Polytope of Type {4,72}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,72}*1152a
if this polytope has a name.
Group : SmallGroup(1152,11999)
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}*576a, {4,36}*576a, {4,72}*576b
3-fold quotients : {4,24}*384a
4-fold quotients : {4,36}*288a, {2,72}*288
6-fold quotients : {4,24}*192a, {4,12}*192a, {4,24}*192b
8-fold quotients : {2,36}*144, {4,18}*144a
9-fold quotients : {4,8}*128a
12-fold quotients : {4,12}*96a, {2,24}*96
16-fold quotients : {2,18}*72
18-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
24-fold quotients : {2,12}*48, {4,6}*48a
32-fold quotients : {2,9}*36
36-fold quotients : {4,4}*32, {2,8}*32
48-fold quotients : {2,6}*24
72-fold quotients : {2,4}*16, {4,2}*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 := ( 1,145)( 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)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,226)( 74,227)( 75,228)( 76,229)( 77,230)( 78,231)( 79,232)( 80,233)
( 81,234)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)( 88,223)
( 89,224)( 90,225)( 91,244)( 92,245)( 93,246)( 94,247)( 95,248)( 96,249)
( 97,250)( 98,251)( 99,252)(100,235)(101,236)(102,237)(103,238)(104,239)
(105,240)(106,241)(107,242)(108,243)(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)(325,469)(326,470)(327,471)(328,472)
(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)
(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)
(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)
(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)
(361,514)(362,515)(363,516)(364,517)(365,518)(366,519)(367,520)(368,521)
(369,522)(370,505)(371,506)(372,507)(373,508)(374,509)(375,510)(376,511)
(377,512)(378,513)(379,532)(380,533)(381,534)(382,535)(383,536)(384,537)
(385,538)(386,539)(387,540)(388,523)(389,524)(390,525)(391,526)(392,527)
(393,528)(394,529)(395,530)(396,531)(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);;
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, 91)( 74, 93)( 75, 92)( 76, 99)( 77, 98)( 78, 97)( 79, 96)( 80, 95)
( 81, 94)( 82,100)( 83,102)( 84,101)( 85,108)( 86,107)( 87,106)( 88,105)
( 89,104)( 90,103)(109,127)(110,129)(111,128)(112,135)(113,134)(114,133)
(115,132)(116,131)(117,130)(118,136)(119,138)(120,137)(121,144)(122,143)
(123,142)(124,141)(125,140)(126,139)(145,181)(146,183)(147,182)(148,189)
(149,188)(150,187)(151,186)(152,185)(153,184)(154,190)(155,192)(156,191)
(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)(163,199)(164,201)
(165,200)(166,207)(167,206)(168,205)(169,204)(170,203)(171,202)(172,208)
(173,210)(174,209)(175,216)(176,215)(177,214)(178,213)(179,212)(180,211)
(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)(289,361)(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)(433,550)(434,552)(435,551)(436,558)
(437,557)(438,556)(439,555)(440,554)(441,553)(442,541)(443,543)(444,542)
(445,549)(446,548)(447,547)(448,546)(449,545)(450,544)(451,568)(452,570)
(453,569)(454,576)(455,575)(456,574)(457,573)(458,572)(459,571)(460,559)
(461,561)(462,560)(463,567)(464,566)(465,565)(466,564)(467,563)(468,562)
(469,514)(470,516)(471,515)(472,522)(473,521)(474,520)(475,519)(476,518)
(477,517)(478,505)(479,507)(480,506)(481,513)(482,512)(483,511)(484,510)
(485,509)(486,508)(487,532)(488,534)(489,533)(490,540)(491,539)(492,538)
(493,537)(494,536)(495,535)(496,523)(497,525)(498,524)(499,531)(500,530)
(501,529)(502,528)(503,527)(504,526);;
s2 := ( 1,292)( 2,294)( 3,293)( 4,289)( 5,291)( 6,290)( 7,297)( 8,296)
( 9,295)( 10,301)( 11,303)( 12,302)( 13,298)( 14,300)( 15,299)( 16,306)
( 17,305)( 18,304)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)( 24,308)
( 25,315)( 26,314)( 27,313)( 28,319)( 29,321)( 30,320)( 31,316)( 32,318)
( 33,317)( 34,324)( 35,323)( 36,322)( 37,337)( 38,339)( 39,338)( 40,334)
( 41,336)( 42,335)( 43,342)( 44,341)( 45,340)( 46,328)( 47,330)( 48,329)
( 49,325)( 50,327)( 51,326)( 52,333)( 53,332)( 54,331)( 55,355)( 56,357)
( 57,356)( 58,352)( 59,354)( 60,353)( 61,360)( 62,359)( 63,358)( 64,346)
( 65,348)( 66,347)( 67,343)( 68,345)( 69,344)( 70,351)( 71,350)( 72,349)
( 73,382)( 74,384)( 75,383)( 76,379)( 77,381)( 78,380)( 79,387)( 80,386)
( 81,385)( 82,391)( 83,393)( 84,392)( 85,388)( 86,390)( 87,389)( 88,396)
( 89,395)( 90,394)( 91,364)( 92,366)( 93,365)( 94,361)( 95,363)( 96,362)
( 97,369)( 98,368)( 99,367)(100,373)(101,375)(102,374)(103,370)(104,372)
(105,371)(106,378)(107,377)(108,376)(109,427)(110,429)(111,428)(112,424)
(113,426)(114,425)(115,432)(116,431)(117,430)(118,418)(119,420)(120,419)
(121,415)(122,417)(123,416)(124,423)(125,422)(126,421)(127,409)(128,411)
(129,410)(130,406)(131,408)(132,407)(133,414)(134,413)(135,412)(136,400)
(137,402)(138,401)(139,397)(140,399)(141,398)(142,405)(143,404)(144,403)
(145,436)(146,438)(147,437)(148,433)(149,435)(150,434)(151,441)(152,440)
(153,439)(154,445)(155,447)(156,446)(157,442)(158,444)(159,443)(160,450)
(161,449)(162,448)(163,454)(164,456)(165,455)(166,451)(167,453)(168,452)
(169,459)(170,458)(171,457)(172,463)(173,465)(174,464)(175,460)(176,462)
(177,461)(178,468)(179,467)(180,466)(181,481)(182,483)(183,482)(184,478)
(185,480)(186,479)(187,486)(188,485)(189,484)(190,472)(191,474)(192,473)
(193,469)(194,471)(195,470)(196,477)(197,476)(198,475)(199,499)(200,501)
(201,500)(202,496)(203,498)(204,497)(205,504)(206,503)(207,502)(208,490)
(209,492)(210,491)(211,487)(212,489)(213,488)(214,495)(215,494)(216,493)
(217,526)(218,528)(219,527)(220,523)(221,525)(222,524)(223,531)(224,530)
(225,529)(226,535)(227,537)(228,536)(229,532)(230,534)(231,533)(232,540)
(233,539)(234,538)(235,508)(236,510)(237,509)(238,505)(239,507)(240,506)
(241,513)(242,512)(243,511)(244,517)(245,519)(246,518)(247,514)(248,516)
(249,515)(250,522)(251,521)(252,520)(253,571)(254,573)(255,572)(256,568)
(257,570)(258,569)(259,576)(260,575)(261,574)(262,562)(263,564)(264,563)
(265,559)(266,561)(267,560)(268,567)(269,566)(270,565)(271,553)(272,555)
(273,554)(274,550)(275,552)(276,551)(277,558)(278,557)(279,556)(280,544)
(281,546)(282,545)(283,541)(284,543)(285,542)(286,549)(287,548)(288,547);;
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,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*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)!( 1,145)( 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)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,226)( 74,227)( 75,228)( 76,229)( 77,230)( 78,231)( 79,232)
( 80,233)( 81,234)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)
( 88,223)( 89,224)( 90,225)( 91,244)( 92,245)( 93,246)( 94,247)( 95,248)
( 96,249)( 97,250)( 98,251)( 99,252)(100,235)(101,236)(102,237)(103,238)
(104,239)(105,240)(106,241)(107,242)(108,243)(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)(325,469)(326,470)(327,471)
(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)
(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)
(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)
(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)
(360,504)(361,514)(362,515)(363,516)(364,517)(365,518)(366,519)(367,520)
(368,521)(369,522)(370,505)(371,506)(372,507)(373,508)(374,509)(375,510)
(376,511)(377,512)(378,513)(379,532)(380,533)(381,534)(382,535)(383,536)
(384,537)(385,538)(386,539)(387,540)(388,523)(389,524)(390,525)(391,526)
(392,527)(393,528)(394,529)(395,530)(396,531)(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);
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, 91)( 74, 93)( 75, 92)( 76, 99)( 77, 98)( 78, 97)( 79, 96)
( 80, 95)( 81, 94)( 82,100)( 83,102)( 84,101)( 85,108)( 86,107)( 87,106)
( 88,105)( 89,104)( 90,103)(109,127)(110,129)(111,128)(112,135)(113,134)
(114,133)(115,132)(116,131)(117,130)(118,136)(119,138)(120,137)(121,144)
(122,143)(123,142)(124,141)(125,140)(126,139)(145,181)(146,183)(147,182)
