Polytope of Type {3,6,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,4,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97530)
Rank : 5
Schlafli Type : {3,6,4,8}
Number of vertices, edges, etc : 3, 9, 12, 16, 8
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 : {3,6,2,8}*576, {3,6,4,4}*576
3-fold quotients : {3,2,4,8}*384a
4-fold quotients : {3,6,2,4}*288, {3,6,4,2}*288
6-fold quotients : {3,2,4,4}*192, {3,2,2,8}*192
8-fold quotients : {3,6,2,2}*144
12-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
24-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 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);;
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)( 37,181)( 38,186)( 39,188)( 40,184)
( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)
( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)
( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)
( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)
( 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)(109,253)(110,258)(111,260)(112,256)
(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)
(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)
(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)
(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)
(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)(325,469)(326,474)(327,476)(328,472)
(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)
(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)
(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)
(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)
(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)(397,541)(398,546)(399,548)(400,544)
(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)
(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)
(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)
(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);;
s3 := ( 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)(433,487)(434,488)(435,489)(436,490)
(437,491)(438,492)(439,493)(440,494)(441,495)(442,496)(443,497)(444,498)
(445,499)(446,500)(447,501)(448,502)(449,503)(450,504)(451,469)(452,470)
(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)(460,478)
(461,479)(462,480)(463,481)(464,482)(465,483)(466,484)(467,485)(468,486)
(505,559)(506,560)(507,561)(508,562)(509,563)(510,564)(511,565)(512,566)
(513,567)(514,568)(515,569)(516,570)(517,571)(518,572)(519,573)(520,574)
(521,575)(522,576)(523,541)(524,542)(525,543)(526,544)(527,545)(528,546)
(529,547)(530,548)(531,549)(532,550)(533,551)(534,552)(535,553)(536,554)
(537,555)(538,556)(539,557)(540,558);;
s4 := ( 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)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 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)( 55,352)( 56,353)
( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)
( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)
( 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)( 91,379)( 92,380)( 93,381)( 94,382)( 95,383)( 96,384)
( 97,385)( 98,386)( 99,387)(100,388)(101,389)(102,390)(103,391)(104,392)
(105,393)(106,394)(107,395)(108,396)(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)(127,424)(128,425)
(129,426)(130,427)(131,428)(132,429)(133,430)(134,431)(135,432)(136,415)
(137,416)(138,417)(139,418)(140,419)(141,420)(142,421)(143,422)(144,423)
(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)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)
(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)
(177,465)(178,466)(179,467)(180,468)(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)(199,496)(200,497)
(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)
(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)
(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)(235,523)(236,524)(237,525)(238,526)(239,527)(240,528)
(241,529)(242,530)(243,531)(244,532)(245,533)(246,534)(247,535)(248,536)
(249,537)(250,538)(251,539)(252,540)(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)(271,568)(272,569)
(273,570)(274,571)(275,572)(276,573)(277,574)(278,575)(279,576)(280,559)
(281,560)(282,561)(283,562)(284,563)(285,564)(286,565)(287,566)(288,567);;
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, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := 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);
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)( 37,181)( 38,186)( 39,188)
( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)
( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)
( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)
( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)
( 72,212)( 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)(109,253)(110,258)(111,260)
(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)
(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)
(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)
(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)
(144,284)(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)(325,469)(326,474)(327,476)
(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)
(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)
(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)
(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)
(360,500)(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)(397,541)(398,546)(399,548)
(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)
(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)
(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)
(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)
(432,572);
s3 := 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)(433,487)(434,488)(435,489)
(436,490)(437,491)(438,492)(439,493)(440,494)(441,495)(442,496)(443,497)
(444,498)(445,499)(446,500)(447,501)(448,502)(449,503)(450,504)(451,469)
(452,470)(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)
(460,478)(461,479)(462,480)(463,481)(464,482)(465,483)(466,484)(467,485)
(468,486)(505,559)(506,560)(507,561)(508,562)(509,563)(510,564)(511,565)
(512,566)(513,567)(514,568)(515,569)(516,570)(517,571)(518,572)(519,573)
(520,574)(521,575)(522,576)(523,541)(524,542)(525,543)(526,544)(527,545)
(528,546)(529,547)(530,548)(531,549)(532,550)(533,551)(534,552)(535,553)
(536,554)(537,555)(538,556)(539,557)(540,558);
s4 := 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)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)
( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 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)( 55,352)
( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)
( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)
( 72,351)( 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)( 91,379)( 92,380)( 93,381)( 94,382)( 95,383)
( 96,384)( 97,385)( 98,386)( 99,387)(100,388)(101,389)(102,390)(103,391)
(104,392)(105,393)(106,394)(107,395)(108,396)(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)(127,424)
(128,425)(129,426)(130,427)(131,428)(132,429)(133,430)(134,431)(135,432)
(136,415)(137,416)(138,417)(139,418)(140,419)(141,420)(142,421)(143,422)
(144,423)(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)(163,451)(164,452)(165,453)(166,454)(167,455)
(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)
(176,464)(177,465)(178,466)(179,467)(180,468)(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)(199,496)
(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)
(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)
(216,495)(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)(235,523)(236,524)(237,525)(238,526)(239,527)
(240,528)(241,529)(242,530)(243,531)(244,532)(245,533)(246,534)(247,535)
(248,536)(249,537)(250,538)(251,539)(252,540)(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)(271,568)
(272,569)(273,570)(274,571)(275,572)(276,573)(277,574)(278,575)(279,576)
(280,559)(281,560)(282,561)(283,562)(284,563)(285,564)(286,565)(287,566)
(288,567);
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, s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope