Polytope of Type {6,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98810)
Rank : 4
Schlafli Type : {6,8,4}
Number of vertices, edges, etc : 18, 72, 48, 4
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 : {6,4,4}*576
4-fold quotients : {6,4,4}*288, {6,4,2}*288
8-fold quotients : {6,4,2}*144
9-fold quotients : {2,8,4}*128b
18-fold quotients : {2,4,4}*64
36-fold quotients : {2,2,4}*32, {2,4,2}*32
72-fold quotients : {2,2,2}*16
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 := ( 1,290)( 2,289)( 3,291)( 4,294)( 5,293)( 6,292)( 7,295)( 8,297)
( 9,296)( 10,299)( 11,298)( 12,300)( 13,303)( 14,302)( 15,301)( 16,304)
( 17,306)( 18,305)( 19,317)( 20,316)( 21,318)( 22,321)( 23,320)( 24,319)
( 25,322)( 26,324)( 27,323)( 28,308)( 29,307)( 30,309)( 31,312)( 32,311)
( 33,310)( 34,313)( 35,315)( 36,314)( 37,335)( 38,334)( 39,336)( 40,339)
( 41,338)( 42,337)( 43,340)( 44,342)( 45,341)( 46,326)( 47,325)( 48,327)
( 49,330)( 50,329)( 51,328)( 52,331)( 53,333)( 54,332)( 55,344)( 56,343)
( 57,345)( 58,348)( 59,347)( 60,346)( 61,349)( 62,351)( 63,350)( 64,353)
( 65,352)( 66,354)( 67,357)( 68,356)( 69,355)( 70,358)( 71,360)( 72,359)
( 73,362)( 74,361)( 75,363)( 76,366)( 77,365)( 78,364)( 79,367)( 80,369)
( 81,368)( 82,371)( 83,370)( 84,372)( 85,375)( 86,374)( 87,373)( 88,376)
( 89,378)( 90,377)( 91,389)( 92,388)( 93,390)( 94,393)( 95,392)( 96,391)
( 97,394)( 98,396)( 99,395)(100,380)(101,379)(102,381)(103,384)(104,383)
(105,382)(106,385)(107,387)(108,386)(109,407)(110,406)(111,408)(112,411)
(113,410)(114,409)(115,412)(116,414)(117,413)(118,398)(119,397)(120,399)
(121,402)(122,401)(123,400)(124,403)(125,405)(126,404)(127,416)(128,415)
(129,417)(130,420)(131,419)(132,418)(133,421)(134,423)(135,422)(136,425)
(137,424)(138,426)(139,429)(140,428)(141,427)(142,430)(143,432)(144,431)
(145,434)(146,433)(147,435)(148,438)(149,437)(150,436)(151,439)(152,441)
(153,440)(154,443)(155,442)(156,444)(157,447)(158,446)(159,445)(160,448)
(161,450)(162,449)(163,461)(164,460)(165,462)(166,465)(167,464)(168,463)
(169,466)(170,468)(171,467)(172,452)(173,451)(174,453)(175,456)(176,455)
(177,454)(178,457)(179,459)(180,458)(181,479)(182,478)(183,480)(184,483)
(185,482)(186,481)(187,484)(188,486)(189,485)(190,470)(191,469)(192,471)
(193,474)(194,473)(195,472)(196,475)(197,477)(198,476)(199,488)(200,487)
(201,489)(202,492)(203,491)(204,490)(205,493)(206,495)(207,494)(208,497)
(209,496)(210,498)(211,501)(212,500)(213,499)(214,502)(215,504)(216,503)
(217,506)(218,505)(219,507)(220,510)(221,509)(222,508)(223,511)(224,513)
(225,512)(226,515)(227,514)(228,516)(229,519)(230,518)(231,517)(232,520)
(233,522)(234,521)(235,533)(236,532)(237,534)(238,537)(239,536)(240,535)
(241,538)(242,540)(243,539)(244,524)(245,523)(246,525)(247,528)(248,527)
(249,526)(250,529)(251,531)(252,530)(253,551)(254,550)(255,552)(256,555)
(257,554)(258,553)(259,556)(260,558)(261,557)(262,542)(263,541)(264,543)
(265,546)(266,545)(267,544)(268,547)(269,549)(270,548)(271,560)(272,559)
(273,561)(274,564)(275,563)(276,562)(277,565)(278,567)(279,566)(280,569)
(281,568)(282,570)(283,573)(284,572)(285,571)(286,574)(287,576)(288,575);;
s2 := ( 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);;
s3 := ( 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);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
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)!( 1,290)( 2,289)( 3,291)( 4,294)( 5,293)( 6,292)( 7,295)
( 8,297)( 9,296)( 10,299)( 11,298)( 12,300)( 13,303)( 14,302)( 15,301)
( 16,304)( 17,306)( 18,305)( 19,317)( 20,316)( 21,318)( 22,321)( 23,320)
( 24,319)( 25,322)( 26,324)( 27,323)( 28,308)( 29,307)( 30,309)( 31,312)
( 32,311)( 33,310)( 34,313)( 35,315)( 36,314)( 37,335)( 38,334)( 39,336)
( 40,339)( 41,338)( 42,337)( 43,340)( 44,342)( 45,341)( 46,326)( 47,325)
( 48,327)( 49,330)( 50,329)( 51,328)( 52,331)( 53,333)( 54,332)( 55,344)
( 56,343)( 57,345)( 58,348)( 59,347)( 60,346)( 61,349)( 62,351)( 63,350)
( 64,353)( 65,352)( 66,354)( 67,357)( 68,356)( 69,355)( 70,358)( 71,360)
( 72,359)( 73,362)( 74,361)( 75,363)( 76,366)( 77,365)( 78,364)( 79,367)
( 80,369)( 81,368)( 82,371)( 83,370)( 84,372)( 85,375)( 86,374)( 87,373)
( 88,376)( 89,378)( 90,377)( 91,389)( 92,388)( 93,390)( 94,393)( 95,392)
( 96,391)( 97,394)( 98,396)( 99,395)(100,380)(101,379)(102,381)(103,384)
(104,383)(105,382)(106,385)(107,387)(108,386)(109,407)(110,406)(111,408)
(112,411)(113,410)(114,409)(115,412)(116,414)(117,413)(118,398)(119,397)
(120,399)(121,402)(122,401)(123,400)(124,403)(125,405)(126,404)(127,416)
(128,415)(129,417)(130,420)(131,419)(132,418)(133,421)(134,423)(135,422)
(136,425)(137,424)(138,426)(139,429)(140,428)(141,427)(142,430)(143,432)
(144,431)(145,434)(146,433)(147,435)(148,438)(149,437)(150,436)(151,439)
(152,441)(153,440)(154,443)(155,442)(156,444)(157,447)(158,446)(159,445)
(160,448)(161,450)(162,449)(163,461)(164,460)(165,462)(166,465)(167,464)
(168,463)(169,466)(170,468)(171,467)(172,452)(173,451)(174,453)(175,456)
(176,455)(177,454)(178,457)(179,459)(180,458)(181,479)(182,478)(183,480)
(184,483)(185,482)(186,481)(187,484)(188,486)(189,485)(190,470)(191,469)
(192,471)(193,474)(194,473)(195,472)(196,475)(197,477)(198,476)(199,488)
(200,487)(201,489)(202,492)(203,491)(204,490)(205,493)(206,495)(207,494)
(208,497)(209,496)(210,498)(211,501)(212,500)(213,499)(214,502)(215,504)
(216,503)(217,506)(218,505)(219,507)(220,510)(221,509)(222,508)(223,511)
(224,513)(225,512)(226,515)(227,514)(228,516)(229,519)(230,518)(231,517)
(232,520)(233,522)(234,521)(235,533)(236,532)(237,534)(238,537)(239,536)
(240,535)(241,538)(242,540)(243,539)(244,524)(245,523)(246,525)(247,528)
(248,527)(249,526)(250,529)(251,531)(252,530)(253,551)(254,550)(255,552)
(256,555)(257,554)(258,553)(259,556)(260,558)(261,557)(262,542)(263,541)
(264,543)(265,546)(266,545)(267,544)(268,547)(269,549)(270,548)(271,560)
(272,559)(273,561)(274,564)(275,563)(276,562)(277,565)(278,567)(279,566)
(280,569)(281,568)(282,570)(283,573)(284,572)(285,571)(286,574)(287,576)
(288,575);
s2 := 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);
s3 := 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);
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,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1 >;
References : None.
to this polytope