Polytope of Type {4,144}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,144}*1152a
Also Known As : {4,144|2}. if this polytope has another name.
Group : SmallGroup(1152,32067)
Rank : 3
Schlafli Type : {4,144}
Number of vertices, edges, etc : 4, 288, 144
Order of s0s1s2 : 144
Order of s0s1s2s1 : 2
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, {2,144}*576
3-fold quotients : {4,48}*384a
4-fold quotients : {4,36}*288a, {2,72}*288
6-fold quotients : {4,24}*192a, {2,48}*192
8-fold quotients : {2,36}*144, {4,18}*144a
9-fold quotients : {4,16}*128a
12-fold quotients : {4,12}*96a, {2,24}*96
16-fold quotients : {2,18}*72
18-fold quotients : {4,8}*64a, {2,16}*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)
( 73,217)( 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)(109,253)(110,254)(111,255)(112,256)
(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)
(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)
(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)
(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)
(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)
(361,505)(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)(397,541)(398,542)(399,543)(400,544)
(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)
(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)
(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)
(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
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)(433,541)(434,543)
(435,542)(436,549)(437,548)(438,547)(439,546)(440,545)(441,544)(442,550)
(443,552)(444,551)(445,558)(446,557)(447,556)(448,555)(449,554)(450,553)
(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)(469,505)(470,507)(471,506)(472,513)(473,512)(474,511)
(475,510)(476,509)(477,508)(478,514)(479,516)(480,515)(481,522)(482,521)
(483,520)(484,519)(485,518)(486,517)(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)( 19,319)( 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)( 37,328)( 38,330)( 39,329)( 40,325)
( 41,327)( 42,326)( 43,333)( 44,332)( 45,331)( 46,337)( 47,339)( 48,338)
( 49,334)( 50,336)( 51,335)( 52,342)( 53,341)( 54,340)( 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)(109,418)(110,420)(111,419)(112,415)
(113,417)(114,416)(115,423)(116,422)(117,421)(118,427)(119,429)(120,428)
(121,424)(122,426)(123,425)(124,432)(125,431)(126,430)(127,400)(128,402)
(129,401)(130,397)(131,399)(132,398)(133,405)(134,404)(135,403)(136,409)
(137,411)(138,410)(139,406)(140,408)(141,407)(142,414)(143,413)(144,412)
(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)(181,472)(182,474)(183,473)(184,469)
(185,471)(186,470)(187,477)(188,476)(189,475)(190,481)(191,483)(192,482)
(193,478)(194,480)(195,479)(196,486)(197,485)(198,484)(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)(253,562)(254,564)(255,563)(256,559)
(257,561)(258,560)(259,567)(260,566)(261,565)(262,571)(263,573)(264,572)
(265,568)(266,570)(267,569)(268,576)(269,575)(270,574)(271,544)(272,546)
(273,545)(274,541)(275,543)(276,542)(277,549)(278,548)(279,547)(280,553)
(281,555)(282,554)(283,550)(284,552)(285,551)(286,558)(287,557)(288,556);;
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*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 73,217)( 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)(109,253)(110,254)(111,255)
(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)
(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)
(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)
(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)
(144,288)(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)(361,505)(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)(397,541)(398,542)(399,543)
(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)
(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)
(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)
(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)
(432,576);
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)(433,541)
(434,543)(435,542)(436,549)(437,548)(438,547)(439,546)(440,545)(441,544)
(442,550)(443,552)(444,551)(445,558)(446,557)(447,556)(448,555)(449,554)
(450,553)(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)(469,505)(470,507)(471,506)(472,513)(473,512)
(474,511)(475,510)(476,509)(477,508)(478,514)(479,516)(480,515)(481,522)
(482,521)(483,520)(484,519)(485,518)(486,517)(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)( 19,319)( 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)( 37,328)( 38,330)( 39,329)
( 40,325)( 41,327)( 42,326)( 43,333)( 44,332)( 45,331)( 46,337)( 47,339)
( 48,338)( 49,334)( 50,336)( 51,335)( 52,342)( 53,341)( 54,340)( 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)(109,418)(110,420)(111,419)
(112,415)(113,417)(114,416)(115,423)(116,422)(117,421)(118,427)(119,429)
(120,428)(121,424)(122,426)(123,425)(124,432)(125,431)(126,430)(127,400)
(128,402)(129,401)(130,397)(131,399)(132,398)(133,405)(134,404)(135,403)
(136,409)(137,411)(138,410)(139,406)(140,408)(141,407)(142,414)(143,413)
(144,412)(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)(181,472)(182,474)(183,473)
(184,469)(185,471)(186,470)(187,477)(188,476)(189,475)(190,481)(191,483)
(192,482)(193,478)(194,480)(195,479)(196,486)(197,485)(198,484)(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)(253,562)(254,564)(255,563)
(256,559)(257,561)(258,560)(259,567)(260,566)(261,565)(262,571)(263,573)
(264,572)(265,568)(266,570)(267,569)(268,576)(269,575)(270,574)(271,544)
(272,546)(273,545)(274,541)(275,543)(276,542)(277,549)(278,548)(279,547)
(280,553)(281,555)(282,554)(283,550)(284,552)(285,551)(286,558)(287,557)
(288,556);
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*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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