Polytope of Type {4,72}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,72}*1152c
if this polytope has a name.
Group : SmallGroup(1152,154349)
Rank : 3
Schlafli Type : {4,72}
Number of vertices, edges, etc : 8, 288, 144
Order of s0s1s2 : 72
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {4,72}*576c, {4,72}*576d, {4,36}*576b
3-fold quotients : {4,24}*384c
4-fold quotients : {2,72}*288, {4,36}*288b, {4,36}*288c, {4,18}*288
6-fold quotients : {4,24}*192c, {4,24}*192d, {4,12}*192b
8-fold quotients : {2,36}*144, {4,9}*144, {4,18}*144b, {4,18}*144c
12-fold quotients : {2,24}*96, {4,12}*96b, {4,12}*96c, {4,6}*96
16-fold quotients : {4,9}*72, {2,18}*72
24-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
32-fold quotients : {2,9}*36
36-fold quotients : {2,8}*32
48-fold quotients : {4,3}*24, {2,6}*24
72-fold quotients : {2,4}*16
96-fold quotients : {2,3}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,291)( 2,292)( 3,289)( 4,290)( 5,295)( 6,296)( 7,293)( 8,294)
( 9,299)( 10,300)( 11,297)( 12,298)( 13,303)( 14,304)( 15,301)( 16,302)
( 17,307)( 18,308)( 19,305)( 20,306)( 21,311)( 22,312)( 23,309)( 24,310)
( 25,315)( 26,316)( 27,313)( 28,314)( 29,319)( 30,320)( 31,317)( 32,318)
( 33,323)( 34,324)( 35,321)( 36,322)( 37,327)( 38,328)( 39,325)( 40,326)
( 41,331)( 42,332)( 43,329)( 44,330)( 45,335)( 46,336)( 47,333)( 48,334)
( 49,339)( 50,340)( 51,337)( 52,338)( 53,343)( 54,344)( 55,341)( 56,342)
( 57,347)( 58,348)( 59,345)( 60,346)( 61,351)( 62,352)( 63,349)( 64,350)
( 65,355)( 66,356)( 67,353)( 68,354)( 69,359)( 70,360)( 71,357)( 72,358)
( 73,363)( 74,364)( 75,361)( 76,362)( 77,367)( 78,368)( 79,365)( 80,366)
( 81,371)( 82,372)( 83,369)( 84,370)( 85,375)( 86,376)( 87,373)( 88,374)
( 89,379)( 90,380)( 91,377)( 92,378)( 93,383)( 94,384)( 95,381)( 96,382)
( 97,387)( 98,388)( 99,385)(100,386)(101,391)(102,392)(103,389)(104,390)
(105,395)(106,396)(107,393)(108,394)(109,399)(110,400)(111,397)(112,398)
(113,403)(114,404)(115,401)(116,402)(117,407)(118,408)(119,405)(120,406)
(121,411)(122,412)(123,409)(124,410)(125,415)(126,416)(127,413)(128,414)
(129,419)(130,420)(131,417)(132,418)(133,423)(134,424)(135,421)(136,422)
(137,427)(138,428)(139,425)(140,426)(141,431)(142,432)(143,429)(144,430)
(145,435)(146,436)(147,433)(148,434)(149,439)(150,440)(151,437)(152,438)
(153,443)(154,444)(155,441)(156,442)(157,447)(158,448)(159,445)(160,446)
(161,451)(162,452)(163,449)(164,450)(165,455)(166,456)(167,453)(168,454)
(169,459)(170,460)(171,457)(172,458)(173,463)(174,464)(175,461)(176,462)
(177,467)(178,468)(179,465)(180,466)(181,471)(182,472)(183,469)(184,470)
(185,475)(186,476)(187,473)(188,474)(189,479)(190,480)(191,477)(192,478)
(193,483)(194,484)(195,481)(196,482)(197,487)(198,488)(199,485)(200,486)
(201,491)(202,492)(203,489)(204,490)(205,495)(206,496)(207,493)(208,494)
(209,499)(210,500)(211,497)(212,498)(213,503)(214,504)(215,501)(216,502)
(217,507)(218,508)(219,505)(220,506)(221,511)(222,512)(223,509)(224,510)
(225,515)(226,516)(227,513)(228,514)(229,519)(230,520)(231,517)(232,518)
(233,523)(234,524)(235,521)(236,522)(237,527)(238,528)(239,525)(240,526)
(241,531)(242,532)(243,529)(244,530)(245,535)(246,536)(247,533)(248,534)
(249,539)(250,540)(251,537)(252,538)(253,543)(254,544)(255,541)(256,542)
(257,547)(258,548)(259,545)(260,546)(261,551)(262,552)(263,549)(264,550)
(265,555)(266,556)(267,553)(268,554)(269,559)(270,560)(271,557)(272,558)
(273,563)(274,564)(275,561)(276,562)(277,567)(278,568)(279,565)(280,566)
(281,571)(282,572)(283,569)(284,570)(285,575)(286,576)(287,573)(288,574);;
s1 := ( 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)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)( 78,118)
( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,141)( 86,142)
( 87,144)( 88,143)( 89,137)( 90,138)( 91,140)( 92,139)( 93,133)( 94,134)
( 95,136)( 96,135)( 97,129)( 98,130)( 99,132)(100,131)(101,125)(102,126)
(103,128)(104,127)(105,121)(106,122)(107,124)(108,123)(145,217)(146,218)
(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)(154,222)
(155,224)(156,223)(157,249)(158,250)(159,252)(160,251)(161,245)(162,246)
(163,248)(164,247)(165,241)(166,242)(167,244)(168,243)(169,237)(170,238)
(171,240)(172,239)(173,233)(174,234)(175,236)(176,235)(177,229)(178,230)
(179,232)(180,231)(181,253)(182,254)(183,256)(184,255)(185,261)(186,262)
(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,285)(194,286)
(195,288)(196,287)(197,281)(198,282)(199,284)(200,283)(201,277)(202,278)
(203,280)(204,279)(205,273)(206,274)(207,276)(208,275)(209,269)(210,270)
(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)(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)
(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)
(369,401)(370,402)(371,404)(372,403)(373,429)(374,430)(375,432)(376,431)
(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)(384,423)
(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)
(393,409)(394,410)(395,412)(396,411)(433,505)(434,506)(435,508)(436,507)
(437,513)(438,514)(439,516)(440,515)(441,509)(442,510)(443,512)(444,511)
(445,537)(446,538)(447,540)(448,539)(449,533)(450,534)(451,536)(452,535)
(453,529)(454,530)(455,532)(456,531)(457,525)(458,526)(459,528)(460,527)
(461,521)(462,522)(463,524)(464,523)(465,517)(466,518)(467,520)(468,519)
(469,541)(470,542)(471,544)(472,543)(473,549)(474,550)(475,552)(476,551)
(477,545)(478,546)(479,548)(480,547)(481,573)(482,574)(483,576)(484,575)
(485,569)(486,570)(487,572)(488,571)(489,565)(490,566)(491,568)(492,567)
(493,561)(494,562)(495,564)(496,563)(497,557)(498,558)(499,560)(500,559)
(501,553)(502,554)(503,556)(504,555);;
s2 := ( 1,157)( 2,160)( 3,159)( 4,158)( 5,165)( 6,168)( 7,167)( 8,166)
( 9,161)( 10,164)( 11,163)( 12,162)( 13,145)( 14,148)( 15,147)( 16,146)
( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)( 24,150)
( 25,177)( 26,180)( 27,179)( 28,178)( 29,173)( 30,176)( 31,175)( 32,174)
( 33,169)( 34,172)( 35,171)( 36,170)( 37,193)( 38,196)( 39,195)( 40,194)
( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)( 48,198)
( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)( 56,190)
( 57,185)( 58,188)( 59,187)( 60,186)( 61,213)( 62,216)( 63,215)( 64,214)
( 65,209)( 66,212)( 67,211)( 68,210)( 69,205)( 70,208)( 71,207)( 72,206)
( 73,265)( 74,268)( 75,267)( 76,266)( 77,273)( 78,276)( 79,275)( 80,274)
( 81,269)( 82,272)( 83,271)( 84,270)( 85,253)( 86,256)( 87,255)( 88,254)
( 89,261)( 90,264)( 91,263)( 92,262)( 93,257)( 94,260)( 95,259)( 96,258)
( 97,285)( 98,288)( 99,287)(100,286)(101,281)(102,284)(103,283)(104,282)
(105,277)(106,280)(107,279)(108,278)(109,229)(110,232)(111,231)(112,230)
(113,237)(114,240)(115,239)(116,238)(117,233)(118,236)(119,235)(120,234)
(121,217)(122,220)(123,219)(124,218)(125,225)(126,228)(127,227)(128,226)
(129,221)(130,224)(131,223)(132,222)(133,249)(134,252)(135,251)(136,250)
(137,245)(138,248)(139,247)(140,246)(141,241)(142,244)(143,243)(144,242)
(289,445)(290,448)(291,447)(292,446)(293,453)(294,456)(295,455)(296,454)
(297,449)(298,452)(299,451)(300,450)(301,433)(302,436)(303,435)(304,434)
(305,441)(306,444)(307,443)(308,442)(309,437)(310,440)(311,439)(312,438)
(313,465)(314,468)(315,467)(316,466)(317,461)(318,464)(319,463)(320,462)
(321,457)(322,460)(323,459)(324,458)(325,481)(326,484)(327,483)(328,482)
(329,489)(330,492)(331,491)(332,490)(333,485)(334,488)(335,487)(336,486)
(337,469)(338,472)(339,471)(340,470)(341,477)(342,480)(343,479)(344,478)
(345,473)(346,476)(347,475)(348,474)(349,501)(350,504)(351,503)(352,502)
(353,497)(354,500)(355,499)(356,498)(357,493)(358,496)(359,495)(360,494)
(361,553)(362,556)(363,555)(364,554)(365,561)(366,564)(367,563)(368,562)
(369,557)(370,560)(371,559)(372,558)(373,541)(374,544)(375,543)(376,542)
(377,549)(378,552)(379,551)(380,550)(381,545)(382,548)(383,547)(384,546)
(385,573)(386,576)(387,575)(388,574)(389,569)(390,572)(391,571)(392,570)
(393,565)(394,568)(395,567)(396,566)(397,517)(398,520)(399,519)(400,518)
(401,525)(402,528)(403,527)(404,526)(405,521)(406,524)(407,523)(408,522)
(409,505)(410,508)(411,507)(412,506)(413,513)(414,516)(415,515)(416,514)
(417,509)(418,512)(419,511)(420,510)(421,537)(422,540)(423,539)(424,538)
(425,533)(426,536)(427,535)(428,534)(429,529)(430,532)(431,531)(432,530);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
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*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)!( 1,291)( 2,292)( 3,289)( 4,290)( 5,295)( 6,296)( 7,293)
( 8,294)( 9,299)( 10,300)( 11,297)( 12,298)( 13,303)( 14,304)( 15,301)
( 16,302)( 17,307)( 18,308)( 19,305)( 20,306)( 21,311)( 22,312)( 23,309)
( 24,310)( 25,315)( 26,316)( 27,313)( 28,314)( 29,319)( 30,320)( 31,317)
( 32,318)( 33,323)( 34,324)( 35,321)( 36,322)( 37,327)( 38,328)( 39,325)
( 40,326)( 41,331)( 42,332)( 43,329)( 44,330)( 45,335)( 46,336)( 47,333)
( 48,334)( 49,339)( 50,340)( 51,337)( 52,338)( 53,343)( 54,344)( 55,341)
( 56,342)( 57,347)( 58,348)( 59,345)( 60,346)( 61,351)( 62,352)( 63,349)
( 64,350)( 65,355)( 66,356)( 67,353)( 68,354)( 69,359)( 70,360)( 71,357)
( 72,358)( 73,363)( 74,364)( 75,361)( 76,362)( 77,367)( 78,368)( 79,365)
( 80,366)( 81,371)( 82,372)( 83,369)( 84,370)( 85,375)( 86,376)( 87,373)
( 88,374)( 89,379)( 90,380)( 91,377)( 92,378)( 93,383)( 94,384)( 95,381)
( 96,382)( 97,387)( 98,388)( 99,385)(100,386)(101,391)(102,392)(103,389)
(104,390)(105,395)(106,396)(107,393)(108,394)(109,399)(110,400)(111,397)
(112,398)(113,403)(114,404)(115,401)(116,402)(117,407)(118,408)(119,405)
(120,406)(121,411)(122,412)(123,409)(124,410)(125,415)(126,416)(127,413)
