Polytope of Type {8,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,4}*1152
Also Known As : {{8,4|2},{4,4}6}. if this polytope has another name.
Group : SmallGroup(1152,119790)
Rank : 4
Schlafli Type : {8,4,4}
Number of vertices, edges, etc : 8, 72, 36, 18
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 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 : {4,4,4}*576b
4-fold quotients : {2,4,4}*288
8-fold quotients : {2,4,4}*144
18-fold quotients : {8,2,2}*64
36-fold quotients : {4,2,2}*32
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,289)( 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)
( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)( 80,404)
( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)( 88,412)
( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)( 96,420)
( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)(104,428)
(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)(112,364)
(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)(120,372)
(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)(128,380)
(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)(136,388)
(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)(144,396)
(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)
(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)(224,548)
(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)(232,556)
(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)(240,564)
(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)(248,572)
(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)(256,508)
(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)(264,516)
(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)(272,524)
(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)(280,532)
(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)(288,540);;
s1 := ( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)( 40, 49)
( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)( 57, 71)
( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 82)( 74, 87)
( 75, 89)( 76, 85)( 77, 90)( 78, 83)( 79, 88)( 80, 84)( 81, 86)( 91,100)
( 92,105)( 93,107)( 94,103)( 95,108)( 96,101)( 97,106)( 98,102)( 99,104)
(110,114)(111,116)(113,117)(119,123)(120,125)(122,126)(128,132)(129,134)
(131,135)(137,141)(138,143)(140,144)(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)
(217,244)(218,249)(219,251)(220,247)(221,252)(222,245)(223,250)(224,246)
(225,248)(226,235)(227,240)(228,242)(229,238)(230,243)(231,236)(232,241)
(233,237)(234,239)(253,271)(254,276)(255,278)(256,274)(257,279)(258,272)
(259,277)(260,273)(261,275)(262,280)(263,285)(264,287)(265,283)(266,288)
(267,281)(268,286)(269,282)(270,284)(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)(433,487)(434,492)(435,494)(436,490)
(437,495)(438,488)(439,493)(440,489)(441,491)(442,496)(443,501)(444,503)
(445,499)(446,504)(447,497)(448,502)(449,498)(450,500)(451,469)(452,474)
(453,476)(454,472)(455,477)(456,470)(457,475)(458,471)(459,473)(460,478)
(461,483)(462,485)(463,481)(464,486)(465,479)(466,484)(467,480)(468,482)
(505,559)(506,564)(507,566)(508,562)(509,567)(510,560)(511,565)(512,561)
(513,563)(514,568)(515,573)(516,575)(517,571)(518,576)(519,569)(520,574)
(521,570)(522,572)(523,541)(524,546)(525,548)(526,544)(527,549)(528,542)
(529,547)(530,543)(531,545)(532,550)(533,555)(534,557)(535,553)(536,558)
(537,551)(538,556)(539,552)(540,554);;
s2 := ( 1,145)( 2,147)( 3,146)( 4,149)( 5,148)( 6,150)( 7,153)( 8,152)
( 9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)( 16,162)
( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)( 24,168)
( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,183)( 39,182)( 40,185)
( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)( 48,191)
( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)( 56,201)
( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)( 64,208)
( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)( 72,214)
( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)( 80,224)
( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)( 88,234)
( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)( 96,240)
( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)(104,247)
(105,249)(106,252)(107,251)(108,250)(109,253)(110,255)(111,254)(112,257)
(113,256)(114,258)(115,261)(116,260)(117,259)(118,262)(119,264)(120,263)
(121,266)(122,265)(123,267)(124,270)(125,269)(126,268)(127,271)(128,273)
(129,272)(130,275)(131,274)(132,276)(133,279)(134,278)(135,277)(136,280)
(137,282)(138,281)(139,284)(140,283)(141,285)(142,288)(143,287)(144,286)
(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)(296,440)
(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)(304,450)
(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)(312,456)
(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)(320,463)
(321,465)(322,468)(323,467)(324,466)(325,469)(326,471)(327,470)(328,473)
(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)(336,479)
(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)(344,489)
(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)(352,496)
(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)(360,502)
(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)(368,512)
(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)(376,522)
(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)(384,528)
(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)(392,535)
(393,537)(394,540)(395,539)(396,538)(397,541)(398,543)(399,542)(400,545)
(401,544)(402,546)(403,549)(404,548)(405,547)(406,550)(407,552)(408,551)
(409,554)(410,553)(411,555)(412,558)(413,557)(414,556)(415,559)(416,561)
(417,560)(418,563)(419,562)(420,564)(421,567)(422,566)(423,565)(424,568)
(425,570)(426,569)(427,572)(428,571)(429,573)(430,576)(431,575)(432,574);;
s3 := ( 1,130)( 2,128)( 3,135)( 4,127)( 5,134)( 6,132)( 7,133)( 8,131)
( 9,129)( 10,139)( 11,137)( 12,144)( 13,136)( 14,143)( 15,141)( 16,142)
( 17,140)( 18,138)( 19,112)( 20,110)( 21,117)( 22,109)( 23,116)( 24,114)
( 25,115)( 26,113)( 27,111)( 28,121)( 29,119)( 30,126)( 31,118)( 32,125)
( 33,123)( 34,124)( 35,122)( 36,120)( 37,103)( 38,101)( 39,108)( 40,100)
( 41,107)( 42,105)( 43,106)( 44,104)( 45,102)( 46, 94)( 47, 92)( 48, 99)
( 49, 91)( 50, 98)( 51, 96)( 52, 97)( 53, 95)( 54, 93)( 55, 85)( 56, 83)
( 57, 90)( 58, 82)( 59, 89)( 60, 87)( 61, 88)( 62, 86)( 63, 84)( 64, 76)
( 65, 74)( 66, 81)( 67, 73)( 68, 80)( 69, 78)( 70, 79)( 71, 77)( 72, 75)
(145,256)(146,254)(147,261)(148,253)(149,260)(150,258)(151,259)(152,257)
(153,255)(154,265)(155,263)(156,270)(157,262)(158,269)(159,267)(160,268)
(161,266)(162,264)(163,274)(164,272)(165,279)(166,271)(167,278)(168,276)
(169,277)(170,275)(171,273)(172,283)(173,281)(174,288)(175,280)(176,287)
(177,285)(178,286)(179,284)(180,282)(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)
(289,382)(290,380)(291,387)(292,379)(293,386)(294,384)(295,385)(296,383)
(297,381)(298,391)(299,389)(300,396)(301,388)(302,395)(303,393)(304,394)
(305,392)(306,390)(307,364)(308,362)(309,369)(310,361)(311,368)(312,366)
(313,367)(314,365)(315,363)(316,373)(317,371)(318,378)(319,370)(320,377)
(321,375)(322,376)(323,374)(324,372)(325,418)(326,416)(327,423)(328,415)
(329,422)(330,420)(331,421)(332,419)(333,417)(334,427)(335,425)(336,432)
(337,424)(338,431)(339,429)(340,430)(341,428)(342,426)(343,400)(344,398)
(345,405)(346,397)(347,404)(348,402)(349,403)(350,401)(351,399)(352,409)
(353,407)(354,414)(355,406)(356,413)(357,411)(358,412)(359,410)(360,408)
(433,508)(434,506)(435,513)(436,505)(437,512)(438,510)(439,511)(440,509)
(441,507)(442,517)(443,515)(444,522)(445,514)(446,521)(447,519)(448,520)
(449,518)(450,516)(451,526)(452,524)(453,531)(454,523)(455,530)(456,528)
(457,529)(458,527)(459,525)(460,535)(461,533)(462,540)(463,532)(464,539)
(465,537)(466,538)(467,536)(468,534)(469,544)(470,542)(471,549)(472,541)
(473,548)(474,546)(475,547)(476,545)(477,543)(478,553)(479,551)(480,558)
(481,550)(482,557)(483,555)(484,556)(485,554)(486,552)(487,562)(488,560)
(489,567)(490,559)(491,566)(492,564)(493,565)(494,563)(495,561)(496,571)
(497,569)(498,576)(499,568)(500,575)(501,573)(502,574)(503,572)(504,570);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
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)( 19,307)( 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)( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)
( 80,404)( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)
( 88,412)( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)
( 96,420)( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)
(104,428)(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)
(112,364)(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)
(120,372)(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)
(128,380)(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)
(136,388)(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)
(144,396)(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)(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)
(224,548)(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)
(232,556)(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)
(240,564)(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)
(248,572)(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)
(256,508)(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)
(264,516)(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)
(272,524)(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)
(280,532)(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)
(288,540);
s1 := Sym(576)!( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)
( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)
( 40, 49)( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)
( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 82)
( 74, 87)( 75, 89)( 76, 85)( 77, 90)( 78, 83)( 79, 88)( 80, 84)( 81, 86)
( 91,100)( 92,105)( 93,107)( 94,103)( 95,108)( 96,101)( 97,106)( 98,102)
( 99,104)(110,114)(111,116)(113,117)(119,123)(120,125)(122,126)(128,132)
(129,134)(131,135)(137,141)(138,143)(140,144)(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)(217,244)(218,249)(219,251)(220,247)(221,252)(222,245)(223,250)
(224,246)(225,248)(226,235)(227,240)(228,242)(229,238)(230,243)(231,236)
(232,241)(233,237)(234,239)(253,271)(254,276)(255,278)(256,274)(257,279)
(258,272)(259,277)(260,273)(261,275)(262,280)(263,285)(264,287)(265,283)
(266,288)(267,281)(268,286)(269,282)(270,284)(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)(433,487)(434,492)(435,494)
(436,490)(437,495)(438,488)(439,493)(440,489)(441,491)(442,496)(443,501)
(444,503)(445,499)(446,504)(447,497)(448,502)(449,498)(450,500)(451,469)
(452,474)(453,476)(454,472)(455,477)(456,470)(457,475)(458,471)(459,473)
(460,478)(461,483)(462,485)(463,481)(464,486)(465,479)(466,484)(467,480)
(468,482)(505,559)(506,564)(507,566)(508,562)(509,567)(510,560)(511,565)
(512,561)(513,563)(514,568)(515,573)(516,575)(517,571)(518,576)(519,569)
(520,574)(521,570)(522,572)(523,541)(524,546)(525,548)(526,544)(527,549)
(528,542)(529,547)(530,543)(531,545)(532,550)(533,555)(534,557)(535,553)
(536,558)(537,551)(538,556)(539,552)(540,554);
s2 := Sym(576)!( 1,145)( 2,147)( 3,146)( 4,149)( 5,148)( 6,150)( 7,153)
( 8,152)( 9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)
( 16,162)( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)
( 24,168)( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,183)( 39,182)
( 40,185)( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)
( 48,191)( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)
( 56,201)( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)
( 64,208)( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)
( 80,224)( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)
( 88,234)( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)
( 96,240)( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)
(104,247)(105,249)(106,252)(107,251)(108,250)(109,253)(110,255)(111,254)
(112,257)(113,256)(114,258)(115,261)(116,260)(117,259)(118,262)(119,264)
(120,263)(121,266)(122,265)(123,267)(124,270)(125,269)(126,268)(127,271)
(128,273)(129,272)(130,275)(131,274)(132,276)(133,279)(134,278)(135,277)
(136,280)(137,282)(138,281)(139,284)(140,283)(141,285)(142,288)(143,287)
(144,286)(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)
(296,440)(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)
(304,450)(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)
(312,456)(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)
(320,463)(321,465)(322,468)(323,467)(324,466)(325,469)(326,471)(327,470)
(328,473)(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)
(336,479)(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)
(344,489)(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)
(352,496)(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)
(360,502)(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)
(368,512)(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)
(376,522)(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)
(384,528)(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)
(392,535)(393,537)(394,540)(395,539)(396,538)(397,541)(398,543)(399,542)
(400,545)(401,544)(402,546)(403,549)(404,548)(405,547)(406,550)(407,552)
(408,551)(409,554)(410,553)(411,555)(412,558)(413,557)(414,556)(415,559)
(416,561)(417,560)(418,563)(419,562)(420,564)(421,567)(422,566)(423,565)
(424,568)(425,570)(426,569)(427,572)(428,571)(429,573)(430,576)(431,575)
(432,574);
s3 := Sym(576)!( 1,130)( 2,128)( 3,135)( 4,127)( 5,134)( 6,132)( 7,133)
( 8,131)( 9,129)( 10,139)( 11,137)( 12,144)( 13,136)( 14,143)( 15,141)
( 16,142)( 17,140)( 18,138)( 19,112)( 20,110)( 21,117)( 22,109)( 23,116)
( 24,114)( 25,115)( 26,113)( 27,111)( 28,121)( 29,119)( 30,126)( 31,118)
( 32,125)( 33,123)( 34,124)( 35,122)( 36,120)( 37,103)( 38,101)( 39,108)
( 40,100)( 41,107)( 42,105)( 43,106)( 44,104)( 45,102)( 46, 94)( 47, 92)
( 48, 99)( 49, 91)( 50, 98)( 51, 96)( 52, 97)( 53, 95)( 54, 93)( 55, 85)
( 56, 83)( 57, 90)( 58, 82)( 59, 89)( 60, 87)( 61, 88)( 62, 86)( 63, 84)
( 64, 76)( 65, 74)( 66, 81)( 67, 73)( 68, 80)( 69, 78)( 70, 79)( 71, 77)
( 72, 75)(145,256)(146,254)(147,261)(148,253)(149,260)(150,258)(151,259)
(152,257)(153,255)(154,265)(155,263)(156,270)(157,262)(158,269)(159,267)
(160,268)(161,266)(162,264)(163,274)(164,272)(165,279)(166,271)(167,278)
(168,276)(169,277)(170,275)(171,273)(172,283)(173,281)(174,288)(175,280)
(176,287)(177,285)(178,286)(179,284)(180,282)(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)(289,382)(290,380)(291,387)(292,379)(293,386)(294,384)(295,385)
(296,383)(297,381)(298,391)(299,389)(300,396)(301,388)(302,395)(303,393)
(304,394)(305,392)(306,390)(307,364)(308,362)(309,369)(310,361)(311,368)
(312,366)(313,367)(314,365)(315,363)(316,373)(317,371)(318,378)(319,370)
(320,377)(321,375)(322,376)(323,374)(324,372)(325,418)(326,416)(327,423)
(328,415)(329,422)(330,420)(331,421)(332,419)(333,417)(334,427)(335,425)
(336,432)(337,424)(338,431)(339,429)(340,430)(341,428)(342,426)(343,400)
(344,398)(345,405)(346,397)(347,404)(348,402)(349,403)(350,401)(351,399)
(352,409)(353,407)(354,414)(355,406)(356,413)(357,411)(358,412)(359,410)
(360,408)(433,508)(434,506)(435,513)(436,505)(437,512)(438,510)(439,511)
(440,509)(441,507)(442,517)(443,515)(444,522)(445,514)(446,521)(447,519)
(448,520)(449,518)(450,516)(451,526)(452,524)(453,531)(454,523)(455,530)
(456,528)(457,529)(458,527)(459,525)(460,535)(461,533)(462,540)(463,532)
(464,539)(465,537)(466,538)(467,536)(468,534)(469,544)(470,542)(471,549)
(472,541)(473,548)(474,546)(475,547)(476,545)(477,543)(478,553)(479,551)
(480,558)(481,550)(482,557)(483,555)(484,556)(485,554)(486,552)(487,562)
(488,560)(489,567)(490,559)(491,566)(492,564)(493,565)(494,563)(495,561)
(496,571)(497,569)(498,576)(499,568)(500,575)(501,573)(502,574)(503,572)
(504,570);
poly := sub<Sym(576)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;
References : None.
to this polytope