Questions?
See the FAQ
or other info.

Polytope of Type {4,36,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,36,4}*1152a
Also Known As : {{4,36|2},{36,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,43002)
Rank : 4
Schlafli Type : {4,36,4}
Number of vertices, edges, etc : 4, 72, 72, 4
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,36,4}*576a, {4,36,2}*576a, {4,18,4}*576a
   3-fold quotients : {4,12,4}*384a
   4-fold quotients : {2,36,2}*288, {2,18,4}*288a, {4,18,2}*288a
   6-fold quotients : {2,12,4}*192a, {4,12,2}*192a, {4,6,4}*192a
   8-fold quotients : {2,18,2}*144
   9-fold quotients : {4,4,4}*128
   12-fold quotients : {2,12,2}*96, {2,6,4}*96a, {4,6,2}*96a
   16-fold quotients : {2,9,2}*72
   18-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   24-fold quotients : {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,3,2}*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 := (  2,  3)(  4,  9)(  5,  8)(  6,  7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)
( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)( 33, 34)
( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)( 51, 52)
( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 65, 66)( 67, 72)( 68, 71)( 69, 70)
( 73,109)( 74,111)( 75,110)( 76,117)( 77,116)( 78,115)( 79,114)( 80,113)
( 81,112)( 82,118)( 83,120)( 84,119)( 85,126)( 86,125)( 87,124)( 88,123)
( 89,122)( 90,121)( 91,127)( 92,129)( 93,128)( 94,135)( 95,134)( 96,133)
( 97,132)( 98,131)( 99,130)(100,136)(101,138)(102,137)(103,144)(104,143)
(105,142)(106,141)(107,140)(108,139)(145,163)(146,165)(147,164)(148,171)
(149,170)(150,169)(151,168)(152,167)(153,166)(154,172)(155,174)(156,173)
(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(181,199)(182,201)
(183,200)(184,207)(185,206)(186,205)(187,204)(188,203)(189,202)(190,208)
(191,210)(192,209)(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)
(217,271)(218,273)(219,272)(220,279)(221,278)(222,277)(223,276)(224,275)
(225,274)(226,280)(227,282)(228,281)(229,288)(230,287)(231,286)(232,285)
(233,284)(234,283)(235,253)(236,255)(237,254)(238,261)(239,260)(240,259)
(241,258)(242,257)(243,256)(244,262)(245,264)(246,263)(247,270)(248,269)
(249,268)(250,267)(251,266)(252,265)(289,325)(290,327)(291,326)(292,333)
(293,332)(294,331)(295,330)(296,329)(297,328)(298,334)(299,336)(300,335)
(301,342)(302,341)(303,340)(304,339)(305,338)(306,337)(307,343)(308,345)
(309,344)(310,351)(311,350)(312,349)(313,348)(314,347)(315,346)(316,352)
(317,354)(318,353)(319,360)(320,359)(321,358)(322,357)(323,356)(324,355)
(362,363)(364,369)(365,368)(366,367)(371,372)(373,378)(374,377)(375,376)
(380,381)(382,387)(383,386)(384,385)(389,390)(391,396)(392,395)(393,394)
(398,399)(400,405)(401,404)(402,403)(407,408)(409,414)(410,413)(411,412)
(416,417)(418,423)(419,422)(420,421)(425,426)(427,432)(428,431)(429,430)
(433,487)(434,489)(435,488)(436,495)(437,494)(438,493)(439,492)(440,491)
(441,490)(442,496)(443,498)(444,497)(445,504)(446,503)(447,502)(448,501)
(449,500)(450,499)(451,469)(452,471)(453,470)(454,477)(455,476)(456,475)
(457,474)(458,473)(459,472)(460,478)(461,480)(462,479)(463,486)(464,485)
(465,484)(466,483)(467,482)(468,481)(505,523)(506,525)(507,524)(508,531)
(509,530)(510,529)(511,528)(512,527)(513,526)(514,532)(515,534)(516,533)
(517,540)(518,539)(519,538)(520,537)(521,536)(522,535)(541,559)(542,561)
(543,560)(544,567)(545,566)(546,565)(547,564)(548,563)(549,562)(550,568)
(551,570)(552,569)(553,576)(554,575)(555,574)(556,573)(557,572)(558,571);;
s2 := (  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,153)(  8,152)
(  9,151)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,162)
( 17,161)( 18,160)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)
( 25,171)( 26,170)( 27,169)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)
( 33,173)( 34,180)( 35,179)( 36,178)( 37,184)( 38,186)( 39,185)( 40,181)
( 41,183)( 42,182)( 43,189)( 44,188)( 45,187)( 46,193)( 47,195)( 48,194)
( 49,190)( 50,192)( 51,191)( 52,198)( 53,197)( 54,196)( 55,202)( 56,204)
( 57,203)( 58,199)( 59,201)( 60,200)( 61,207)( 62,206)( 63,205)( 64,211)
( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,216)( 71,215)( 72,214)
( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,225)( 80,224)
( 81,223)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)( 88,234)
( 89,233)( 90,232)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)( 96,236)
( 97,243)( 98,242)( 99,241)(100,247)(101,249)(102,248)(103,244)(104,246)
(105,245)(106,252)(107,251)(108,250)(109,256)(110,258)(111,257)(112,253)
(113,255)(114,254)(115,261)(116,260)(117,259)(118,265)(119,267)(120,266)
(121,262)(122,264)(123,263)(124,270)(125,269)(126,268)(127,274)(128,276)
(129,275)(130,271)(131,273)(132,272)(133,279)(134,278)(135,277)(136,283)
(137,285)(138,284)(139,280)(140,282)(141,281)(142,288)(143,287)(144,286)
(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,441)(296,440)
(297,439)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,450)
(305,449)(306,448)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)
(313,459)(314,458)(315,457)(316,463)(317,465)(318,464)(319,460)(320,462)
(321,461)(322,468)(323,467)(324,466)(325,472)(326,474)(327,473)(328,469)
(329,471)(330,470)(331,477)(332,476)(333,475)(334,481)(335,483)(336,482)
(337,478)(338,480)(339,479)(340,486)(341,485)(342,484)(343,490)(344,492)
(345,491)(346,487)(347,489)(348,488)(349,495)(350,494)(351,493)(352,499)
(353,501)(354,500)(355,496)(356,498)(357,497)(358,504)(359,503)(360,502)
(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,513)(368,512)
(369,511)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)(376,522)
(377,521)(378,520)(379,526)(380,528)(381,527)(382,523)(383,525)(384,524)
(385,531)(386,530)(387,529)(388,535)(389,537)(390,536)(391,532)(392,534)
(393,533)(394,540)(395,539)(396,538)(397,544)(398,546)(399,545)(400,541)
(401,543)(402,542)(403,549)(404,548)(405,547)(406,553)(407,555)(408,554)
(409,550)(410,552)(411,551)(412,558)(413,557)(414,556)(415,562)(416,564)
(417,563)(418,559)(419,561)(420,560)(421,567)(422,566)(423,565)(424,571)
(425,573)(426,572)(427,568)(428,570)(429,569)(430,576)(431,575)(432,574);;
s3 := (  1,361)(  2,362)(  3,363)(  4,364)(  5,365)(  6,366)(  7,367)(  8,368)
(  9,369)( 10,370)( 11,371)( 12,372)( 13,373)( 14,374)( 15,375)( 16,376)
( 17,377)( 18,378)( 19,379)( 20,380)( 21,381)( 22,382)( 23,383)( 24,384)