(128,414)(129,419)(130,420)(131,417)(132,418)(133,423)(134,424)(135,421)
(136,422)(137,427)(138,428)(139,425)(140,426)(141,431)(142,432)(143,429)
(144,430)(145,435)(146,436)(147,433)(148,434)(149,439)(150,440)(151,437)
(152,438)(153,443)(154,444)(155,441)(156,442)(157,447)(158,448)(159,445)
(160,446)(161,451)(162,452)(163,449)(164,450)(165,455)(166,456)(167,453)
(168,454)(169,459)(170,460)(171,457)(172,458)(173,463)(174,464)(175,461)
(176,462)(177,467)(178,468)(179,465)(180,466)(181,471)(182,472)(183,469)
(184,470)(185,475)(186,476)(187,473)(188,474)(189,479)(190,480)(191,477)
(192,478)(193,483)(194,484)(195,481)(196,482)(197,487)(198,488)(199,485)
(200,486)(201,491)(202,492)(203,489)(204,490)(205,495)(206,496)(207,493)
(208,494)(209,499)(210,500)(211,497)(212,498)(213,503)(214,504)(215,501)
(216,502)(217,507)(218,508)(219,505)(220,506)(221,511)(222,512)(223,509)
(224,510)(225,515)(226,516)(227,513)(228,514)(229,519)(230,520)(231,517)
(232,518)(233,523)(234,524)(235,521)(236,522)(237,527)(238,528)(239,525)
(240,526)(241,531)(242,532)(243,529)(244,530)(245,535)(246,536)(247,533)
(248,534)(249,539)(250,540)(251,537)(252,538)(253,543)(254,544)(255,541)
(256,542)(257,547)(258,548)(259,545)(260,546)(261,551)(262,552)(263,549)
(264,550)(265,555)(266,556)(267,553)(268,554)(269,559)(270,560)(271,557)
(272,558)(273,563)(274,564)(275,561)(276,562)(277,567)(278,568)(279,565)
(280,566)(281,571)(282,572)(283,569)(284,570)(285,575)(286,576)(287,573)
(288,574);
s1 := 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)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)
( 78,118)( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,141)
( 86,142)( 87,144)( 88,143)( 89,137)( 90,138)( 91,140)( 92,139)( 93,133)
( 94,134)( 95,136)( 96,135)( 97,129)( 98,130)( 99,132)(100,131)(101,125)
(102,126)(103,128)(104,127)(105,121)(106,122)(107,124)(108,123)(145,217)
(146,218)(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)
(154,222)(155,224)(156,223)(157,249)(158,250)(159,252)(160,251)(161,245)
(162,246)(163,248)(164,247)(165,241)(166,242)(167,244)(168,243)(169,237)
(170,238)(171,240)(172,239)(173,233)(174,234)(175,236)(176,235)(177,229)
(178,230)(179,232)(180,231)(181,253)(182,254)(183,256)(184,255)(185,261)
(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,285)
(194,286)(195,288)(196,287)(197,281)(198,282)(199,284)(200,283)(201,277)
(202,278)(203,280)(204,279)(205,273)(206,274)(207,276)(208,275)(209,269)
(210,270)(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)(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)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)
(368,407)(369,401)(370,402)(371,404)(372,403)(373,429)(374,430)(375,432)
(376,431)(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)
(384,423)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)
(392,415)(393,409)(394,410)(395,412)(396,411)(433,505)(434,506)(435,508)
(436,507)(437,513)(438,514)(439,516)(440,515)(441,509)(442,510)(443,512)
(444,511)(445,537)(446,538)(447,540)(448,539)(449,533)(450,534)(451,536)
(452,535)(453,529)(454,530)(455,532)(456,531)(457,525)(458,526)(459,528)
(460,527)(461,521)(462,522)(463,524)(464,523)(465,517)(466,518)(467,520)
(468,519)(469,541)(470,542)(471,544)(472,543)(473,549)(474,550)(475,552)
(476,551)(477,545)(478,546)(479,548)(480,547)(481,573)(482,574)(483,576)
(484,575)(485,569)(486,570)(487,572)(488,571)(489,565)(490,566)(491,568)
(492,567)(493,561)(494,562)(495,564)(496,563)(497,557)(498,558)(499,560)
(500,559)(501,553)(502,554)(503,556)(504,555);
s2 := Sym(576)!( 1,157)( 2,160)( 3,159)( 4,158)( 5,165)( 6,168)( 7,167)
( 8,166)( 9,161)( 10,164)( 11,163)( 12,162)( 13,145)( 14,148)( 15,147)
( 16,146)( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)
( 24,150)( 25,177)( 26,180)( 27,179)( 28,178)( 29,173)( 30,176)( 31,175)
( 32,174)( 33,169)( 34,172)( 35,171)( 36,170)( 37,193)( 38,196)( 39,195)
( 40,194)( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)
( 48,198)( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)
( 56,190)( 57,185)( 58,188)( 59,187)( 60,186)( 61,213)( 62,216)( 63,215)
( 64,214)( 65,209)( 66,212)( 67,211)( 68,210)( 69,205)( 70,208)( 71,207)
( 72,206)( 73,265)( 74,268)( 75,267)( 76,266)( 77,273)( 78,276)( 79,275)
( 80,274)( 81,269)( 82,272)( 83,271)( 84,270)( 85,253)( 86,256)( 87,255)
( 88,254)( 89,261)( 90,264)( 91,263)( 92,262)( 93,257)( 94,260)( 95,259)
( 96,258)( 97,285)( 98,288)( 99,287)(100,286)(101,281)(102,284)(103,283)
(104,282)(105,277)(106,280)(107,279)(108,278)(109,229)(110,232)(111,231)
(112,230)(113,237)(114,240)(115,239)(116,238)(117,233)(118,236)(119,235)
(120,234)(121,217)(122,220)(123,219)(124,218)(125,225)(126,228)(127,227)
(128,226)(129,221)(130,224)(131,223)(132,222)(133,249)(134,252)(135,251)
(136,250)(137,245)(138,248)(139,247)(140,246)(141,241)(142,244)(143,243)
(144,242)(289,445)(290,448)(291,447)(292,446)(293,453)(294,456)(295,455)
(296,454)(297,449)(298,452)(299,451)(300,450)(301,433)(302,436)(303,435)
(304,434)(305,441)(306,444)(307,443)(308,442)(309,437)(310,440)(311,439)
(312,438)(313,465)(314,468)(315,467)(316,466)(317,461)(318,464)(319,463)
(320,462)(321,457)(322,460)(323,459)(324,458)(325,481)(326,484)(327,483)
(328,482)(329,489)(330,492)(331,491)(332,490)(333,485)(334,488)(335,487)
(336,486)(337,469)(338,472)(339,471)(340,470)(341,477)(342,480)(343,479)
(344,478)(345,473)(346,476)(347,475)(348,474)(349,501)(350,504)(351,503)
(352,502)(353,497)(354,500)(355,499)(356,498)(357,493)(358,496)(359,495)
(360,494)(361,553)(362,556)(363,555)(364,554)(365,561)(366,564)(367,563)
(368,562)(369,557)(370,560)(371,559)(372,558)(373,541)(374,544)(375,543)
(376,542)(377,549)(378,552)(379,551)(380,550)(381,545)(382,548)(383,547)
(384,546)(385,573)(386,576)(387,575)(388,574)(389,569)(390,572)(391,571)
(392,570)(393,565)(394,568)(395,567)(396,566)(397,517)(398,520)(399,519)
(400,518)(401,525)(402,528)(403,527)(404,526)(405,521)(406,524)(407,523)
(408,522)(409,505)(410,508)(411,507)(412,506)(413,513)(414,516)(415,515)
(416,514)(417,509)(418,512)(419,511)(420,510)(421,537)(422,540)(423,539)
(424,538)(425,533)(426,536)(427,535)(428,534)(429,529)(430,532)(431,531)
(432,530);
poly := sub<Sym(576)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
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*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