Polytope of Type {4,144}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,144}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32283)
Rank : 3
Schlafli Type : {4,144}
Number of vertices, edges, etc : 4, 288, 144
Order of s0s1s2 : 144
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {4,72}*576a
3-fold quotients : {4,48}*384b
4-fold quotients : {4,36}*288a, {2,72}*288
6-fold quotients : {4,24}*192a
8-fold quotients : {2,36}*144, {4,18}*144a
9-fold quotients : {4,16}*128b
12-fold quotients : {4,12}*96a, {2,24}*96
16-fold quotients : {2,18}*72
18-fold quotients : {4,8}*64a
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)
( 19, 28)( 20, 30)( 21, 29)( 22, 36)( 23, 35)( 24, 34)( 25, 33)( 26, 32)
( 27, 31)( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)
( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)( 61, 69)
( 62, 68)( 63, 67)( 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)
(163,208)(164,210)(165,209)(166,216)(167,215)(168,214)(169,213)(170,212)
(171,211)(172,199)(173,201)(174,200)(175,207)(176,206)(177,205)(178,204)
(179,203)(180,202)(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)
(307,388)(308,390)(309,389)(310,396)(311,395)(312,394)(313,393)(314,392)
(315,391)(316,379)(317,381)(318,380)(319,387)(320,386)(321,385)(322,384)
(323,383)(324,382)(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)(343,424)(344,426)(345,425)(346,432)
(347,431)(348,430)(349,429)(350,428)(351,427)(352,415)(353,417)(354,416)
(355,423)(356,422)(357,421)(358,420)(359,419)(360,418)(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)
(451,559)(452,561)(453,560)(454,567)(455,566)(456,565)(457,564)(458,563)
(459,562)(460,568)(461,570)(462,569)(463,576)(464,575)(465,574)(466,573)
(467,572)(468,571)(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)(487,523)(488,525)(489,524)(490,531)
(491,530)(492,529)(493,528)(494,527)(495,526)(496,532)(497,534)(498,533)
(499,540)(500,539)(501,538)(502,537)(503,536)(504,535);;
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)( 19,319)( 20,321)( 21,320)( 22,316)( 23,318)( 24,317)
( 25,324)( 26,323)( 27,322)( 28,310)( 29,312)( 30,311)( 31,307)( 32,309)
( 33,308)( 34,315)( 35,314)( 36,313)( 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)( 55,346)( 56,348)
( 57,347)( 58,343)( 59,345)( 60,344)( 61,351)( 62,350)( 63,349)( 64,355)
( 65,357)( 66,356)( 67,352)( 68,354)( 69,353)( 70,360)( 71,359)( 72,358)
( 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)(163,463)(164,465)(165,464)(166,460)(167,462)(168,461)
(169,468)(170,467)(171,466)(172,454)(173,456)(174,455)(175,451)(176,453)
(177,452)(178,459)(179,458)(180,457)(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)(199,490)(200,492)
(201,491)(202,487)(203,489)(204,488)(205,495)(206,494)(207,493)(208,499)
(209,501)(210,500)(211,496)(212,498)(213,497)(214,504)(215,503)(216,502)
(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,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
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)( 19, 28)( 20, 30)( 21, 29)( 22, 36)( 23, 35)( 24, 34)( 25, 33)
( 26, 32)( 27, 31)( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)
( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)
( 61, 69)( 62, 68)( 63, 67)( 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)(163,208)(164,210)(165,209)(166,216)(167,215)(168,214)(169,213)
(170,212)(171,211)(172,199)(173,201)(174,200)(175,207)(176,206)(177,205)
(178,204)(179,203)(180,202)(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)(307,388)(308,390)(309,389)(310,396)(311,395)(312,394)(313,393)
(314,392)(315,391)(316,379)(317,381)(318,380)(319,387)(320,386)(321,385)
(322,384)(323,383)(324,382)(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)(343,424)(344,426)(345,425)
(346,432)(347,431)(348,430)(349,429)(350,428)(351,427)(352,415)(353,417)
(354,416)(355,423)(356,422)(357,421)(358,420)(359,419)(360,418)(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)(451,559)(452,561)(453,560)(454,567)(455,566)(456,565)(457,564)
(458,563)(459,562)(460,568)(461,570)(462,569)(463,576)(464,575)(465,574)
(466,573)(467,572)(468,571)(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)(487,523)(488,525)(489,524)
(490,531)(491,530)(492,529)(493,528)(494,527)(495,526)(496,532)(497,534)
(498,533)(499,540)(500,539)(501,538)(502,537)(503,536)(504,535);
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)( 19,319)( 20,321)( 21,320)( 22,316)( 23,318)
( 24,317)( 25,324)( 26,323)( 27,322)( 28,310)( 29,312)( 30,311)( 31,307)
( 32,309)( 33,308)( 34,315)( 35,314)( 36,313)( 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)( 55,346)
( 56,348)( 57,347)( 58,343)( 59,345)( 60,344)( 61,351)( 62,350)( 63,349)
( 64,355)( 65,357)( 66,356)( 67,352)( 68,354)( 69,353)( 70,360)( 71,359)
( 72,358)( 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)(163,463)(164,465)(165,464)(166,460)(167,462)
(168,461)(169,468)(170,467)(171,466)(172,454)(173,456)(174,455)(175,451)
(176,453)(177,452)(178,459)(179,458)(180,457)(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)(199,490)
(200,492)(201,491)(202,487)(203,489)(204,488)(205,495)(206,494)(207,493)
(208,499)(209,501)(210,500)(211,496)(212,498)(213,497)(214,504)(215,503)
(216,502)(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,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope