Polytope of Type {18,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,4,4}*1152d
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 4
Schlafli Type : {18,4,4}
Number of vertices, edges, etc : 36, 72, 16, 4
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 : {9,4,4}*576b, {18,4,2}*576
3-fold quotients : {6,4,4}*384d
4-fold quotients : {18,2,4}*288, {9,4,2}*288, {18,4,2}*288b, {18,4,2}*288c
6-fold quotients : {3,4,4}*192b, {6,4,2}*192
8-fold quotients : {9,2,4}*144, {9,4,2}*144, {18,2,2}*144
12-fold quotients : {6,2,4}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
16-fold quotients : {9,2,2}*72
24-fold quotients : {3,2,4}*48, {3,4,2}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32
48-fold quotients : {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 69)( 50, 70)
( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)
( 59, 64)( 60, 63)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 85,105)
( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)( 93, 97)
( 94, 98)( 95,100)( 96, 99)(111,112)(113,117)(114,118)(115,120)(116,119)
(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)
(129,133)(130,134)(131,136)(132,135)(147,148)(149,153)(150,154)(151,156)
(152,155)(157,177)(158,178)(159,180)(160,179)(161,173)(162,174)(163,176)
(164,175)(165,169)(166,170)(167,172)(168,171)(183,184)(185,189)(186,190)
(187,192)(188,191)(193,213)(194,214)(195,216)(196,215)(197,209)(198,210)
(199,212)(200,211)(201,205)(202,206)(203,208)(204,207)(219,220)(221,225)
(222,226)(223,228)(224,227)(229,249)(230,250)(231,252)(232,251)(233,245)
(234,246)(235,248)(236,247)(237,241)(238,242)(239,244)(240,243)(255,256)
(257,261)(258,262)(259,264)(260,263)(265,285)(266,286)(267,288)(268,287)
(269,281)(270,282)(271,284)(272,283)(273,277)(274,278)(275,280)(276,279)
(291,292)(293,297)(294,298)(295,300)(296,299)(301,321)(302,322)(303,324)
(304,323)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)
(312,315)(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)
(339,360)(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)
(347,352)(348,351)(363,364)(365,369)(366,370)(367,372)(368,371)(373,393)
(374,394)(375,396)(376,395)(377,389)(378,390)(379,392)(380,391)(381,385)
(382,386)(383,388)(384,387)(399,400)(401,405)(402,406)(403,408)(404,407)
(409,429)(410,430)(411,432)(412,431)(413,425)(414,426)(415,428)(416,427)
(417,421)(418,422)(419,424)(420,423)(435,436)(437,441)(438,442)(439,444)
(440,443)(445,465)(446,466)(447,468)(448,467)(449,461)(450,462)(451,464)
(452,463)(453,457)(454,458)(455,460)(456,459)(471,472)(473,477)(474,478)
(475,480)(476,479)(481,501)(482,502)(483,504)(484,503)(485,497)(486,498)
(487,500)(488,499)(489,493)(490,494)(491,496)(492,495)(507,508)(509,513)
(510,514)(511,516)(512,515)(517,537)(518,538)(519,540)(520,539)(521,533)
(522,534)(523,536)(524,535)(525,529)(526,530)(527,532)(528,531)(543,544)
(545,549)(546,550)(547,552)(548,551)(553,573)(554,574)(555,576)(556,575)
(557,569)(558,570)(559,572)(560,571)(561,565)(562,566)(563,568)(564,567);;
s1 := ( 1,301)( 2,304)( 3,303)( 4,302)( 5,309)( 6,312)( 7,311)( 8,310)
( 9,305)( 10,308)( 11,307)( 12,306)( 13,289)( 14,292)( 15,291)( 16,290)
( 17,297)( 18,300)( 19,299)( 20,298)( 21,293)( 22,296)( 23,295)( 24,294)
( 25,321)( 26,324)( 27,323)( 28,322)( 29,317)( 30,320)( 31,319)( 32,318)
( 33,313)( 34,316)( 35,315)( 36,314)( 37,337)( 38,340)( 39,339)( 40,338)
( 41,345)( 42,348)( 43,347)( 44,346)( 45,341)( 46,344)( 47,343)( 48,342)
( 49,325)( 50,328)( 51,327)( 52,326)( 53,333)( 54,336)( 55,335)( 56,334)
( 57,329)( 58,332)( 59,331)( 60,330)( 61,357)( 62,360)( 63,359)( 64,358)
( 65,353)( 66,356)( 67,355)( 68,354)( 69,349)( 70,352)( 71,351)( 72,350)
( 73,373)( 74,376)( 75,375)( 76,374)( 77,381)( 78,384)( 79,383)( 80,382)
( 81,377)( 82,380)( 83,379)( 84,378)( 85,361)( 86,364)( 87,363)( 88,362)
( 89,369)( 90,372)( 91,371)( 92,370)( 93,365)( 94,368)( 95,367)( 96,366)
( 97,393)( 98,396)( 99,395)(100,394)(101,389)(102,392)(103,391)(104,390)
(105,385)(106,388)(107,387)(108,386)(109,409)(110,412)(111,411)(112,410)
(113,417)(114,420)(115,419)(116,418)(117,413)(118,416)(119,415)(120,414)
(121,397)(122,400)(123,399)(124,398)(125,405)(126,408)(127,407)(128,406)
(129,401)(130,404)(131,403)(132,402)(133,429)(134,432)(135,431)(136,430)
(137,425)(138,428)(139,427)(140,426)(141,421)(142,424)(143,423)(144,422)
(145,445)(146,448)(147,447)(148,446)(149,453)(150,456)(151,455)(152,454)
(153,449)(154,452)(155,451)(156,450)(157,433)(158,436)(159,435)(160,434)
(161,441)(162,444)(163,443)(164,442)(165,437)(166,440)(167,439)(168,438)
(169,465)(170,468)(171,467)(172,466)(173,461)(174,464)(175,463)(176,462)
(177,457)(178,460)(179,459)(180,458)(181,481)(182,484)(183,483)(184,482)
(185,489)(186,492)(187,491)(188,490)(189,485)(190,488)(191,487)(192,486)
(193,469)(194,472)(195,471)(196,470)(197,477)(198,480)(199,479)(200,478)
(201,473)(202,476)(203,475)(204,474)(205,501)(206,504)(207,503)(208,502)
(209,497)(210,500)(211,499)(212,498)(213,493)(214,496)(215,495)(216,494)
(217,517)(218,520)(219,519)(220,518)(221,525)(222,528)(223,527)(224,526)
(225,521)(226,524)(227,523)(228,522)(229,505)(230,508)(231,507)(232,506)
(233,513)(234,516)(235,515)(236,514)(237,509)(238,512)(239,511)(240,510)
(241,537)(242,540)(243,539)(244,538)(245,533)(246,536)(247,535)(248,534)
(249,529)(250,532)(251,531)(252,530)(253,553)(254,556)(255,555)(256,554)
(257,561)(258,564)(259,563)(260,562)(261,557)(262,560)(263,559)(264,558)
(265,541)(266,544)(267,543)(268,542)(269,549)(270,552)(271,551)(272,550)
(273,545)(274,548)(275,547)(276,546)(277,573)(278,576)(279,575)(280,574)
(281,569)(282,572)(283,571)(284,570)(285,565)(286,568)(287,567)(288,566);;
s2 := ( 1,146)( 2,145)( 3,148)( 4,147)( 5,150)( 6,149)( 7,152)( 8,151)
( 9,154)( 10,153)( 11,156)( 12,155)( 13,158)( 14,157)( 15,160)( 16,159)
( 17,162)( 18,161)( 19,164)( 20,163)( 21,166)( 22,165)( 23,168)( 24,167)
( 25,170)( 26,169)( 27,172)( 28,171)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,178)( 34,177)( 35,180)( 36,179)( 37,182)( 38,181)( 39,184)( 40,183)
( 41,186)( 42,185)( 43,188)( 44,187)( 45,190)( 46,189)( 47,192)( 48,191)
( 49,194)( 50,193)( 51,196)( 52,195)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,202)( 58,201)( 59,204)( 60,203)( 61,206)( 62,205)( 63,208)( 64,207)
( 65,210)( 66,209)( 67,212)( 68,211)( 69,214)( 70,213)( 71,216)( 72,215)
( 73,254)( 74,253)( 75,256)( 76,255)( 77,258)( 78,257)( 79,260)( 80,259)
( 81,262)( 82,261)( 83,264)( 84,263)( 85,266)( 86,265)( 87,268)( 88,267)
( 89,270)( 90,269)( 91,272)( 92,271)( 93,274)( 94,273)( 95,276)( 96,275)
( 97,278)( 98,277)( 99,280)(100,279)(101,282)(102,281)(103,284)(104,283)
(105,286)(106,285)(107,288)(108,287)(109,218)(110,217)(111,220)(112,219)
(113,222)(114,221)(115,224)(116,223)(117,226)(118,225)(119,228)(120,227)
(121,230)(122,229)(123,232)(124,231)(125,234)(126,233)(127,236)(128,235)
(129,238)(130,237)(131,240)(132,239)(133,242)(134,241)(135,244)(136,243)
(137,246)(138,245)(139,248)(140,247)(141,250)(142,249)(143,252)(144,251)
(289,434)(290,433)(291,436)(292,435)(293,438)(294,437)(295,440)(296,439)
(297,442)(298,441)(299,444)(300,443)(301,446)(302,445)(303,448)(304,447)
(305,450)(306,449)(307,452)(308,451)(309,454)(310,453)(311,456)(312,455)
(313,458)(314,457)(315,460)(316,459)(317,462)(318,461)(319,464)(320,463)
(321,466)(322,465)(323,468)(324,467)(325,470)(326,469)(327,472)(328,471)
(329,474)(330,473)(331,476)(332,475)(333,478)(334,477)(335,480)(336,479)
(337,482)(338,481)(339,484)(340,483)(341,486)(342,485)(343,488)(344,487)
(345,490)(346,489)(347,492)(348,491)(349,494)(350,493)(351,496)(352,495)
(353,498)(354,497)(355,500)(356,499)(357,502)(358,501)(359,504)(360,503)
(361,542)(362,541)(363,544)(364,543)(365,546)(366,545)(367,548)(368,547)
(369,550)(370,549)(371,552)(372,551)(373,554)(374,553)(375,556)(376,555)
(377,558)(378,557)(379,560)(380,559)(381,562)(382,561)(383,564)(384,563)
(385,566)(386,565)(387,568)(388,567)(389,570)(390,569)(391,572)(392,571)
(393,574)(394,573)(395,576)(396,575)(397,506)(398,505)(399,508)(400,507)
(401,510)(402,509)(403,512)(404,511)(405,514)(406,513)(407,516)(408,515)
(409,518)(410,517)(411,520)(412,519)(413,522)(414,521)(415,524)(416,523)
(417,526)(418,525)(419,528)(420,527)(421,530)(422,529)(423,532)(424,531)
(425,534)(426,533)(427,536)(428,535)(429,538)(430,537)(431,540)(432,539);;
s3 := ( 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);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 69)
( 50, 70)( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)
( 58, 62)( 59, 64)( 60, 63)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)
( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)
( 93, 97)( 94, 98)( 95,100)( 96, 99)(111,112)(113,117)(114,118)(115,120)
(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)
(128,139)(129,133)(130,134)(131,136)(132,135)(147,148)(149,153)(150,154)
(151,156)(152,155)(157,177)(158,178)(159,180)(160,179)(161,173)(162,174)
(163,176)(164,175)(165,169)(166,170)(167,172)(168,171)(183,184)(185,189)
(186,190)(187,192)(188,191)(193,213)(194,214)(195,216)(196,215)(197,209)
(198,210)(199,212)(200,211)(201,205)(202,206)(203,208)(204,207)(219,220)
(221,225)(222,226)(223,228)(224,227)(229,249)(230,250)(231,252)(232,251)
(233,245)(234,246)(235,248)(236,247)(237,241)(238,242)(239,244)(240,243)
(255,256)(257,261)(258,262)(259,264)(260,263)(265,285)(266,286)(267,288)
(268,287)(269,281)(270,282)(271,284)(272,283)(273,277)(274,278)(275,280)
(276,279)(291,292)(293,297)(294,298)(295,300)(296,299)(301,321)(302,322)
(303,324)(304,323)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)
(311,316)(312,315)(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)
(338,358)(339,360)(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)
(346,350)(347,352)(348,351)(363,364)(365,369)(366,370)(367,372)(368,371)
(373,393)(374,394)(375,396)(376,395)(377,389)(378,390)(379,392)(380,391)
(381,385)(382,386)(383,388)(384,387)(399,400)(401,405)(402,406)(403,408)
(404,407)(409,429)(410,430)(411,432)(412,431)(413,425)(414,426)(415,428)
(416,427)(417,421)(418,422)(419,424)(420,423)(435,436)(437,441)(438,442)
(439,444)(440,443)(445,465)(446,466)(447,468)(448,467)(449,461)(450,462)
(451,464)(452,463)(453,457)(454,458)(455,460)(456,459)(471,472)(473,477)
(474,478)(475,480)(476,479)(481,501)(482,502)(483,504)(484,503)(485,497)
(486,498)(487,500)(488,499)(489,493)(490,494)(491,496)(492,495)(507,508)
(509,513)(510,514)(511,516)(512,515)(517,537)(518,538)(519,540)(520,539)
(521,533)(522,534)(523,536)(524,535)(525,529)(526,530)(527,532)(528,531)
(543,544)(545,549)(546,550)(547,552)(548,551)(553,573)(554,574)(555,576)
(556,575)(557,569)(558,570)(559,572)(560,571)(561,565)(562,566)(563,568)
(564,567);
s1 := Sym(576)!( 1,301)( 2,304)( 3,303)( 4,302)( 5,309)( 6,312)( 7,311)
( 8,310)( 9,305)( 10,308)( 11,307)( 12,306)( 13,289)( 14,292)( 15,291)
( 16,290)( 17,297)( 18,300)( 19,299)( 20,298)( 21,293)( 22,296)( 23,295)
( 24,294)( 25,321)( 26,324)( 27,323)( 28,322)( 29,317)( 30,320)( 31,319)
( 32,318)( 33,313)( 34,316)( 35,315)( 36,314)( 37,337)( 38,340)( 39,339)
( 40,338)( 41,345)( 42,348)( 43,347)( 44,346)( 45,341)( 46,344)( 47,343)
( 48,342)( 49,325)( 50,328)( 51,327)( 52,326)( 53,333)( 54,336)( 55,335)
( 56,334)( 57,329)( 58,332)( 59,331)( 60,330)( 61,357)( 62,360)( 63,359)
( 64,358)( 65,353)( 66,356)( 67,355)( 68,354)( 69,349)( 70,352)( 71,351)
( 72,350)( 73,373)( 74,376)( 75,375)( 76,374)( 77,381)( 78,384)( 79,383)
( 80,382)( 81,377)( 82,380)( 83,379)( 84,378)( 85,361)( 86,364)( 87,363)
( 88,362)( 89,369)( 90,372)( 91,371)( 92,370)( 93,365)( 94,368)( 95,367)
( 96,366)( 97,393)( 98,396)( 99,395)(100,394)(101,389)(102,392)(103,391)
(104,390)(105,385)(106,388)(107,387)(108,386)(109,409)(110,412)(111,411)
(112,410)(113,417)(114,420)(115,419)(116,418)(117,413)(118,416)(119,415)
(120,414)(121,397)(122,400)(123,399)(124,398)(125,405)(126,408)(127,407)
(128,406)(129,401)(130,404)(131,403)(132,402)(133,429)(134,432)(135,431)
(136,430)(137,425)(138,428)(139,427)(140,426)(141,421)(142,424)(143,423)
(144,422)(145,445)(146,448)(147,447)(148,446)(149,453)(150,456)(151,455)
(152,454)(153,449)(154,452)(155,451)(156,450)(157,433)(158,436)(159,435)
(160,434)(161,441)(162,444)(163,443)(164,442)(165,437)(166,440)(167,439)
(168,438)(169,465)(170,468)(171,467)(172,466)(173,461)(174,464)(175,463)
(176,462)(177,457)(178,460)(179,459)(180,458)(181,481)(182,484)(183,483)
(184,482)(185,489)(186,492)(187,491)(188,490)(189,485)(190,488)(191,487)
(192,486)(193,469)(194,472)(195,471)(196,470)(197,477)(198,480)(199,479)
(200,478)(201,473)(202,476)(203,475)(204,474)(205,501)(206,504)(207,503)
(208,502)(209,497)(210,500)(211,499)(212,498)(213,493)(214,496)(215,495)
(216,494)(217,517)(218,520)(219,519)(220,518)(221,525)(222,528)(223,527)
(224,526)(225,521)(226,524)(227,523)(228,522)(229,505)(230,508)(231,507)
(232,506)(233,513)(234,516)(235,515)(236,514)(237,509)(238,512)(239,511)
(240,510)(241,537)(242,540)(243,539)(244,538)(245,533)(246,536)(247,535)
(248,534)(249,529)(250,532)(251,531)(252,530)(253,553)(254,556)(255,555)
(256,554)(257,561)(258,564)(259,563)(260,562)(261,557)(262,560)(263,559)
(264,558)(265,541)(266,544)(267,543)(268,542)(269,549)(270,552)(271,551)
(272,550)(273,545)(274,548)(275,547)(276,546)(277,573)(278,576)(279,575)
(280,574)(281,569)(282,572)(283,571)(284,570)(285,565)(286,568)(287,567)
(288,566);
s2 := Sym(576)!( 1,146)( 2,145)( 3,148)( 4,147)( 5,150)( 6,149)( 7,152)
( 8,151)( 9,154)( 10,153)( 11,156)( 12,155)( 13,158)( 14,157)( 15,160)
( 16,159)( 17,162)( 18,161)( 19,164)( 20,163)( 21,166)( 22,165)( 23,168)
( 24,167)( 25,170)( 26,169)( 27,172)( 28,171)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,178)( 34,177)( 35,180)( 36,179)( 37,182)( 38,181)( 39,184)
( 40,183)( 41,186)( 42,185)( 43,188)( 44,187)( 45,190)( 46,189)( 47,192)
( 48,191)( 49,194)( 50,193)( 51,196)( 52,195)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,202)( 58,201)( 59,204)( 60,203)( 61,206)( 62,205)( 63,208)
( 64,207)( 65,210)( 66,209)( 67,212)( 68,211)( 69,214)( 70,213)( 71,216)
( 72,215)( 73,254)( 74,253)( 75,256)( 76,255)( 77,258)( 78,257)( 79,260)
( 80,259)( 81,262)( 82,261)( 83,264)( 84,263)( 85,266)( 86,265)( 87,268)
( 88,267)( 89,270)( 90,269)( 91,272)( 92,271)( 93,274)( 94,273)( 95,276)
( 96,275)( 97,278)( 98,277)( 99,280)(100,279)(101,282)(102,281)(103,284)
(104,283)(105,286)(106,285)(107,288)(108,287)(109,218)(110,217)(111,220)
(112,219)(113,222)(114,221)(115,224)(116,223)(117,226)(118,225)(119,228)
(120,227)(121,230)(122,229)(123,232)(124,231)(125,234)(126,233)(127,236)
(128,235)(129,238)(130,237)(131,240)(132,239)(133,242)(134,241)(135,244)
(136,243)(137,246)(138,245)(139,248)(140,247)(141,250)(142,249)(143,252)
(144,251)(289,434)(290,433)(291,436)(292,435)(293,438)(294,437)(295,440)
(296,439)(297,442)(298,441)(299,444)(300,443)(301,446)(302,445)(303,448)
(304,447)(305,450)(306,449)(307,452)(308,451)(309,454)(310,453)(311,456)
(312,455)(313,458)(314,457)(315,460)(316,459)(317,462)(318,461)(319,464)
(320,463)(321,466)(322,465)(323,468)(324,467)(325,470)(326,469)(327,472)
(328,471)(329,474)(330,473)(331,476)(332,475)(333,478)(334,477)(335,480)
(336,479)(337,482)(338,481)(339,484)(340,483)(341,486)(342,485)(343,488)
(344,487)(345,490)(346,489)(347,492)(348,491)(349,494)(350,493)(351,496)
(352,495)(353,498)(354,497)(355,500)(356,499)(357,502)(358,501)(359,504)
(360,503)(361,542)(362,541)(363,544)(364,543)(365,546)(366,545)(367,548)
(368,547)(369,550)(370,549)(371,552)(372,551)(373,554)(374,553)(375,556)
(376,555)(377,558)(378,557)(379,560)(380,559)(381,562)(382,561)(383,564)
(384,563)(385,566)(386,565)(387,568)(388,567)(389,570)(390,569)(391,572)
(392,571)(393,574)(394,573)(395,576)(396,575)(397,506)(398,505)(399,508)
(400,507)(401,510)(402,509)(403,512)(404,511)(405,514)(406,513)(407,516)
(408,515)(409,518)(410,517)(411,520)(412,519)(413,522)(414,521)(415,524)
(416,523)(417,526)(418,525)(419,528)(420,527)(421,530)(422,529)(423,532)
(424,531)(425,534)(426,533)(427,536)(428,535)(429,538)(430,537)(431,540)
(432,539);
s3 := 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);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope