Polytope of Type {4,4,36}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,36}*1152
Also Known As : {{4,4|2},{4,36|2}}. if this polytope has another name.
Group : SmallGroup(1152,42999)
Rank : 4
Schlafli Type : {4,4,36}
Number of vertices, edges, etc : 4, 8, 72, 36
Order of s0s1s2s3 : 36
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 : {2,4,36}*576a, {4,2,36}*576, {4,4,18}*576
3-fold quotients : {4,4,12}*384
4-fold quotients : {2,2,36}*288, {2,4,18}*288a, {4,2,18}*288
6-fold quotients : {2,4,12}*192a, {4,2,12}*192, {4,4,6}*192
8-fold quotients : {4,2,9}*144, {2,2,18}*144
9-fold quotients : {4,4,4}*128
12-fold quotients : {2,2,12}*96, {2,4,6}*96a, {4,2,6}*96
16-fold quotients : {2,2,9}*72
18-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
24-fold quotients : {4,2,3}*48, {2,2,6}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
48-fold quotients : {2,2,3}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)
( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)
( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)
( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)
( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)
( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)
(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)
(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288)
(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)(296,368)
(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)(304,376)
(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)(312,384)
(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)(320,392)
(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)
(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)(336,408)
(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)(344,416)
(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)(352,424)
(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)(360,432)
(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)(440,512)
(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)(448,520)
(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)(456,528)
(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)(464,536)
(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)(472,544)
(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)(480,552)
(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)(488,560)
(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)(496,568)
(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)(504,576);;
s1 := ( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)
( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)
( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)
(105,141)(106,142)(107,143)(108,144)(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)(181,199)(182,200)
(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)(189,207)(190,208)
(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)(197,215)(198,216)
(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)(224,278)
(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)(232,286)
(233,287)(234,288)(235,253)(236,254)(237,255)(238,256)(239,257)(240,258)
(241,259)(242,260)(243,261)(244,262)(245,263)(246,264)(247,265)(248,266)
(249,267)(250,268)(251,269)(252,270)(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)
(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)(505,523)(506,524)(507,525)(508,526)
(509,527)(510,528)(511,529)(512,530)(513,531)(514,532)(515,533)(516,534)
(517,535)(518,536)(519,537)(520,538)(521,539)(522,540)(541,559)(542,560)
(543,561)(544,562)(545,563)(546,564)(547,565)(548,566)(549,567)(550,568)
(551,569)(552,570)(553,571)(554,572)(555,573)(556,574)(557,575)(558,576);;
s2 := ( 1,145)( 2,147)( 3,146)( 4,153)( 5,152)( 6,151)( 7,150)( 8,149)
( 9,148)( 10,154)( 11,156)( 12,155)( 13,162)( 14,161)( 15,160)( 16,159)
( 17,158)( 18,157)( 19,163)( 20,165)( 21,164)( 22,171)( 23,170)( 24,169)
( 25,168)( 26,167)( 27,166)( 28,172)( 29,174)( 30,173)( 31,180)( 32,179)
( 33,178)( 34,177)( 35,176)( 36,175)( 37,181)( 38,183)( 39,182)( 40,189)
( 41,188)( 42,187)( 43,186)( 44,185)( 45,184)( 46,190)( 47,192)( 48,191)
( 49,198)( 50,197)( 51,196)( 52,195)( 53,194)( 54,193)( 55,199)( 56,201)
( 57,200)( 58,207)( 59,206)( 60,205)( 61,204)( 62,203)( 63,202)( 64,208)
( 65,210)( 66,209)( 67,216)( 68,215)( 69,214)( 70,213)( 71,212)( 72,211)
( 73,217)( 74,219)( 75,218)( 76,225)( 77,224)( 78,223)( 79,222)( 80,221)
( 81,220)( 82,226)( 83,228)( 84,227)( 85,234)( 86,233)( 87,232)( 88,231)
( 89,230)( 90,229)( 91,235)( 92,237)( 93,236)( 94,243)( 95,242)( 96,241)
( 97,240)( 98,239)( 99,238)(100,244)(101,246)(102,245)(103,252)(104,251)
(105,250)(106,249)(107,248)(108,247)(109,253)(110,255)(111,254)(112,261)
(113,260)(114,259)(115,258)(116,257)(117,256)(118,262)(119,264)(120,263)
(121,270)(122,269)(123,268)(124,267)(125,266)(126,265)(127,271)(128,273)
(129,272)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)(136,280)
(137,282)(138,281)(139,288)(140,287)(141,286)(142,285)(143,284)(144,283)
(289,433)(290,435)(291,434)(292,441)(293,440)(294,439)(295,438)(296,437)
(297,436)(298,442)(299,444)(300,443)(301,450)(302,449)(303,448)(304,447)
(305,446)(306,445)(307,451)(308,453)(309,452)(310,459)(311,458)(312,457)
(313,456)(314,455)(315,454)(316,460)(317,462)(318,461)(319,468)(320,467)
(321,466)(322,465)(323,464)(324,463)(325,469)(326,471)(327,470)(328,477)
(329,476)(330,475)(331,474)(332,473)(333,472)(334,478)(335,480)(336,479)
(337,486)(338,485)(339,484)(340,483)(341,482)(342,481)(343,487)(344,489)
(345,488)(346,495)(347,494)(348,493)(349,492)(350,491)(351,490)(352,496)
(353,498)(354,497)(355,504)(356,503)(357,502)(358,501)(359,500)(360,499)
(361,505)(362,507)(363,506)(364,513)(365,512)(366,511)(367,510)(368,509)
(369,508)(370,514)(371,516)(372,515)(373,522)(374,521)(375,520)(376,519)
(377,518)(378,517)(379,523)(380,525)(381,524)(382,531)(383,530)(384,529)
(385,528)(386,527)(387,526)(388,532)(389,534)(390,533)(391,540)(392,539)
(393,538)(394,537)(395,536)(396,535)(397,541)(398,543)(399,542)(400,549)
(401,548)(402,547)(403,546)(404,545)(405,544)(406,550)(407,552)(408,551)
(409,558)(410,557)(411,556)(412,555)(413,554)(414,553)(415,559)(416,561)
(417,560)(418,567)(419,566)(420,565)(421,564)(422,563)(423,562)(424,568)
(425,570)(426,569)(427,576)(428,575)(429,574)(430,573)(431,572)(432,571);;
s3 := ( 1,364)( 2,366)( 3,365)( 4,361)( 5,363)( 6,362)( 7,369)( 8,368)
( 9,367)( 10,373)( 11,375)( 12,374)( 13,370)( 14,372)( 15,371)( 16,378)
( 17,377)( 18,376)( 19,382)( 20,384)( 21,383)( 22,379)( 23,381)( 24,380)
( 25,387)( 26,386)( 27,385)( 28,391)( 29,393)( 30,392)( 31,388)( 32,390)
( 33,389)( 34,396)( 35,395)( 36,394)( 37,400)( 38,402)( 39,401)( 40,397)
( 41,399)( 42,398)( 43,405)( 44,404)( 45,403)( 46,409)( 47,411)( 48,410)
( 49,406)( 50,408)( 51,407)( 52,414)( 53,413)( 54,412)( 55,418)( 56,420)
( 57,419)( 58,415)( 59,417)( 60,416)( 61,423)( 62,422)( 63,421)( 64,427)
( 65,429)( 66,428)( 67,424)( 68,426)( 69,425)( 70,432)( 71,431)( 72,430)
( 73,292)( 74,294)( 75,293)( 76,289)( 77,291)( 78,290)( 79,297)( 80,296)
( 81,295)( 82,301)( 83,303)( 84,302)( 85,298)( 86,300)( 87,299)( 88,306)
( 89,305)( 90,304)( 91,310)( 92,312)( 93,311)( 94,307)( 95,309)( 96,308)
( 97,315)( 98,314)( 99,313)(100,319)(101,321)(102,320)(103,316)(104,318)
(105,317)(106,324)(107,323)(108,322)(109,328)(110,330)(111,329)(112,325)
(113,327)(114,326)(115,333)(116,332)(117,331)(118,337)(119,339)(120,338)
(121,334)(122,336)(123,335)(124,342)(125,341)(126,340)(127,346)(128,348)
(129,347)(130,343)(131,345)(132,344)(133,351)(134,350)(135,349)(136,355)
(137,357)(138,356)(139,352)(140,354)(141,353)(142,360)(143,359)(144,358)
(145,517)(146,519)(147,518)(148,514)(149,516)(150,515)(151,522)(152,521)
(153,520)(154,508)(155,510)(156,509)(157,505)(158,507)(159,506)(160,513)
(161,512)(162,511)(163,535)(164,537)(165,536)(166,532)(167,534)(168,533)
(169,540)(170,539)(171,538)(172,526)(173,528)(174,527)(175,523)(176,525)
(177,524)(178,531)(179,530)(180,529)(181,553)(182,555)(183,554)(184,550)
(185,552)(186,551)(187,558)(188,557)(189,556)(190,544)(191,546)(192,545)
(193,541)(194,543)(195,542)(196,549)(197,548)(198,547)(199,571)(200,573)
(201,572)(202,568)(203,570)(204,569)(205,576)(206,575)(207,574)(208,562)
(209,564)(210,563)(211,559)(212,561)(213,560)(214,567)(215,566)(216,565)
(217,445)(218,447)(219,446)(220,442)(221,444)(222,443)(223,450)(224,449)
(225,448)(226,436)(227,438)(228,437)(229,433)(230,435)(231,434)(232,441)
(233,440)(234,439)(235,463)(236,465)(237,464)(238,460)(239,462)(240,461)
(241,468)(242,467)(243,466)(244,454)(245,456)(246,455)(247,451)(248,453)
(249,452)(250,459)(251,458)(252,457)(253,481)(254,483)(255,482)(256,478)
(257,480)(258,479)(259,486)(260,485)(261,484)(262,472)(263,474)(264,473)
(265,469)(266,471)(267,470)(268,477)(269,476)(270,475)(271,499)(272,501)
(273,500)(274,496)(275,498)(276,497)(277,504)(278,503)(279,502)(280,490)
(281,492)(282,491)(283,487)(284,489)(285,488)(286,495)(287,494)(288,493);;
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*s0*s1*s0*s1*s0*s1,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)
( 8, 80)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)
( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)
( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)
( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)
( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)
( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)
( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)
(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)
(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)
(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)
(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)
(216,288)(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)
(296,368)(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)
(304,376)(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)
(312,384)(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)
(320,392)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)
(328,400)(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)
(336,408)(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)
(344,416)(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)
(352,424)(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)
(360,432)(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)
(440,512)(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)
(448,520)(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)
(456,528)(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)
(464,536)(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)
(472,544)(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)
(480,552)(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)
(488,560)(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)
(496,568)(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)
(504,576);
s1 := Sym(576)!( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)
( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)
( 96,132)( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)
(104,140)(105,141)(106,142)(107,143)(108,144)(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)(181,199)
(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)(189,207)
(190,208)(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)(197,215)
(198,216)(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)
(224,278)(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)
(232,286)(233,287)(234,288)(235,253)(236,254)(237,255)(238,256)(239,257)
(240,258)(241,259)(242,260)(243,261)(244,262)(245,263)(246,264)(247,265)
(248,266)(249,267)(250,268)(251,269)(252,270)(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)(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)(505,523)(506,524)(507,525)
(508,526)(509,527)(510,528)(511,529)(512,530)(513,531)(514,532)(515,533)
(516,534)(517,535)(518,536)(519,537)(520,538)(521,539)(522,540)(541,559)
(542,560)(543,561)(544,562)(545,563)(546,564)(547,565)(548,566)(549,567)
(550,568)(551,569)(552,570)(553,571)(554,572)(555,573)(556,574)(557,575)
(558,576);
s2 := Sym(576)!( 1,145)( 2,147)( 3,146)( 4,153)( 5,152)( 6,151)( 7,150)
( 8,149)( 9,148)( 10,154)( 11,156)( 12,155)( 13,162)( 14,161)( 15,160)
( 16,159)( 17,158)( 18,157)( 19,163)( 20,165)( 21,164)( 22,171)( 23,170)
( 24,169)( 25,168)( 26,167)( 27,166)( 28,172)( 29,174)( 30,173)( 31,180)
( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,181)( 38,183)( 39,182)
( 40,189)( 41,188)( 42,187)( 43,186)( 44,185)( 45,184)( 46,190)( 47,192)
( 48,191)( 49,198)( 50,197)( 51,196)( 52,195)( 53,194)( 54,193)( 55,199)
( 56,201)( 57,200)( 58,207)( 59,206)( 60,205)( 61,204)( 62,203)( 63,202)
( 64,208)( 65,210)( 66,209)( 67,216)( 68,215)( 69,214)( 70,213)( 71,212)
( 72,211)( 73,217)( 74,219)( 75,218)( 76,225)( 77,224)( 78,223)( 79,222)
( 80,221)( 81,220)( 82,226)( 83,228)( 84,227)( 85,234)( 86,233)( 87,232)
( 88,231)( 89,230)( 90,229)( 91,235)( 92,237)( 93,236)( 94,243)( 95,242)
( 96,241)( 97,240)( 98,239)( 99,238)(100,244)(101,246)(102,245)(103,252)
(104,251)(105,250)(106,249)(107,248)(108,247)(109,253)(110,255)(111,254)
(112,261)(113,260)(114,259)(115,258)(116,257)(117,256)(118,262)(119,264)
(120,263)(121,270)(122,269)(123,268)(124,267)(125,266)(126,265)(127,271)
(128,273)(129,272)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)
(136,280)(137,282)(138,281)(139,288)(140,287)(141,286)(142,285)(143,284)
(144,283)(289,433)(290,435)(291,434)(292,441)(293,440)(294,439)(295,438)
(296,437)(297,436)(298,442)(299,444)(300,443)(301,450)(302,449)(303,448)
(304,447)(305,446)(306,445)(307,451)(308,453)(309,452)(310,459)(311,458)
(312,457)(313,456)(314,455)(315,454)(316,460)(317,462)(318,461)(319,468)
(320,467)(321,466)(322,465)(323,464)(324,463)(325,469)(326,471)(327,470)
(328,477)(329,476)(330,475)(331,474)(332,473)(333,472)(334,478)(335,480)
(336,479)(337,486)(338,485)(339,484)(340,483)(341,482)(342,481)(343,487)
(344,489)(345,488)(346,495)(347,494)(348,493)(349,492)(350,491)(351,490)
(352,496)(353,498)(354,497)(355,504)(356,503)(357,502)(358,501)(359,500)
(360,499)(361,505)(362,507)(363,506)(364,513)(365,512)(366,511)(367,510)
(368,509)(369,508)(370,514)(371,516)(372,515)(373,522)(374,521)(375,520)
(376,519)(377,518)(378,517)(379,523)(380,525)(381,524)(382,531)(383,530)
(384,529)(385,528)(386,527)(387,526)(388,532)(389,534)(390,533)(391,540)
(392,539)(393,538)(394,537)(395,536)(396,535)(397,541)(398,543)(399,542)
(400,549)(401,548)(402,547)(403,546)(404,545)(405,544)(406,550)(407,552)
(408,551)(409,558)(410,557)(411,556)(412,555)(413,554)(414,553)(415,559)
(416,561)(417,560)(418,567)(419,566)(420,565)(421,564)(422,563)(423,562)
(424,568)(425,570)(426,569)(427,576)(428,575)(429,574)(430,573)(431,572)
(432,571);
s3 := Sym(576)!( 1,364)( 2,366)( 3,365)( 4,361)( 5,363)( 6,362)( 7,369)
( 8,368)( 9,367)( 10,373)( 11,375)( 12,374)( 13,370)( 14,372)( 15,371)
( 16,378)( 17,377)( 18,376)( 19,382)( 20,384)( 21,383)( 22,379)( 23,381)
( 24,380)( 25,387)( 26,386)( 27,385)( 28,391)( 29,393)( 30,392)( 31,388)
( 32,390)( 33,389)( 34,396)( 35,395)( 36,394)( 37,400)( 38,402)( 39,401)
( 40,397)( 41,399)( 42,398)( 43,405)( 44,404)( 45,403)( 46,409)( 47,411)
( 48,410)( 49,406)( 50,408)( 51,407)( 52,414)( 53,413)( 54,412)( 55,418)
( 56,420)( 57,419)( 58,415)( 59,417)( 60,416)( 61,423)( 62,422)( 63,421)
( 64,427)( 65,429)( 66,428)( 67,424)( 68,426)( 69,425)( 70,432)( 71,431)
( 72,430)( 73,292)( 74,294)( 75,293)( 76,289)( 77,291)( 78,290)( 79,297)
( 80,296)( 81,295)( 82,301)( 83,303)( 84,302)( 85,298)( 86,300)( 87,299)
( 88,306)( 89,305)( 90,304)( 91,310)( 92,312)( 93,311)( 94,307)( 95,309)
( 96,308)( 97,315)( 98,314)( 99,313)(100,319)(101,321)(102,320)(103,316)
(104,318)(105,317)(106,324)(107,323)(108,322)(109,328)(110,330)(111,329)
(112,325)(113,327)(114,326)(115,333)(116,332)(117,331)(118,337)(119,339)
(120,338)(121,334)(122,336)(123,335)(124,342)(125,341)(126,340)(127,346)
(128,348)(129,347)(130,343)(131,345)(132,344)(133,351)(134,350)(135,349)
(136,355)(137,357)(138,356)(139,352)(140,354)(141,353)(142,360)(143,359)
(144,358)(145,517)(146,519)(147,518)(148,514)(149,516)(150,515)(151,522)
(152,521)(153,520)(154,508)(155,510)(156,509)(157,505)(158,507)(159,506)
(160,513)(161,512)(162,511)(163,535)(164,537)(165,536)(166,532)(167,534)
(168,533)(169,540)(170,539)(171,538)(172,526)(173,528)(174,527)(175,523)
(176,525)(177,524)(178,531)(179,530)(180,529)(181,553)(182,555)(183,554)
(184,550)(185,552)(186,551)(187,558)(188,557)(189,556)(190,544)(191,546)
(192,545)(193,541)(194,543)(195,542)(196,549)(197,548)(198,547)(199,571)
(200,573)(201,572)(202,568)(203,570)(204,569)(205,576)(206,575)(207,574)
(208,562)(209,564)(210,563)(211,559)(212,561)(213,560)(214,567)(215,566)
(216,565)(217,445)(218,447)(219,446)(220,442)(221,444)(222,443)(223,450)
(224,449)(225,448)(226,436)(227,438)(228,437)(229,433)(230,435)(231,434)
(232,441)(233,440)(234,439)(235,463)(236,465)(237,464)(238,460)(239,462)
(240,461)(241,468)(242,467)(243,466)(244,454)(245,456)(246,455)(247,451)
(248,453)(249,452)(250,459)(251,458)(252,457)(253,481)(254,483)(255,482)
(256,478)(257,480)(258,479)(259,486)(260,485)(261,484)(262,472)(263,474)
(264,473)(265,469)(266,471)(267,470)(268,477)(269,476)(270,475)(271,499)
(272,501)(273,500)(274,496)(275,498)(276,497)(277,504)(278,503)(279,502)
(280,490)(281,492)(282,491)(283,487)(284,489)(285,488)(286,495)(287,494)
(288,493);
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*s0*s1*s0*s1*s0*s1, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope