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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,6,4}*1152a
Also Known As : {{6,4|2},{4,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,136336)
Rank : 5
Schlafli Type : {6,4,6,4}
Number of vertices, edges, etc : 6, 12, 12, 12, 4
Order of s0s1s2s3s4 : 12
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 : {6,2,6,4}*576a, {6,4,6,2}*576
   3-fold quotients : {2,4,6,4}*384a, {6,4,2,4}*384a
   4-fold quotients : {3,2,6,4}*288a, {6,2,6,2}*288
   6-fold quotients : {2,2,6,4}*192a, {2,4,6,2}*192a, {6,2,2,4}*192, {6,4,2,2}*192a
   8-fold quotients : {3,2,6,2}*144, {6,2,3,2}*144
   9-fold quotients : {2,4,2,4}*128
   12-fold quotients : {3,2,2,4}*96, {2,2,6,2}*96, {6,2,2,2}*96
   16-fold quotients : {3,2,3,2}*72
   18-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
   24-fold quotients : {2,2,3,2}*48, {3,2,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 37)(  2, 42)(  3, 44)(  4, 40)(  5, 45)(  6, 38)(  7, 43)(  8, 39)
(  9, 41)( 10, 46)( 11, 51)( 12, 53)( 13, 49)( 14, 54)( 15, 47)( 16, 52)
( 17, 48)( 18, 50)( 19, 55)( 20, 60)( 21, 62)( 22, 58)( 23, 63)( 24, 56)
( 25, 61)( 26, 57)( 27, 59)( 28, 64)( 29, 69)( 30, 71)( 31, 67)( 32, 72)
( 33, 65)( 34, 70)( 35, 66)( 36, 68)( 73,109)( 74,114)( 75,116)( 76,112)
( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)
( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,127)( 92,132)
( 93,134)( 94,130)( 95,135)( 96,128)( 97,133)( 98,129)( 99,131)(100,136)
(101,141)(102,143)(103,139)(104,144)(105,137)(106,142)(107,138)(108,140)
(145,181)(146,186)(147,188)(148,184)(149,189)(150,182)(151,187)(152,183)
(153,185)(154,190)(155,195)(156,197)(157,193)(158,198)(159,191)(160,196)
(161,192)(162,194)(163,199)(164,204)(165,206)(166,202)(167,207)(168,200)
(169,205)(170,201)(171,203)(172,208)(173,213)(174,215)(175,211)(176,216)
(177,209)(178,214)(179,210)(180,212)(217,253)(218,258)(219,260)(220,256)
(221,261)(222,254)(223,259)(224,255)(225,257)(226,262)(227,267)(228,269)
(229,265)(230,270)(231,263)(232,268)(233,264)(234,266)(235,271)(236,276)
(237,278)(238,274)(239,279)(240,272)(241,277)(242,273)(243,275)(244,280)
(245,285)(246,287)(247,283)(248,288)(249,281)(250,286)(251,282)(252,284)
(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)
(433,469)(434,474)(435,476)(436,472)(437,477)(438,470)(439,475)(440,471)
(441,473)(442,478)(443,483)(444,485)(445,481)(446,486)(447,479)(448,484)
(449,480)(450,482)(451,487)(452,492)(453,494)(454,490)(455,495)(456,488)
(457,493)(458,489)(459,491)(460,496)(461,501)(462,503)(463,499)(464,504)
(465,497)(466,502)(467,498)(468,500)(505,541)(506,546)(507,548)(508,544)
(509,549)(510,542)(511,547)(512,543)(513,545)(514,550)(515,555)(516,557)
(517,553)(518,558)(519,551)(520,556)(521,552)(522,554)(523,559)(524,564)
(525,566)(526,562)(527,567)(528,560)(529,565)(530,561)(531,563)(532,568)
(533,573)(534,575)(535,571)(536,576)(537,569)(538,574)(539,570)(540,572);;
s1 := (  1,329)(  2,331)(  3,327)(  4,332)(  5,325)(  6,330)(  7,326)(  8,328)
(  9,333)( 10,338)( 11,340)( 12,336)( 13,341)( 14,334)( 15,339)( 16,335)
( 17,337)( 18,342)( 19,347)( 20,349)( 21,345)( 22,350)( 23,343)( 24,348)
( 25,344)( 26,346)( 27,351)( 28,356)( 29,358)( 30,354)( 31,359)( 32,352)
( 33,357)( 34,353)( 35,355)( 36,360)( 37,293)( 38,295)( 39,291)( 40,296)
( 41,289)( 42,294)( 43,290)( 44,292)( 45,297)( 46,302)( 47,304)( 48,300)
( 49,305)( 50,298)( 51,303)( 52,299)( 53,301)( 54,306)( 55,311)( 56,313)
( 57,309)( 58,314)( 59,307)( 60,312)( 61,308)( 62,310)( 63,315)( 64,320)
( 65,322)( 66,318)( 67,323)( 68,316)( 69,321)( 70,317)( 71,319)( 72,324)
( 73,419)( 74,421)( 75,417)( 76,422)( 77,415)( 78,420)( 79,416)( 80,418)
( 81,423)( 82,428)( 83,430)( 84,426)( 85,431)( 86,424)( 87,429)( 88,425)
( 89,427)( 90,432)( 91,401)( 92,403)( 93,399)( 94,404)( 95,397)( 96,402)
( 97,398)( 98,400)( 99,405)(100,410)(101,412)(102,408)(103,413)(104,406)
(105,411)(106,407)(107,409)(108,414)(109,383)(110,385)(111,381)(112,386)
(113,379)(114,384)(115,380)(116,382)(117,387)(118,392)(119,394)(120,390)
(121,395)(122,388)(123,393)(124,389)(125,391)(126,396)(127,365)(128,367)
(129,363)(130,368)(131,361)(132,366)(133,362)(134,364)(135,369)(136,374)
(137,376)(138,372)(139,377)(140,370)(141,375)(142,371)(143,373)(144,378)
(145,473)(146,475)(147,471)(148,476)(149,469)(150,474)(151,470)(152,472)
(153,477)(154,482)(155,484)(156,480)(157,485)(158,478)(159,483)(160,479)
(161,481)(162,486)(163,491)(164,493)(165,489)(166,494)(167,487)(168,492)
(169,488)(170,490)(171,495)(172,500)(173,502)(174,498)(175,503)(176,496)
(177,501)(178,497)(179,499)(180,504)(181,437)(182,439)(183,435)(184,440)
(185,433)(186,438)(187,434)(188,436)(189,441)(190,446)(191,448)(192,444)
(193,449)(194,442)(195,447)(196,443)(197,445)(198,450)(199,455)(200,457)
(201,453)(202,458)(203,451)(204,456)(205,452)(206,454)(207,459)(208,464)
(209,466)(210,462)(211,467)(212,460)(213,465)(214,461)(215,463)(216,468)
(217,563)(218,565)(219,561)(220,566)(221,559)(222,564)(223,560)(224,562)
(225,567)(226,572)(227,574)(228,570)(229,575)(230,568)(231,573)(232,569)
(233,571)(234,576)(235,545)(236,547)(237,543)(238,548)(239,541)(240,546)
(241,542)(242,544)(243,549)(244,554)(245,556)(246,552)(247,557)(248,550)
(249,555)(250,551)(251,553)(252,558)(253,527)(254,529)(255,525)(256,530)
(257,523)(258,528)(259,524)(260,526)(261,531)(262,536)(263,538)(264,534)
(265,539)(266,532)(267,537)(268,533)(269,535)(270,540)(271,509)(272,511)
(273,507)(274,512)(275,505)(276,510)(277,506)(278,508)(279,513)(280,518)
(281,520)(282,516)(283,521)(284,514)(285,519)(286,515)(287,517)(288,522);;
s2 := (  1,109)(  2,116)(  3,114)(  4,115)(  5,113)(  6,111)(  7,112)(  8,110)
(  9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)( 16,121)
( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)( 24,129)
( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)( 32,140)
( 33,138)( 34,139)( 35,137)( 36,144)( 37, 73)( 38, 80)( 39, 78)( 40, 79)
( 41, 77)( 42, 75)( 43, 76)( 44, 74)( 45, 81)( 46, 82)( 47, 89)( 48, 87)
( 49, 88)( 50, 86)( 51, 84)( 52, 85)( 53, 83)( 54, 90)( 55, 91)( 56, 98)
( 57, 96)( 58, 97)( 59, 95)( 60, 93)( 61, 94)( 62, 92)( 63, 99)( 64,100)
( 65,107)( 66,105)( 67,106)( 68,104)( 69,102)( 70,103)( 71,101)( 72,108)
(145,253)(146,260)(147,258)(148,259)(149,257)(150,255)(151,256)(152,254)
(153,261)(154,262)(155,269)(156,267)(157,268)(158,266)(159,264)(160,265)
(161,263)(162,270)(163,271)(164,278)(165,276)(166,277)(167,275)(168,273)
(169,274)(170,272)(171,279)(172,280)(173,287)(174,285)(175,286)(176,284)
(177,282)(178,283)(179,281)(180,288)(181,217)(182,224)(183,222)(184,223)
(185,221)(186,219)(187,220)(188,218)(189,225)(190,226)(191,233)(192,231)
(193,232)(194,230)(195,228)(196,229)(197,227)(198,234)(199,235)(200,242)
(201,240)(202,241)(203,239)(204,237)(205,238)(206,236)(207,243)(208,244)
(209,251)(210,249)(211,250)(212,248)(213,246)(214,247)(215,245)(216,252)
(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)
(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)
(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)
(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)
(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)
(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)
(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)
(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)
(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)
(433,541)(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)(440,542)
(441,549)(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)(448,553)
(449,551)(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)(456,561)
(457,562)(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)(464,572)
(465,570)(466,571)(467,569)(468,576)(469,505)(470,512)(471,510)(472,511)
(473,509)(474,507)(475,508)(476,506)(477,513)(478,514)(479,521)(480,519)
(481,520)(482,518)(483,516)(484,517)(485,515)(486,522)(487,523)(488,530)
(489,528)(490,529)(491,527)(492,525)(493,526)(494,524)(495,531)(496,532)
(497,539)(498,537)(499,538)(500,536)(501,534)(502,535)(503,533)(504,540);;
s3 := (  1,112)(  2,110)(  3,117)(  4,109)(  5,116)(  6,114)(  7,115)(  8,113)
(  9,111)( 10,121)( 11,119)( 12,126)( 13,118)( 14,125)( 15,123)( 16,124)
( 17,122)( 18,120)( 19,130)( 20,128)( 21,135)( 22,127)( 23,134)( 24,132)
( 25,133)( 26,131)( 27,129)( 28,139)( 29,137)( 30,144)( 31,136)( 32,143)
( 33,141)( 34,142)( 35,140)( 36,138)( 37, 76)( 38, 74)( 39, 81)( 40, 73)
( 41, 80)( 42, 78)( 43, 79)( 44, 77)( 45, 75)( 46, 85)( 47, 83)( 48, 90)
( 49, 82)( 50, 89)( 51, 87)( 52, 88)( 53, 86)( 54, 84)( 55, 94)( 56, 92)
( 57, 99)( 58, 91)( 59, 98)( 60, 96)( 61, 97)( 62, 95)( 63, 93)( 64,103)
( 65,101)( 66,108)( 67,100)( 68,107)( 69,105)( 70,106)( 71,104)( 72,102)
(145,265)(146,263)(147,270)(148,262)(149,269)(150,267)(151,268)(152,266)
(153,264)(154,256)(155,254)(156,261)(157,253)(158,260)(159,258)(160,259)
(161,257)(162,255)(163,283)(164,281)(165,288)(166,280)(167,287)(168,285)
(169,286)(170,284)(171,282)(172,274)(173,272)(174,279)(175,271)(176,278)
(177,276)(178,277)(179,275)(180,273)(181,229)(182,227)(183,234)(184,226)
(185,233)(186,231)(187,232)(188,230)(189,228)(190,220)(191,218)(192,225)
(193,217)(194,224)(195,222)(196,223)(197,221)(198,219)(199,247)(200,245)
(201,252)(202,244)(203,251)(204,249)(205,250)(206,248)(207,246)(208,238)
(209,236)(210,243)(211,235)(212,242)(213,240)(214,241)(215,239)(216,237)
(289,418)(290,416)(291,423)(292,415)(293,422)(294,420)(295,421)(296,419)
(297,417)(298,427)(299,425)(300,432)(301,424)(302,431)(303,429)(304,430)
(305,428)(306,426)(307,400)(308,398)(309,405)(310,397)(311,404)(312,402)
(313,403)(314,401)(315,399)(316,409)(317,407)(318,414)(319,406)(320,413)
(321,411)(322,412)(323,410)(324,408)(325,382)(326,380)(327,387)(328,379)
(329,386)(330,384)(331,385)(332,383)(333,381)(334,391)(335,389)(336,396)
(337,388)(338,395)(339,393)(340,394)(341,392)(342,390)(343,364)(344,362)
(345,369)(346,361)(347,368)(348,366)(349,367)(350,365)(351,363)(352,373)
(353,371)(354,378)(355,370)(356,377)(357,375)(358,376)(359,374)(360,372)
(433,571)(434,569)(435,576)(436,568)(437,575)(438,573)(439,574)(440,572)
(441,570)(442,562)(443,560)(444,567)(445,559)(446,566)(447,564)(448,565)
(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)(455,557)(456,555)
(457,556)(458,554)(459,552)(460,544)(461,542)(462,549)(463,541)(464,548)
(465,546)(466,547)(467,545)(468,543)(469,535)(470,533)(471,540)(472,532)
(473,539)(474,537)(475,538)(476,536)(477,534)(478,526)(479,524)(480,531)
(481,523)(482,530)(483,528)(484,529)(485,527)(486,525)(487,517)(488,515)
(489,522)(490,514)(491,521)(492,519)(493,520)(494,518)(495,516)(496,508)
(497,506)(498,513)(499,505)(500,512)(501,510)(502,511)(503,509)(504,507);;
s4 := (  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);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1, 37)(  2, 42)(  3, 44)(  4, 40)(  5, 45)(  6, 38)(  7, 43)
(  8, 39)(  9, 41)( 10, 46)( 11, 51)( 12, 53)( 13, 49)( 14, 54)( 15, 47)
( 16, 52)( 17, 48)( 18, 50)( 19, 55)( 20, 60)( 21, 62)( 22, 58)( 23, 63)
( 24, 56)( 25, 61)( 26, 57)( 27, 59)( 28, 64)( 29, 69)( 30, 71)( 31, 67)
( 32, 72)( 33, 65)( 34, 70)( 35, 66)( 36, 68)( 73,109)( 74,114)( 75,116)
( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)
( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,127)
( 92,132)( 93,134)( 94,130)( 95,135)( 96,128)( 97,133)( 98,129)( 99,131)
(100,136)(101,141)(102,143)(103,139)(104,144)(105,137)(106,142)(107,138)
(108,140)(145,181)(146,186)(147,188)(148,184)(149,189)(150,182)(151,187)
(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)(158,198)(159,191)
(160,196)(161,192)(162,194)(163,199)(164,204)(165,206)(166,202)(167,207)
(168,200)(169,205)(170,201)(171,203)(172,208)(173,213)(174,215)(175,211)
(176,216)(177,209)(178,214)(179,210)(180,212)(217,253)(218,258)(219,260)
(220,256)(221,261)(222,254)(223,259)(224,255)(225,257)(226,262)(227,267)
(228,269)(229,265)(230,270)(231,263)(232,268)(233,264)(234,266)(235,271)
(236,276)(237,278)(238,274)(239,279)(240,272)(241,277)(242,273)(243,275)
(244,280)(245,285)(246,287)(247,283)(248,288)(249,281)(250,286)(251,282)
(252,284)(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)(433,469)(434,474)(435,476)(436,472)(437,477)(438,470)(439,475)
(440,471)(441,473)(442,478)(443,483)(444,485)(445,481)(446,486)(447,479)
(448,484)(449,480)(450,482)(451,487)(452,492)(453,494)(454,490)(455,495)
(456,488)(457,493)(458,489)(459,491)(460,496)(461,501)(462,503)(463,499)
(464,504)(465,497)(466,502)(467,498)(468,500)(505,541)(506,546)(507,548)
(508,544)(509,549)(510,542)(511,547)(512,543)(513,545)(514,550)(515,555)
(516,557)(517,553)(518,558)(519,551)(520,556)(521,552)(522,554)(523,559)
(524,564)(525,566)(526,562)(527,567)(528,560)(529,565)(530,561)(531,563)
(532,568)(533,573)(534,575)(535,571)(536,576)(537,569)(538,574)(539,570)
(540,572);
s1 := Sym(576)!(  1,329)(  2,331)(  3,327)(  4,332)(  5,325)(  6,330)(  7,326)
(  8,328)(  9,333)( 10,338)( 11,340)( 12,336)( 13,341)( 14,334)( 15,339)
( 16,335)( 17,337)( 18,342)( 19,347)( 20,349)( 21,345)( 22,350)( 23,343)
( 24,348)( 25,344)( 26,346)( 27,351)( 28,356)( 29,358)( 30,354)( 31,359)
( 32,352)( 33,357)( 34,353)( 35,355)( 36,360)( 37,293)( 38,295)( 39,291)
( 40,296)( 41,289)( 42,294)( 43,290)( 44,292)( 45,297)( 46,302)( 47,304)
( 48,300)( 49,305)( 50,298)( 51,303)( 52,299)( 53,301)( 54,306)( 55,311)
( 56,313)( 57,309)( 58,314)( 59,307)( 60,312)( 61,308)( 62,310)( 63,315)
( 64,320)( 65,322)( 66,318)( 67,323)( 68,316)( 69,321)( 70,317)( 71,319)
( 72,324)( 73,419)( 74,421)( 75,417)( 76,422)( 77,415)( 78,420)( 79,416)
( 80,418)( 81,423)( 82,428)( 83,430)( 84,426)( 85,431)( 86,424)( 87,429)
( 88,425)( 89,427)( 90,432)( 91,401)( 92,403)( 93,399)( 94,404)( 95,397)
( 96,402)( 97,398)( 98,400)( 99,405)(100,410)(101,412)(102,408)(103,413)
(104,406)(105,411)(106,407)(107,409)(108,414)(109,383)(110,385)(111,381)
(112,386)(113,379)(114,384)(115,380)(116,382)(117,387)(118,392)(119,394)
(120,390)(121,395)(122,388)(123,393)(124,389)(125,391)(126,396)(127,365)
(128,367)(129,363)(130,368)(131,361)(132,366)(133,362)(134,364)(135,369)
(136,374)(137,376)(138,372)(139,377)(140,370)(141,375)(142,371)(143,373)
(144,378)(145,473)(146,475)(147,471)(148,476)(149,469)(150,474)(151,470)
(152,472)(153,477)(154,482)(155,484)(156,480)(157,485)(158,478)(159,483)
(160,479)(161,481)(162,486)(163,491)(164,493)(165,489)(166,494)(167,487)
(168,492)(169,488)(170,490)(171,495)(172,500)(173,502)(174,498)(175,503)
(176,496)(177,501)(178,497)(179,499)(180,504)(181,437)(182,439)(183,435)
(184,440)(185,433)(186,438)(187,434)(188,436)(189,441)(190,446)(191,448)
(192,444)(193,449)(194,442)(195,447)(196,443)(197,445)(198,450)(199,455)
(200,457)(201,453)(202,458)(203,451)(204,456)(205,452)(206,454)(207,459)
(208,464)(209,466)(210,462)(211,467)(212,460)(213,465)(214,461)(215,463)
(216,468)(217,563)(218,565)(219,561)(220,566)(221,559)(222,564)(223,560)
(224,562)(225,567)(226,572)(227,574)(228,570)(229,575)(230,568)(231,573)
(232,569)(233,571)(234,576)(235,545)(236,547)(237,543)(238,548)(239,541)
(240,546)(241,542)(242,544)(243,549)(244,554)(245,556)(246,552)(247,557)
(248,550)(249,555)(250,551)(251,553)(252,558)(253,527)(254,529)(255,525)
(256,530)(257,523)(258,528)(259,524)(260,526)(261,531)(262,536)(263,538)
(264,534)(265,539)(266,532)(267,537)(268,533)(269,535)(270,540)(271,509)
(272,511)(273,507)(274,512)(275,505)(276,510)(277,506)(278,508)(279,513)
(280,518)(281,520)(282,516)(283,521)(284,514)(285,519)(286,515)(287,517)
(288,522);
s2 := Sym(576)!(  1,109)(  2,116)(  3,114)(  4,115)(  5,113)(  6,111)(  7,112)
(  8,110)(  9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)
( 16,121)( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)
( 24,129)( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)
( 32,140)( 33,138)( 34,139)( 35,137)( 36,144)( 37, 73)( 38, 80)( 39, 78)
( 40, 79)( 41, 77)( 42, 75)( 43, 76)( 44, 74)( 45, 81)( 46, 82)( 47, 89)
( 48, 87)( 49, 88)( 50, 86)( 51, 84)( 52, 85)( 53, 83)( 54, 90)( 55, 91)
( 56, 98)( 57, 96)( 58, 97)( 59, 95)( 60, 93)( 61, 94)( 62, 92)( 63, 99)
( 64,100)( 65,107)( 66,105)( 67,106)( 68,104)( 69,102)( 70,103)( 71,101)
( 72,108)(145,253)(146,260)(147,258)(148,259)(149,257)(150,255)(151,256)
(152,254)(153,261)(154,262)(155,269)(156,267)(157,268)(158,266)(159,264)
(160,265)(161,263)(162,270)(163,271)(164,278)(165,276)(166,277)(167,275)
(168,273)(169,274)(170,272)(171,279)(172,280)(173,287)(174,285)(175,286)
(176,284)(177,282)(178,283)(179,281)(180,288)(181,217)(182,224)(183,222)
(184,223)(185,221)(186,219)(187,220)(188,218)(189,225)(190,226)(191,233)
(192,231)(193,232)(194,230)(195,228)(196,229)(197,227)(198,234)(199,235)
(200,242)(201,240)(202,241)(203,239)(204,237)(205,238)(206,236)(207,243)
(208,244)(209,251)(210,249)(211,250)(212,248)(213,246)(214,247)(215,245)
(216,252)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)
(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)
(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)
(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)
(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)
(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)
(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)
(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)
(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)
(360,396)(433,541)(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)
(440,542)(441,549)(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)
(448,553)(449,551)(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)
(456,561)(457,562)(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)
(464,572)(465,570)(466,571)(467,569)(468,576)(469,505)(470,512)(471,510)
(472,511)(473,509)(474,507)(475,508)(476,506)(477,513)(478,514)(479,521)
(480,519)(481,520)(482,518)(483,516)(484,517)(485,515)(486,522)(487,523)
(488,530)(489,528)(490,529)(491,527)(492,525)(493,526)(494,524)(495,531)
(496,532)(497,539)(498,537)(499,538)(500,536)(501,534)(502,535)(503,533)
(504,540);
s3 := Sym(576)!(  1,112)(  2,110)(  3,117)(  4,109)(  5,116)(  6,114)(  7,115)
(  8,113)(  9,111)( 10,121)( 11,119)( 12,126)( 13,118)( 14,125)( 15,123)
( 16,124)( 17,122)( 18,120)( 19,130)( 20,128)( 21,135)( 22,127)( 23,134)
( 24,132)( 25,133)( 26,131)( 27,129)( 28,139)( 29,137)( 30,144)( 31,136)
( 32,143)( 33,141)( 34,142)( 35,140)( 36,138)( 37, 76)( 38, 74)( 39, 81)
( 40, 73)( 41, 80)( 42, 78)( 43, 79)( 44, 77)( 45, 75)( 46, 85)( 47, 83)
( 48, 90)( 49, 82)( 50, 89)( 51, 87)( 52, 88)( 53, 86)( 54, 84)( 55, 94)
( 56, 92)( 57, 99)( 58, 91)( 59, 98)( 60, 96)( 61, 97)( 62, 95)( 63, 93)
( 64,103)( 65,101)( 66,108)( 67,100)( 68,107)( 69,105)( 70,106)( 71,104)
( 72,102)(145,265)(146,263)(147,270)(148,262)(149,269)(150,267)(151,268)
(152,266)(153,264)(154,256)(155,254)(156,261)(157,253)(158,260)(159,258)
(160,259)(161,257)(162,255)(163,283)(164,281)(165,288)(166,280)(167,287)
(168,285)(169,286)(170,284)(171,282)(172,274)(173,272)(174,279)(175,271)
(176,278)(177,276)(178,277)(179,275)(180,273)(181,229)(182,227)(183,234)
(184,226)(185,233)(186,231)(187,232)(188,230)(189,228)(190,220)(191,218)
(192,225)(193,217)(194,224)(195,222)(196,223)(197,221)(198,219)(199,247)
(200,245)(201,252)(202,244)(203,251)(204,249)(205,250)(206,248)(207,246)
(208,238)(209,236)(210,243)(211,235)(212,242)(213,240)(214,241)(215,239)
(216,237)(289,418)(290,416)(291,423)(292,415)(293,422)(294,420)(295,421)
(296,419)(297,417)(298,427)(299,425)(300,432)(301,424)(302,431)(303,429)
(304,430)(305,428)(306,426)(307,400)(308,398)(309,405)(310,397)(311,404)
(312,402)(313,403)(314,401)(315,399)(316,409)(317,407)(318,414)(319,406)
(320,413)(321,411)(322,412)(323,410)(324,408)(325,382)(326,380)(327,387)
(328,379)(329,386)(330,384)(331,385)(332,383)(333,381)(334,391)(335,389)
(336,396)(337,388)(338,395)(339,393)(340,394)(341,392)(342,390)(343,364)
(344,362)(345,369)(346,361)(347,368)(348,366)(349,367)(350,365)(351,363)
(352,373)(353,371)(354,378)(355,370)(356,377)(357,375)(358,376)(359,374)
(360,372)(433,571)(434,569)(435,576)(436,568)(437,575)(438,573)(439,574)
(440,572)(441,570)(442,562)(443,560)(444,567)(445,559)(446,566)(447,564)
(448,565)(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)(455,557)
(456,555)(457,556)(458,554)(459,552)(460,544)(461,542)(462,549)(463,541)
(464,548)(465,546)(466,547)(467,545)(468,543)(469,535)(470,533)(471,540)
(472,532)(473,539)(474,537)(475,538)(476,536)(477,534)(478,526)(479,524)
(480,531)(481,523)(482,530)(483,528)(484,529)(485,527)(486,525)(487,517)
(488,515)(489,522)(490,514)(491,521)(492,519)(493,520)(494,518)(495,516)
(496,508)(497,506)(498,513)(499,505)(500,512)(501,510)(502,511)(503,509)
(504,507);
s4 := 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);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope