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Polytope of Type {8,4,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,6,3}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98784)
Rank : 5
Schlafli Type : {8,4,6,3}
Number of vertices, edges, etc : 8, 16, 12, 9, 3
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 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 : {4,4,6,3}*576
   3-fold quotients : {8,4,2,3}*384b
   4-fold quotients : {4,2,6,3}*288, {2,4,6,3}*288
   6-fold quotients : {4,4,2,3}*192
   8-fold quotients : {2,2,6,3}*144
   12-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96
   24-fold quotients : {2,2,2,3}*48
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 := ( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)
( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)
( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)(114,123)
(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)(131,140)
(132,141)(133,142)(134,143)(135,144)(145,163)(146,164)(147,165)(148,166)
(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)(156,174)
(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,208)(182,209)
(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)(190,199)
(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)(198,207)
(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)(224,242)
(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)(232,250)
(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)(258,285)
(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)(266,275)
(267,276)(268,277)(269,278)(270,279)(289,325)(290,326)(291,327)(292,328)
(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)
(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)(308,344)
(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)(316,352)
(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)(324,360)
(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)(368,404)
(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)(376,412)
(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)(384,420)
(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)(392,428)
(393,429)(394,430)(395,431)(396,432)(433,496)(434,497)(435,498)(436,499)
(437,500)(438,501)(439,502)(440,503)(441,504)(442,487)(443,488)(444,489)
(445,490)(446,491)(447,492)(448,493)(449,494)(450,495)(451,478)(452,479)
(453,480)(454,481)(455,482)(456,483)(457,484)(458,485)(459,486)(460,469)
(461,470)(462,471)(463,472)(464,473)(465,474)(466,475)(467,476)(468,477)
(505,568)(506,569)(507,570)(508,571)(509,572)(510,573)(511,574)(512,575)
(513,576)(514,559)(515,560)(516,561)(517,562)(518,563)(519,564)(520,565)
(521,566)(522,567)(523,550)(524,551)(525,552)(526,553)(527,554)(528,555)
(529,556)(530,557)(531,558)(532,541)(533,542)(534,543)(535,544)(536,545)
(537,546)(538,547)(539,548)(540,549);;
s2 := (  1,145)(  2,150)(  3,152)(  4,148)(  5,153)(  6,146)(  7,151)(  8,147)
(  9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)
( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)
( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)
( 33,173)( 34,178)( 35,174)( 36,176)( 37,190)( 38,195)( 39,197)( 40,193)
( 41,198)( 42,191)( 43,196)( 44,192)( 45,194)( 46,181)( 47,186)( 48,188)
( 49,184)( 50,189)( 51,182)( 52,187)( 53,183)( 54,185)( 55,208)( 56,213)
( 57,215)( 58,211)( 59,216)( 60,209)( 61,214)( 62,210)( 63,212)( 64,199)
( 65,204)( 66,206)( 67,202)( 68,207)( 69,200)( 70,205)( 71,201)( 72,203)
( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)( 80,219)
( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)( 88,232)
( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)( 96,236)
( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)(104,252)
(105,245)(106,250)(107,246)(108,248)(109,262)(110,267)(111,269)(112,265)
(113,270)(114,263)(115,268)(116,264)(117,266)(118,253)(119,258)(120,260)
(121,256)(122,261)(123,254)(124,259)(125,255)(126,257)(127,280)(128,285)
(129,287)(130,283)(131,288)(132,281)(133,286)(134,282)(135,284)(136,271)
(137,276)(138,278)(139,274)(140,279)(141,272)(142,277)(143,273)(144,275)
(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)
(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)
(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)
(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)
(321,461)(322,466)(323,462)(324,464)(325,478)(326,483)(327,485)(328,481)
(329,486)(330,479)(331,484)(332,480)(333,482)(334,469)(335,474)(336,476)
(337,472)(338,477)(339,470)(340,475)(341,471)(342,473)(343,496)(344,501)
(345,503)(346,499)(347,504)(348,497)(349,502)(350,498)(351,500)(352,487)
(353,492)(354,494)(355,490)(356,495)(357,488)(358,493)(359,489)(360,491)
(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)(368,507)
(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)(376,520)
(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)(384,524)
(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)(392,540)
(393,533)(394,538)(395,534)(396,536)(397,550)(398,555)(399,557)(400,553)
(401,558)(402,551)(403,556)(404,552)(405,554)(406,541)(407,546)(408,548)
(409,544)(410,549)(411,542)(412,547)(413,543)(414,545)(415,568)(416,573)
(417,575)(418,571)(419,576)(420,569)(421,574)(422,570)(423,572)(424,559)
(425,564)(426,566)(427,562)(428,567)(429,560)(430,565)(431,561)(432,563);;
s3 := (  1, 74)(  2, 73)(  3, 75)(  4, 80)(  5, 79)(  6, 81)(  7, 77)(  8, 76)
(  9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)
( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)( 24, 99)
( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)( 32,106)
( 33,108)( 34,104)( 35,103)( 36,105)( 37,110)( 38,109)( 39,111)( 40,116)
( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)( 48,120)
( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)( 56,127)
( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)
( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141)
(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)(152,220)
(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)(160,230)
(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)(168,243)
(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)(176,250)
(177,252)(178,248)(179,247)(180,249)(181,254)(182,253)(183,255)(184,260)
(185,259)(186,261)(187,257)(188,256)(189,258)(190,263)(191,262)(192,264)
(193,269)(194,268)(195,270)(196,266)(197,265)(198,267)(199,272)(200,271)
(201,273)(202,278)(203,277)(204,279)(205,275)(206,274)(207,276)(208,281)
(209,280)(210,282)(211,287)(212,286)(213,288)(214,284)(215,283)(216,285)
(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)
(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)
(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)
(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)
(321,396)(322,392)(323,391)(324,393)(325,398)(326,397)(327,399)(328,404)
(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)(336,408)
(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)(344,415)
(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)(352,425)
(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)(360,429)
(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)(440,508)
(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)(448,518)
(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)(456,531)
(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)(464,538)
(465,540)(466,536)(467,535)(468,537)(469,542)(470,541)(471,543)(472,548)
(473,547)(474,549)(475,545)(476,544)(477,546)(478,551)(479,550)(480,552)
(481,557)(482,556)(483,558)(484,554)(485,553)(486,555)(487,560)(488,559)
(489,561)(490,566)(491,565)(492,567)(493,563)(494,562)(495,564)(496,569)
(497,568)(498,570)(499,575)(500,574)(501,576)(502,572)(503,571)(504,573);;
s4 := (  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)(  8, 78)
(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)( 16, 85)
( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)
( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)
( 33,107)( 34,103)( 35,105)( 36,104)( 37,109)( 38,111)( 39,110)( 40,115)
( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)( 48,119)
( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)( 56,129)
( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)( 64,136)
( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)( 72,140)
(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)(152,222)
(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)(160,229)
(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)(168,242)
(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)(176,252)
(177,251)(178,247)(179,249)(180,248)(181,253)(182,255)(183,254)(184,259)
(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)(192,263)
(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)(200,273)
(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)(208,280)
(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)(216,284)
(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)(296,366)
(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)(304,373)
(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)(312,386)
(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)(320,396)
(321,395)(322,391)(323,393)(324,392)(325,397)(326,399)(327,398)(328,403)
(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)(336,407)
(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)(344,417)
(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)(352,424)
(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)(360,428)
(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)(440,510)
(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)(448,517)
(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)(456,530)
(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)(464,540)
(465,539)(466,535)(467,537)(468,536)(469,541)(470,543)(471,542)(472,547)
(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)(480,551)
(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)(488,561)
(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)(496,568)
(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)(504,572);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s4*s2*s3*s2*s3*s4*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)!( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)
( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)
( 61, 70)( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)
(114,123)(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)
(131,140)(132,141)(133,142)(134,143)(135,144)(145,163)(146,164)(147,165)
(148,166)(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)
(156,174)(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,208)
(182,209)(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)
(190,199)(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)
(198,207)(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)
(224,242)(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)
(232,250)(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)
(258,285)(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)
(266,275)(267,276)(268,277)(269,278)(270,279)(289,325)(290,326)(291,327)
(292,328)(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)
(300,336)(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)
(308,344)(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)
(316,352)(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)
(324,360)(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)
(368,404)(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)
(376,412)(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)
(384,420)(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)
(392,428)(393,429)(394,430)(395,431)(396,432)(433,496)(434,497)(435,498)
(436,499)(437,500)(438,501)(439,502)(440,503)(441,504)(442,487)(443,488)
(444,489)(445,490)(446,491)(447,492)(448,493)(449,494)(450,495)(451,478)
(452,479)(453,480)(454,481)(455,482)(456,483)(457,484)(458,485)(459,486)
(460,469)(461,470)(462,471)(463,472)(464,473)(465,474)(466,475)(467,476)
(468,477)(505,568)(506,569)(507,570)(508,571)(509,572)(510,573)(511,574)
(512,575)(513,576)(514,559)(515,560)(516,561)(517,562)(518,563)(519,564)
(520,565)(521,566)(522,567)(523,550)(524,551)(525,552)(526,553)(527,554)
(528,555)(529,556)(530,557)(531,558)(532,541)(533,542)(534,543)(535,544)
(536,545)(537,546)(538,547)(539,548)(540,549);
s2 := Sym(576)!(  1,145)(  2,150)(  3,152)(  4,148)(  5,153)(  6,146)(  7,151)
(  8,147)(  9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)
( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)
( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)
( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,190)( 38,195)( 39,197)
( 40,193)( 41,198)( 42,191)( 43,196)( 44,192)( 45,194)( 46,181)( 47,186)
( 48,188)( 49,184)( 50,189)( 51,182)( 52,187)( 53,183)( 54,185)( 55,208)
( 56,213)( 57,215)( 58,211)( 59,216)( 60,209)( 61,214)( 62,210)( 63,212)
( 64,199)( 65,204)( 66,206)( 67,202)( 68,207)( 69,200)( 70,205)( 71,201)
( 72,203)( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)
( 80,219)( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)
( 88,232)( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)
( 96,236)( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)
(104,252)(105,245)(106,250)(107,246)(108,248)(109,262)(110,267)(111,269)
(112,265)(113,270)(114,263)(115,268)(116,264)(117,266)(118,253)(119,258)
(120,260)(121,256)(122,261)(123,254)(124,259)(125,255)(126,257)(127,280)
(128,285)(129,287)(130,283)(131,288)(132,281)(133,286)(134,282)(135,284)
(136,271)(137,276)(138,278)(139,274)(140,279)(141,272)(142,277)(143,273)
(144,275)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)
(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)
(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)
(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)
(320,468)(321,461)(322,466)(323,462)(324,464)(325,478)(326,483)(327,485)
(328,481)(329,486)(330,479)(331,484)(332,480)(333,482)(334,469)(335,474)
(336,476)(337,472)(338,477)(339,470)(340,475)(341,471)(342,473)(343,496)
(344,501)(345,503)(346,499)(347,504)(348,497)(349,502)(350,498)(351,500)
(352,487)(353,492)(354,494)(355,490)(356,495)(357,488)(358,493)(359,489)
(360,491)(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)
(368,507)(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)
(376,520)(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)
(384,524)(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)
(392,540)(393,533)(394,538)(395,534)(396,536)(397,550)(398,555)(399,557)
(400,553)(401,558)(402,551)(403,556)(404,552)(405,554)(406,541)(407,546)
(408,548)(409,544)(410,549)(411,542)(412,547)(413,543)(414,545)(415,568)
(416,573)(417,575)(418,571)(419,576)(420,569)(421,574)(422,570)(423,572)
(424,559)(425,564)(426,566)(427,562)(428,567)(429,560)(430,565)(431,561)
(432,563);
s3 := Sym(576)!(  1, 74)(  2, 73)(  3, 75)(  4, 80)(  5, 79)(  6, 81)(  7, 77)
(  8, 76)(  9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)
( 16, 86)( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)
( 24, 99)( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)
( 32,106)( 33,108)( 34,104)( 35,103)( 36,105)( 37,110)( 38,109)( 39,111)
( 40,116)( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)
( 48,120)( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)
( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)
( 64,137)( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)
( 72,141)(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)
(152,220)(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)
(160,230)(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)
(168,243)(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)
(176,250)(177,252)(178,248)(179,247)(180,249)(181,254)(182,253)(183,255)
(184,260)(185,259)(186,261)(187,257)(188,256)(189,258)(190,263)(191,262)
(192,264)(193,269)(194,268)(195,270)(196,266)(197,265)(198,267)(199,272)
(200,271)(201,273)(202,278)(203,277)(204,279)(205,275)(206,274)(207,276)
(208,281)(209,280)(210,282)(211,287)(212,286)(213,288)(214,284)(215,283)
(216,285)(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)
(296,364)(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)
(304,374)(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)
(312,387)(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)
(320,394)(321,396)(322,392)(323,391)(324,393)(325,398)(326,397)(327,399)
(328,404)(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)
(336,408)(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)
(344,415)(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)
(352,425)(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)
(360,429)(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)
(440,508)(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)
(448,518)(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)
(456,531)(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)
(464,538)(465,540)(466,536)(467,535)(468,537)(469,542)(470,541)(471,543)
(472,548)(473,547)(474,549)(475,545)(476,544)(477,546)(478,551)(479,550)
(480,552)(481,557)(482,556)(483,558)(484,554)(485,553)(486,555)(487,560)
(488,559)(489,561)(490,566)(491,565)(492,567)(493,563)(494,562)(495,564)
(496,569)(497,568)(498,570)(499,575)(500,574)(501,576)(502,572)(503,571)
(504,573);
s4 := Sym(576)!(  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)
(  8, 78)(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)
( 16, 85)( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)
( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)
( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,109)( 38,111)( 39,110)
( 40,115)( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)
( 48,119)( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)
( 56,129)( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)
( 64,136)( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)
( 72,140)(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)
(152,222)(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)
(160,229)(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)
(168,242)(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)
(176,252)(177,251)(178,247)(179,249)(180,248)(181,253)(182,255)(183,254)
(184,259)(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)
(192,263)(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)
(200,273)(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)
(208,280)(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)
(216,284)(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)
(296,366)(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)
(304,373)(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)
(312,386)(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)
(320,396)(321,395)(322,391)(323,393)(324,392)(325,397)(326,399)(327,398)
(328,403)(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)
(336,407)(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)
(344,417)(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)
(352,424)(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)
(360,428)(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)
(440,510)(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)
(448,517)(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)
(456,530)(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)
(464,540)(465,539)(466,535)(467,537)(468,536)(469,541)(470,543)(471,542)
(472,547)(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)
(480,551)(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)
(488,561)(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)
(496,568)(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)
(504,572);
poly := sub<Sym(576)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 >; 
 
References : None.
to this polytope