,499)(446,504)(447,497)(448,502)(449,498)(450,500)(451,469)
(452,474)(453,476)(454,472)(455,477)(456,470)(457,475)(458,471)(459,473)
(460,478)(461,483)(462,485)(463,481)(464,486)(465,479)(466,484)(467,480)
(468,482)(505,559)(506,564)(507,566)(508,562)(509,567)(510,560)(511,565)
(512,561)(513,563)(514,568)(515,573)(516,575)(517,571)(518,576)(519,569)
(520,574)(521,570)(522,572)(523,541)(524,546)(525,548)(526,544)(527,549)
(528,542)(529,547)(530,543)(531,545)(532,550)(533,555)(534,557)(535,553)
(536,558)(537,551)(538,556)(539,552)(540,554);
s2 := 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)( 19,307)( 20,309)( 21,308)( 22,311)( 23,310)
( 24,312)( 25,315)( 26,314)( 27,313)( 28,316)( 29,318)( 30,317)( 31,320)
( 32,319)( 33,321)( 34,324)( 35,323)( 36,322)( 37,334)( 38,336)( 39,335)
( 40,338)( 41,337)( 42,339)( 43,342)( 44,341)( 45,340)( 46,325)( 47,327)
( 48,326)( 49,329)( 50,328)( 51,330)( 52,333)( 53,332)( 54,331)( 55,352)
( 56,354)( 57,353)( 58,356)( 59,355)( 60,357)( 61,360)( 62,359)( 63,358)
( 64,343)( 65,345)( 66,344)( 67,347)( 68,346)( 69,348)( 70,351)( 71,350)
( 72,349)( 73,361)( 74,363)( 75,362)( 76,365)( 77,364)( 78,366)( 79,369)
( 80,368)( 81,367)( 82,370)( 83,372)( 84,371)( 85,374)( 86,373)( 87,375)
( 88,378)( 89,377)( 90,376)( 91,379)( 92,381)( 93,380)( 94,383)( 95,382)
( 96,384)( 97,387)( 98,386)( 99,385)(100,388)(101,390)(102,389)(103,392)
(104,391)(105,393)(106,396)(107,395)(108,394)(109,406)(110,408)(111,407)
(112,410)(113,409)(114,411)(115,414)(116,413)(117,412)(118,397)(119,399)
(120,398)(121,401)(122,400)(123,402)(124,405)(125,404)(126,403)(127,424)
(128,426)(129,425)(130,428)(131,427)(132,429)(133,432)(134,431)(135,430)
(136,415)(137,417)(138,416)(139,419)(140,418)(141,420)(142,423)(143,422)
(144,421)(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)(163,451)(164,453)(165,452)(166,455)(167,454)
(168,456)(169,459)(170,458)(171,457)(172,460)(173,462)(174,461)(175,464)
(176,463)(177,465)(178,468)(179,467)(180,466)(181,478)(182,480)(183,479)
(184,482)(185,481)(186,483)(187,486)(188,485)(189,484)(190,469)(191,471)
(192,470)(193,473)(194,472)(195,474)(196,477)(197,476)(198,475)(199,496)
(200,498)(201,497)(202,500)(203,499)(204,501)(205,504)(206,503)(207,502)
(208,487)(209,489)(210,488)(211,491)(212,490)(213,492)(214,495)(215,494)
(216,493)(217,505)(218,507)(219,506)(220,509)(221,508)(222,510)(223,513)
(224,512)(225,511)(226,514)(227,516)(228,515)(229,518)(230,517)(231,519)
(232,522)(233,521)(234,520)(235,523)(236,525)(237,524)(238,527)(239,526)
(240,528)(241,531)(242,530)(243,529)(244,532)(245,534)(246,533)(247,536)
(248,535)(249,537)(250,540)(251,539)(252,538)(253,550)(254,552)(255,551)
(256,554)(257,553)(258,555)(259,558)(260,557)(261,556)(262,541)(263,543)
(264,542)(265,545)(266,544)(267,546)(268,549)(269,548)(270,547)(271,568)
(272,570)(273,569)(274,572)(275,571)(276,573)(277,576)(278,575)(279,574)
(280,559)(281,561)(282,560)(283,563)(284,562)(285,564)(286,567)(287,566)
(288,565);
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope