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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}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98810)
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 :
   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 : {4,8,2}*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 := (  1,145)(  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)( 37,190)( 38,191)( 39,192)( 40,193)
( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)( 48,183)
( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)( 56,209)
( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)( 64,199)
( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)
( 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)(109,262)(110,263)(111,264)(112,265)
(113,266)(114,267)(115,268)(116,269)(117,270)(118,253)(119,254)(120,255)
(121,256)(122,257)(123,258)(124,259)(125,260)(126,261)(127,280)(128,281)
(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)(136,271)
(137,272)(138,273)(139,274)(140,275)(141,276)(142,277)(143,278)(144,279)
(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)(325,478)(326,479)(327,480)(328,481)
(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)(336,471)
(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)(344,497)
(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)(352,487)
(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)(360,495)
(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)(397,550)(398,551)(399,552)(400,553)
(401,554)(402,555)(403,556)(404,557)(405,558)(406,541)(407,542)(408,543)
(409,544)(410,545)(411,546)(412,547)(413,548)(414,549)(415,568)(416,569)
(417,570)(418,571)(419,572)(420,573)(421,574)(422,575)(423,576)(424,559)
(425,560)(426,561)(427,562)(428,563)(429,564)(430,565)(431,566)(432,567);;
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 := (  1,289)(  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)( 37,334)( 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)( 55,343)( 56,345)
( 57,344)( 58,347)( 59,346)( 60,348)( 61,351)( 62,350)( 63,349)( 64,352)
( 65,354)( 66,353)( 67,356)( 68,355)( 69,357)( 70,360)( 71,359)( 72,358)
( 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)( 91,388)( 92,390)( 93,389)( 94,392)( 95,391)( 96,393)
( 97,396)( 98,395)( 99,394)(100,379)(101,381)(102,380)(103,383)(104,382)
(105,384)(106,387)(107,386)(108,385)(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)(127,415)(128,417)
(129,416)(130,419)(131,418)(132,420)(133,423)(134,422)(135,421)(136,424)
(137,426)(138,425)(139,428)(140,427)(141,429)(142,432)(143,431)(144,430)
(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)(181,478)(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)(199,487)(200,489)
(201,488)(202,491)(203,490)(204,492)(205,495)(206,494)(207,493)(208,496)
(209,498)(210,497)(211,500)(212,499)(213,501)(214,504)(215,503)(216,502)
(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)(235,532)(236,534)(237,533)(238,536)(239,535)(240,537)
(241,540)(242,539)(243,538)(244,523)(245,525)(246,524)(247,527)(248,526)
(249,528)(250,531)(251,530)(252,529)(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)(271,559)(272,561)
(273,560)(274,563)(275,562)(276,564)(277,567)(278,566)(279,565)(280,568)
(281,570)(282,569)(283,572)(284,571)(285,573)(286,576)(287,575)(288,574);;
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s0*s2*s1*s3*s2*s3*s1*s2*s3*s0*s1*s2*s1 ];;
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)( 37,190)( 38,191)( 39,192)
( 40,193)( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)
( 48,183)( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)
( 56,209)( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)
( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)
( 72,207)( 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)(109,262)(110,263)(111,264)
(112,265)(113,266)(114,267)(115,268)(116,269)(117,270)(118,253)(119,254)
(120,255)(121,256)(122,257)(123,258)(124,259)(125,260)(126,261)(127,280)
(128,281)(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)
(136,271)(137,272)(138,273)(139,274)(140,275)(141,276)(142,277)(143,278)
(144,279)(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)(325,478)(326,479)(327,480)
(328,481)(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)
(336,471)(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)
(344,497)(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)
(352,487)(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)
(360,495)(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)(397,550)(398,551)(399,552)
(400,553)(401,554)(402,555)(403,556)(404,557)(405,558)(406,541)(407,542)
(408,543)(409,544)(410,545)(411,546)(412,547)(413,548)(414,549)(415,568)
(416,569)(417,570)(418,571)(419,572)(420,573)(421,574)(422,575)(423,576)
(424,559)(425,560)(426,561)(427,562)(428,563)(429,564)(430,565)(431,566)
(432,567);
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)!(  1,289)(  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)( 37,334)( 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)( 55,343)
( 56,345)( 57,344)( 58,347)( 59,346)( 60,348)( 61,351)( 62,350)( 63,349)
( 64,352)( 65,354)( 66,353)( 67,356)( 68,355)( 69,357)( 70,360)( 71,359)
( 72,358)( 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)( 91,388)( 92,390)( 93,389)( 94,392)( 95,391)
( 96,393)( 97,396)( 98,395)( 99,394)(100,379)(101,381)(102,380)(103,383)
(104,382)(105,384)(106,387)(107,386)(108,385)(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)(127,415)
(128,417)(129,416)(130,419)(131,418)(132,420)(133,423)(134,422)(135,421)
(136,424)(137,426)(138,425)(139,428)(140,427)(141,429)(142,432)(143,431)
(144,430)(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)(181,478)(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)(199,487)
(200,489)(201,488)(202,491)(203,490)(204,492)(205,495)(206,494)(207,493)
(208,496)(209,498)(210,497)(211,500)(212,499)(213,501)(214,504)(215,503)
(216,502)(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)(235,532)(236,534)(237,533)(238,536)(239,535)
(240,537)(241,540)(242,539)(243,538)(244,523)(245,525)(246,524)(247,527)
(248,526)(249,528)(250,531)(251,530)(252,529)(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)(271,559)
(272,561)(273,560)(274,563)(275,562)(276,564)(277,567)(278,566)(279,565)
(280,568)(281,570)(282,569)(283,572)(284,571)(285,573)(286,576)(287,575)
(288,574);
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s0*s2*s1*s3*s2*s3*s1*s2*s3*s0*s1*s2*s1 >; 
 
References : None.
to this polytope