(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,190)(155,192)
(156,191)(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)(163,199)
(164,201)(165,200)(166,207)(167,206)(168,205)(169,204)(170,203)(171,202)
(172,208)(173,210)(174,209)(175,216)(176,215)(177,214)(178,213)(179,212)
(180,211)(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)(289,361)(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)(433,550)(434,552)(435,551)
(436,558)(437,557)(438,556)(439,555)(440,554)(441,553)(442,541)(443,543)
(444,542)(445,549)(446,548)(447,547)(448,546)(449,545)(450,544)(451,568)
(452,570)(453,569)(454,576)(455,575)(456,574)(457,573)(458,572)(459,571)
(460,559)(461,561)(462,560)(463,567)(464,566)(465,565)(466,564)(467,563)
(468,562)(469,514)(470,516)(471,515)(472,522)(473,521)(474,520)(475,519)
(476,518)(477,517)(478,505)(479,507)(480,506)(481,513)(482,512)(483,511)
(484,510)(485,509)(486,508)(487,532)(488,534)(489,533)(490,540)(491,539)
(492,538)(493,537)(494,536)(495,535)(496,523)(497,525)(498,524)(499,531)
(500,530)(501,529)(502,528)(503,527)(504,526);
s2 := Sym(576)!( 1,292)( 2,294)( 3,293)( 4,289)( 5,291)( 6,290)( 7,297)
( 8,296)( 9,295)( 10,301)( 11,303)( 12,302)( 13,298)( 14,300)( 15,299)
( 16,306)( 17,305)( 18,304)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)
( 24,308)( 25,315)( 26,314)( 27,313)( 28,319)( 29,321)( 30,320)( 31,316)
( 32,318)( 33,317)( 34,324)( 35,323)( 36,322)( 37,337)( 38,339)( 39,338)
( 40,334)( 41,336)( 42,335)( 43,342)( 44,341)( 45,340)( 46,328)( 47,330)
( 48,329)( 49,325)( 50,327)( 51,326)( 52,333)( 53,332)( 54,331)( 55,355)
( 56,357)( 57,356)( 58,352)( 59,354)( 60,353)( 61,360)( 62,359)( 63,358)
( 64,346)( 65,348)( 66,347)( 67,343)( 68,345)( 69,344)( 70,351)( 71,350)
( 72,349)( 73,382)( 74,384)( 75,383)( 76,379)( 77,381)( 78,380)( 79,387)
( 80,386)( 81,385)( 82,391)( 83,393)( 84,392)( 85,388)( 86,390)( 87,389)
( 88,396)( 89,395)( 90,394)( 91,364)( 92,366)( 93,365)( 94,361)( 95,363)
( 96,362)( 97,369)( 98,368)( 99,367)(100,373)(101,375)(102,374)(103,370)
(104,372)(105,371)(106,378)(107,377)(108,376)(109,427)(110,429)(111,428)
(112,424)(113,426)(114,425)(115,432)(116,431)(117,430)(118,418)(119,420)
(120,419)(121,415)(122,417)(123,416)(124,423)(125,422)(126,421)(127,409)
(128,411)(129,410)(130,406)(131,408)(132,407)(133,414)(134,413)(135,412)
(136,400)(137,402)(138,401)(139,397)(140,399)(141,398)(142,405)(143,404)
(144,403)(145,436)(146,438)(147,437)(148,433)(149,435)(150,434)(151,441)
(152,440)(153,439)(154,445)(155,447)(156,446)(157,442)(158,444)(159,443)
(160,450)(161,449)(162,448)(163,454)(164,456)(165,455)(166,451)(167,453)
(168,452)(169,459)(170,458)(171,457)(172,463)(173,465)(174,464)(175,460)
(176,462)(177,461)(178,468)(179,467)(180,466)(181,481)(182,483)(183,482)
(184,478)(185,480)(186,479)(187,486)(188,485)(189,484)(190,472)(191,474)
(192,473)(193,469)(194,471)(195,470)(196,477)(197,476)(198,475)(199,499)
(200,501)(201,500)(202,496)(203,498)(204,497)(205,504)(206,503)(207,502)
(208,490)(209,492)(210,491)(211,487)(212,489)(213,488)(214,495)(215,494)
(216,493)(217,526)(218,528)(219,527)(220,523)(221,525)(222,524)(223,531)
(224,530)(225,529)(226,535)(227,537)(228,536)(229,532)(230,534)(231,533)
(232,540)(233,539)(234,538)(235,508)(236,510)(237,509)(238,505)(239,507)
(240,506)(241,513)(242,512)(243,511)(244,517)(245,519)(246,518)(247,514)
(248,516)(249,515)(250,522)(251,521)(252,520)(253,571)(254,573)(255,572)
(256,568)(257,570)(258,569)(259,576)(260,575)(261,574)(262,562)(263,564)
(264,563)(265,559)(266,561)(267,560)(268,567)(269,566)(270,565)(271,553)
(272,555)(273,554)(274,550)(275,552)(276,551)(277,558)(278,557)(279,556)
(280,544)(281,546)(282,545)(283,541)(284,543)(285,542)(286,549)(287,548)
(288,547);
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,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*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