( 25,385)( 26,386)( 27,387)( 28,388)( 29,389)( 30,390)( 31,391)( 32,392)
( 33,393)( 34,394)( 35,395)( 36,396)( 37,397)( 38,398)( 39,399)( 40,400)
( 41,401)( 42,402)( 43,403)( 44,404)( 45,405)( 46,406)( 47,407)( 48,408)
( 49,409)( 50,410)( 51,411)( 52,412)( 53,413)( 54,414)( 55,415)( 56,416)
( 57,417)( 58,418)( 59,419)( 60,420)( 61,421)( 62,422)( 63,423)( 64,424)
( 65,425)( 66,426)( 67,427)( 68,428)( 69,429)( 70,430)( 71,431)( 72,432)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)
(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)
(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)
(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)
(145,514)(146,515)(147,516)(148,517)(149,518)(150,519)(151,520)(152,521)
(153,522)(154,505)(155,506)(156,507)(157,508)(158,509)(159,510)(160,511)
(161,512)(162,513)(163,532)(164,533)(165,534)(166,535)(167,536)(168,537)
(169,538)(170,539)(171,540)(172,523)(173,524)(174,525)(175,526)(176,527)
(177,528)(178,529)(179,530)(180,531)(181,550)(182,551)(183,552)(184,553)
(185,554)(186,555)(187,556)(188,557)(189,558)(190,541)(191,542)(192,543)
(193,544)(194,545)(195,546)(196,547)(197,548)(198,549)(199,568)(200,569)
(201,570)(202,571)(203,572)(204,573)(205,574)(206,575)(207,576)(208,559)
(209,560)(210,561)(211,562)(212,563)(213,564)(214,565)(215,566)(216,567)
(217,442)(218,443)(219,444)(220,445)(221,446)(222,447)(223,448)(224,449)
(225,450)(226,433)(227,434)(228,435)(229,436)(230,437)(231,438)(232,439)
(233,440)(234,441)(235,460)(236,461)(237,462)(238,463)(239,464)(240,465)
(241,466)(242,467)(243,468)(244,451)(245,452)(246,453)(247,454)(248,455)
(249,456)(250,457)(251,458)(252,459)(253,478)(254,479)(255,480)(256,481)
(257,482)(258,483)(259,484)(260,485)(261,486)(262,469)(263,470)(264,471)
(265,472)(266,473)(267,474)(268,475)(269,476)(270,477)(271,496)(272,497)
(273,498)(274,499)(275,500)(276,501)(277,502)(278,503)(279,504)(280,487)
(281,488)(282,489)(283,490)(284,491)(285,492)(286,493)(287,494)(288,495);;
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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)!(  2,  3)(  4,  9)(  5,  8)(  6,  7)( 11, 12)( 13, 18)( 14, 17)
( 15, 16)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)
( 33, 34)( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)
( 51, 52)( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 65, 66)( 67, 72)( 68, 71)
( 69, 70)( 73,109)( 74,111)( 75,110)( 76,117)( 77,116)( 78,115)( 79,114)
( 80,113)( 81,112)( 82,118)( 83,120)( 84,119)( 85,126)( 86,125)( 87,124)
( 88,123)( 89,122)( 90,121)( 91,127)( 92,129)( 93,128)( 94,135)( 95,134)
( 96,133)( 97,132)( 98,131)( 99,130)(100,136)(101,138)(102,137)(103,144)
(104,143)(105,142)(106,141)(107,140)(108,139)(145,163)(146,165)(147,164)
(148,171)(149,170)(150,169)(151,168)(152,167)(153,166)(154,172)(155,174)
(156,173)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(181,199)
(182,201)(183,200)(184,207)(185,206)(186,205)(187,204)(188,203)(189,202)
(190,208)(191,210)(192,209)(193,216)(194,215)(195,214)(196,213)(197,212)
(198,211)(217,271)(218,273)(219,272)(220,279)(221,278)(222,277)(223,276)
(224,275)(225,274)(226,280)(227,282)(228,281)(229,288)(230,287)(231,286)
(232,285)(233,284)(234,283)(235,253)(236,255)(237,254)(238,261)(239,260)
(240,259)(241,258)(242,257)(243,256)(244,262)(245,264)(246,263)(247,270)
(248,269)(249,268)(250,267)(251,266)(252,265)(289,325)(290,327)(291,326)
(292,333)(293,332)(294,331)(295,330)(296,329)(297,328)(298,334)(299,336)
(300,335)(301,342)(302,341)(303,340)(304,339)(305,338)(306,337)(307,343)
(308,345)(309,344)(310,351)(311,350)(312,349)(313,348)(314,347)(315,346)
(316,352)(317,354)(318,353)(319,360)(320,359)(321,358)(322,357)(323,356)
(324,355)(362,363)(364,369)(365,368)(366,367)(371,372)(373,378)(374,377)
(375,376)(380,381)(382,387)(383,386)(384,385)(389,390)(391,396)(392,395)
(393,394)(398,399)(400,405)(401,404)(402,403)(407,408)(409,414)(410,413)
(411,412)(416,417)(418,423)(419,422)(420,421)(425,426)(427,432)(428,431)
(429,430)(433,487)(434,489)(435,488)(436,495)(437,494)(438,493)(439,492)
(440,491)(441,490)(442,496)(443,498)(444,497)(445,504)(446,503)(447,502)
(448,501)(449,500)(450,499)(451,469)(452,471)(453,470)(454,477)(455,476)
(456,475)(457,474)(458,473)(459,472)(460,478)(461,480)(462,479)(463,486)
(464,485)(465,484)(466,483)(467,482)(468,481)(505,523)(506,525)(507,524)
(508,531)(509,530)(510,529)(511,528)(512,527)(513,526)(514,532)(515,534)
(516,533)(517,540)(518,539)(519,538)(520,537)(521,536)(522,535)(541,559)
(542,561)(543,560)(544,567)(545,566)(546,565)(547,564)(548,563)(549,562)
(550,568)(551,570)(552,569)(553,576)(554,575)(555,574)(556,573)(557,572)
(558,571);
s2 := Sym(576)!(  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,153)
(  8,152)(  9,151)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)
( 16,162)( 17,161)( 18,160)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)
( 24,164)( 25,171)( 26,170)( 27,169)( 28,175)( 29,177)( 30,176)( 31,172)
( 32,174)( 33,173)( 34,180)( 35,179)( 36,178)( 37,184)( 38,186)( 39,185)
( 40,181)( 41,183)( 42,182)( 43,189)( 44,188)( 45,187)( 46,193)( 47,195)
( 48,194)( 49,190)( 50,192)( 51,191)( 52,198)( 53,197)( 54,196)( 55,202)
( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,207)( 62,206)( 63,205)
( 64,211)( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,216)( 71,215)
( 72,214)( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,225)
( 80,224)( 81,223)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)
( 88,234)( 89,233)( 90,232)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)
( 96,236)( 97,243)( 98,242)( 99,241)(100,247)(101,249)(102,248)(103,244)
(104,246)(105,245)(106,252)(107,251)(108,250)(109,256)(110,258)(111,257)
(112,253)(113,255)(114,254)(115,261)(116,260)(117,259)(118,265)(119,267)
(120,266)(121,262)(122,264)(123,263)(124,270)(125,269)(126,268)(127,274)
(128,276)(129,275)(130,271)(131,273)(132,272)(133,279)(134,278)(135,277)
(136,283)(137,285)(138,284)(139,280)(140,282)(141,281)(142,288)(143,287)
(144,286)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,441)
(296,440)(297,439)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)
(304,450)(305,449)(306,448)(307,454)(308,456)(309,455)(310,451)(311,453)
(312,452)(313,459)(314,458)(315,457)(316,463)(317,465)(318,464)(319,460)
(320,462)(321,461)(322,468)(323,467)(324,466)(325,472)(326,474)(327,473)
(328,469)(329,471)(330,470)(331,477)(332,476)(333,475)(334,481)(335,483)
(336,482)(337,478)(338,480)(339,479)(340,486)(341,485)(342,484)(343,490)
(344,492)(345,491)(346,487)(347,489)(348,488)(349,495)(350,494)(351,493)
(352,499)(353,501)(354,500)(355,496)(356,498)(357,497)(358,504)(359,503)
(360,502)(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,513)
(368,512)(369,511)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)
(376,522)(377,521)(378,520)(379,526)(380,528)(381,527)(382,523)(383,525)
(384,524)(385,531)(386,530)(387,529)(388,535)(389,537)(390,536)(391,532)
(392,534)(393,533)(394,540)(395,539)(396,538)(397,544)(398,546)(399,545)
(400,541)(401,543)(402,542)(403,549)(404,548)(405,547)(406,553)(407,555)
(408,554)(409,550)(410,552)(411,551)(412,558)(413,557)(414,556)(415,562)
(416,564)(417,563)(418,559)(419,561)(420,560)(421,567)(422,566)(423,565)
(424,571)(425,573)(426,572)(427,568)(428,570)(429,569)(430,576)(431,575)
(432,574);
s3 := Sym(576)!(  1,361)(  2,362)(  3,363)(  4,364)(  5,365)(  6,366)(  7,367)
(  8,368)(  9,369)( 10,370)( 11,371)( 12,372)( 13,373)( 14,374)( 15,375)
( 16,376)( 17,377)( 18,378)( 19,379)( 20,380)( 21,381)( 22,382)( 23,383)
( 24,384)( 25,385)( 26,386)( 27,387)( 28,388)( 29,389)( 30,390)( 31,391)
( 32,392)( 33,393)( 34,394)( 35,395)( 36,396)( 37,397)( 38,398)( 39,399)
( 40,400)( 41,401)( 42,402)( 43,403)( 44,404)( 45,405)( 46,406)( 47,407)
( 48,408)( 49,409)( 50,410)( 51,411)( 52,412)( 53,413)( 54,414)( 55,415)
( 56,416)( 57,417)( 58,418)( 59,419)( 60,420)( 61,421)( 62,422)( 63,423)
( 64,424)( 65,425)( 66,426)( 67,427)( 68,428)( 69,429)( 70,430)( 71,431)
( 72,432)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)
(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)
(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)
(144,360)(145,514)(146,515)(147,516)(148,517)(149,518)(150,519)(151,520)
(152,521)(153,522)(154,505)(155,506)(156,507)(157,508)(158,509)(159,510)
(160,511)(161,512)(162,513)(163,532)(164,533)(165,534)(166,535)(167,536)
(168,537)(169,538)(170,539)(171,540)(172,523)(173,524)(174,525)(175,526)
(176,527)(177,528)(178,529)(179,530)(180,531)(181,550)(182,551)(183,552)
(184,553)(185,554)(186,555)(187,556)(188,557)(189,558)(190,541)(191,542)
(192,543)(193,544)(194,545)(195,546)(196,547)(197,548)(198,549)(199,568)
(200,569)(201,570)(202,571)(203,572)(204,573)(205,574)(206,575)(207,576)
(208,559)(209,560)(210,561)(211,562)(212,563)(213,564)(214,565)(215,566)
(216,567)(217,442)(218,443)(219,444)(220,445)(221,446)(222,447)(223,448)
(224,449)(225,450)(226,433)(227,434)(228,435)(229,436)(230,437)(231,438)
(232,439)(233,440)(234,441)(235,460)(236,461)(237,462)(238,463)(239,464)
(240,465)(241,466)(242,467)(243,468)(244,451)(245,452)(246,453)(247,454)
(248,455)(249,456)(250,457)(251,458)(252,459)(253,478)(254,479)(255,480)
(256,481)(257,482)(258,483)(259,484)(260,485)(261,486)(262,469)(263,470)
(264,471)(265,472)(266,473)(267,474)(268,475)(269,476)(270,477)(271,496)
(272,497)(273,498)(274,499)(275,500)(276,501)(277,502)(278,503)(279,504)
(280,487)(281,488)(282,489)(283,490)(284,491)(285,492)(286,493)(287,494)
(288,495);
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope