Polytope of Type {18,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,8,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98765)
Rank : 4
Schlafli Type : {18,8,4}
Number of vertices, edges, etc : 18, 72, 16, 4
Order of s0s1s2s3 : 72
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 : {18,4,4}*576
3-fold quotients : {6,8,4}*384b
4-fold quotients : {18,2,4}*288, {18,4,2}*288a
6-fold quotients : {6,4,4}*192
8-fold quotients : {9,2,4}*144, {18,2,2}*144
9-fold quotients : {2,8,4}*128b
12-fold quotients : {6,2,4}*96, {6,4,2}*96a
16-fold quotients : {9,2,2}*72
18-fold quotients : {2,4,4}*64
24-fold quotients : {3,2,4}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*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 := ( 1, 73)( 2, 75)( 3, 74)( 4, 81)( 5, 80)( 6, 79)( 7, 78)( 8, 77)
( 9, 76)( 10, 82)( 11, 84)( 12, 83)( 13, 90)( 14, 89)( 15, 88)( 16, 87)
( 17, 86)( 18, 85)( 19, 91)( 20, 93)( 21, 92)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28,100)( 29,102)( 30,101)( 31,108)( 32,107)
( 33,106)( 34,105)( 35,104)( 36,103)( 37,109)( 38,111)( 39,110)( 40,117)
( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,118)( 47,120)( 48,119)
( 49,126)( 50,125)( 51,124)( 52,123)( 53,122)( 54,121)( 55,127)( 56,129)
( 57,128)( 58,135)( 59,134)( 60,133)( 61,132)( 62,131)( 63,130)( 64,136)
( 65,138)( 66,137)( 67,144)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139)
(145,217)(146,219)(147,218)(148,225)(149,224)(150,223)(151,222)(152,221)
(153,220)(154,226)(155,228)(156,227)(157,234)(158,233)(159,232)(160,231)
(161,230)(162,229)(163,235)(164,237)(165,236)(166,243)(167,242)(168,241)
(169,240)(170,239)(171,238)(172,244)(173,246)(174,245)(175,252)(176,251)
(177,250)(178,249)(179,248)(180,247)(181,253)(182,255)(183,254)(184,261)
(185,260)(186,259)(187,258)(188,257)(189,256)(190,262)(191,264)(192,263)
(193,270)(194,269)(195,268)(196,267)(197,266)(198,265)(199,271)(200,273)
(201,272)(202,279)(203,278)(204,277)(205,276)(206,275)(207,274)(208,280)
(209,282)(210,281)(211,288)(212,287)(213,286)(214,285)(215,284)(216,283)
(289,361)(290,363)(291,362)(292,369)(293,368)(294,367)(295,366)(296,365)
(297,364)(298,370)(299,372)(300,371)(301,378)(302,377)(303,376)(304,375)
(305,374)(306,373)(307,379)(308,381)(309,380)(310,387)(311,386)(312,385)
(313,384)(314,383)(315,382)(316,388)(317,390)(318,389)(319,396)(320,395)
(321,394)(322,393)(323,392)(324,391)(325,397)(326,399)(327,398)(328,405)
(329,404)(330,403)(331,402)(332,401)(333,400)(334,406)(335,408)(336,407)
(337,414)(338,413)(339,412)(340,411)(341,410)(342,409)(343,415)(344,417)
(345,416)(346,423)(347,422)(348,421)(349,420)(350,419)(351,418)(352,424)
(353,426)(354,425)(355,432)(356,431)(357,430)(358,429)(359,428)(360,427)
(433,505)(434,507)(435,506)(436,513)(437,512)(438,511)(439,510)(440,509)
(441,508)(442,514)(443,516)(444,515)(445,522)(446,521)(447,520)(448,519)
(449,518)(450,517)(451,523)(452,525)(453,524)(454,531)(455,530)(456,529)
(457,528)(458,527)(459,526)(460,532)(461,534)(462,533)(463,540)(464,539)
(465,538)(466,537)(467,536)(468,535)(469,541)(470,543)(471,542)(472,549)
(473,548)(474,547)(475,546)(476,545)(477,544)(478,550)(479,552)(480,551)
(481,558)(482,557)(483,556)(484,555)(485,554)(486,553)(487,559)(488,561)
(489,560)(490,567)(491,566)(492,565)(493,564)(494,563)(495,562)(496,568)
(497,570)(498,569)(499,576)(500,575)(501,574)(502,573)(503,572)(504,571);;
s1 := ( 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)( 19,391)( 20,393)( 21,392)( 22,388)( 23,390)( 24,389)
( 25,396)( 26,395)( 27,394)( 28,382)( 29,384)( 30,383)( 31,379)( 32,381)
( 33,380)( 34,387)( 35,386)( 36,385)( 37,409)( 38,411)( 39,410)( 40,406)
( 41,408)( 42,407)( 43,414)( 44,413)( 45,412)( 46,400)( 47,402)( 48,401)
( 49,397)( 50,399)( 51,398)( 52,405)( 53,404)( 54,403)( 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)( 91,319)( 92,321)( 93,320)( 94,316)( 95,318)( 96,317)
( 97,324)( 98,323)( 99,322)(100,310)(101,312)(102,311)(103,307)(104,309)
(105,308)(106,315)(107,314)(108,313)(109,337)(110,339)(111,338)(112,334)
(113,336)(114,335)(115,342)(116,341)(117,340)(118,328)(119,330)(120,329)
(121,325)(122,327)(123,326)(124,333)(125,332)(126,331)(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)
(145,508)(146,510)(147,509)(148,505)(149,507)(150,506)(151,513)(152,512)
(153,511)(154,517)(155,519)(156,518)(157,514)(158,516)(159,515)(160,522)
(161,521)(162,520)(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)(199,562)(200,564)
(201,563)(202,559)(203,561)(204,560)(205,567)(206,566)(207,565)(208,571)
(209,573)(210,572)(211,568)(212,570)(213,569)(214,576)(215,575)(216,574)
(217,436)(218,438)(219,437)(220,433)(221,435)(222,434)(223,441)(224,440)
(225,439)(226,445)(227,447)(228,446)(229,442)(230,444)(231,443)(232,450)
(233,449)(234,448)(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)(271,490)(272,492)
(273,491)(274,487)(275,489)(276,488)(277,495)(278,494)(279,493)(280,499)
(281,501)(282,500)(283,496)(284,498)(285,497)(286,504)(287,503)(288,502);;
s2 := ( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)
( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)
( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)(114,123)
(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)(131,140)
(132,141)(133,142)(134,143)(135,144)(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)(181,208)(182,209)
(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)(190,199)
(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)(198,207)
(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)(224,242)
(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)(232,250)
(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)(258,285)
(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)(266,275)
(267,276)(268,277)(269,278)(270,279)(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)
(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)(368,404)
(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)(376,412)
(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)(384,420)
(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)(392,428)
(393,429)(394,430)(395,431)(396,432)(433,496)(434,497)(435,498)(436,499)
(437,500)(438,501)(439,502)(440,503)(441,504)(442,487)(443,488)(444,489)
(445,490)(446,491)(447,492)(448,493)(449,494)(450,495)(451,478)(452,479)
(453,480)(454,481)(455,482)(456,483)(457,484)(458,485)(459,486)(460,469)
(461,470)(462,471)(463,472)(464,473)(465,474)(466,475)(467,476)(468,477)
(505,568)(506,569)(507,570)(508,571)(509,572)(510,573)(511,574)(512,575)
(513,576)(514,559)(515,560)(516,561)(517,562)(518,563)(519,564)(520,565)
(521,566)(522,567)(523,550)(524,551)(525,552)(526,553)(527,554)(528,555)
(529,556)(530,557)(531,558)(532,541)(533,542)(534,543)(535,544)(536,545)
(537,546)(538,547)(539,548)(540,549);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
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*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)!( 1, 73)( 2, 75)( 3, 74)( 4, 81)( 5, 80)( 6, 79)( 7, 78)
( 8, 77)( 9, 76)( 10, 82)( 11, 84)( 12, 83)( 13, 90)( 14, 89)( 15, 88)
( 16, 87)( 17, 86)( 18, 85)( 19, 91)( 20, 93)( 21, 92)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28,100)( 29,102)( 30,101)( 31,108)
( 32,107)( 33,106)( 34,105)( 35,104)( 36,103)( 37,109)( 38,111)( 39,110)
( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,118)( 47,120)
( 48,119)( 49,126)( 50,125)( 51,124)( 52,123)( 53,122)( 54,121)( 55,127)
( 56,129)( 57,128)( 58,135)( 59,134)( 60,133)( 61,132)( 62,131)( 63,130)
( 64,136)( 65,138)( 66,137)( 67,144)( 68,143)( 69,142)( 70,141)( 71,140)
( 72,139)(145,217)(146,219)(147,218)(148,225)(149,224)(150,223)(151,222)
(152,221)(153,220)(154,226)(155,228)(156,227)(157,234)(158,233)(159,232)
(160,231)(161,230)(162,229)(163,235)(164,237)(165,236)(166,243)(167,242)
(168,241)(169,240)(170,239)(171,238)(172,244)(173,246)(174,245)(175,252)
(176,251)(177,250)(178,249)(179,248)(180,247)(181,253)(182,255)(183,254)
(184,261)(185,260)(186,259)(187,258)(188,257)(189,256)(190,262)(191,264)
(192,263)(193,270)(194,269)(195,268)(196,267)(197,266)(198,265)(199,271)
(200,273)(201,272)(202,279)(203,278)(204,277)(205,276)(206,275)(207,274)
(208,280)(209,282)(210,281)(211,288)(212,287)(213,286)(214,285)(215,284)
(216,283)(289,361)(290,363)(291,362)(292,369)(293,368)(294,367)(295,366)
(296,365)(297,364)(298,370)(299,372)(300,371)(301,378)(302,377)(303,376)
(304,375)(305,374)(306,373)(307,379)(308,381)(309,380)(310,387)(311,386)
(312,385)(313,384)(314,383)(315,382)(316,388)(317,390)(318,389)(319,396)
(320,395)(321,394)(322,393)(323,392)(324,391)(325,397)(326,399)(327,398)
(328,405)(329,404)(330,403)(331,402)(332,401)(333,400)(334,406)(335,408)
(336,407)(337,414)(338,413)(339,412)(340,411)(341,410)(342,409)(343,415)
(344,417)(345,416)(346,423)(347,422)(348,421)(349,420)(350,419)(351,418)
(352,424)(353,426)(354,425)(355,432)(356,431)(357,430)(358,429)(359,428)
(360,427)(433,505)(434,507)(435,506)(436,513)(437,512)(438,511)(439,510)
(440,509)(441,508)(442,514)(443,516)(444,515)(445,522)(446,521)(447,520)
(448,519)(449,518)(450,517)(451,523)(452,525)(453,524)(454,531)(455,530)
(456,529)(457,528)(458,527)(459,526)(460,532)(461,534)(462,533)(463,540)
(464,539)(465,538)(466,537)(467,536)(468,535)(469,541)(470,543)(471,542)
(472,549)(473,548)(474,547)(475,546)(476,545)(477,544)(478,550)(479,552)
(480,551)(481,558)(482,557)(483,556)(484,555)(485,554)(486,553)(487,559)
(488,561)(489,560)(490,567)(491,566)(492,565)(493,564)(494,563)(495,562)
(496,568)(497,570)(498,569)(499,576)(500,575)(501,574)(502,573)(503,572)
(504,571);
s1 := 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)( 19,391)( 20,393)( 21,392)( 22,388)( 23,390)
( 24,389)( 25,396)( 26,395)( 27,394)( 28,382)( 29,384)( 30,383)( 31,379)
( 32,381)( 33,380)( 34,387)( 35,386)( 36,385)( 37,409)( 38,411)( 39,410)
( 40,406)( 41,408)( 42,407)( 43,414)( 44,413)( 45,412)( 46,400)( 47,402)
( 48,401)( 49,397)( 50,399)( 51,398)( 52,405)( 53,404)( 54,403)( 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)( 91,319)( 92,321)( 93,320)( 94,316)( 95,318)
( 96,317)( 97,324)( 98,323)( 99,322)(100,310)(101,312)(102,311)(103,307)
(104,309)(105,308)(106,315)(107,314)(108,313)(109,337)(110,339)(111,338)
(112,334)(113,336)(114,335)(115,342)(116,341)(117,340)(118,328)(119,330)
(120,329)(121,325)(122,327)(123,326)(124,333)(125,332)(126,331)(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)(145,508)(146,510)(147,509)(148,505)(149,507)(150,506)(151,513)
(152,512)(153,511)(154,517)(155,519)(156,518)(157,514)(158,516)(159,515)
(160,522)(161,521)(162,520)(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)(199,562)
(200,564)(201,563)(202,559)(203,561)(204,560)(205,567)(206,566)(207,565)
(208,571)(209,573)(210,572)(211,568)(212,570)(213,569)(214,576)(215,575)
(216,574)(217,436)(218,438)(219,437)(220,433)(221,435)(222,434)(223,441)
(224,440)(225,439)(226,445)(227,447)(228,446)(229,442)(230,444)(231,443)
(232,450)(233,449)(234,448)(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)(271,490)
(272,492)(273,491)(274,487)(275,489)(276,488)(277,495)(278,494)(279,493)
(280,499)(281,501)(282,500)(283,496)(284,498)(285,497)(286,504)(287,503)
(288,502);
s2 := Sym(576)!( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)
( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)
( 61, 70)( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)
(114,123)(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)
(131,140)(132,141)(133,142)(134,143)(135,144)(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)(181,208)
(182,209)(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)
(190,199)(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)
(198,207)(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)
(224,242)(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)
(232,250)(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)
(258,285)(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)
(266,275)(267,276)(268,277)(269,278)(270,279)(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)(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)
(368,404)(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)
(376,412)(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)
(384,420)(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)
(392,428)(393,429)(394,430)(395,431)(396,432)(433,496)(434,497)(435,498)
(436,499)(437,500)(438,501)(439,502)(440,503)(441,504)(442,487)(443,488)
(444,489)(445,490)(446,491)(447,492)(448,493)(449,494)(450,495)(451,478)
(452,479)(453,480)(454,481)(455,482)(456,483)(457,484)(458,485)(459,486)
(460,469)(461,470)(462,471)(463,472)(464,473)(465,474)(466,475)(467,476)
(468,477)(505,568)(506,569)(507,570)(508,571)(509,572)(510,573)(511,574)
(512,575)(513,576)(514,559)(515,560)(516,561)(517,562)(518,563)(519,564)
(520,565)(521,566)(522,567)(523,550)(524,551)(525,552)(526,553)(527,554)
(528,555)(529,556)(530,557)(531,558)(532,541)(533,542)(534,543)(535,544)
(536,545)(537,546)(538,547)(539,548)(540,549);
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,
s0*s1*s2*s1*s0*s1*s2*s1, 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*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