Polytope of Type {144,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {144,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32283)
Rank : 3
Schlafli Type : {144,4}
Number of vertices, edges, etc : 144, 288, 4
Order of s0s1s2 : 144
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {72,4}*576a
3-fold quotients : {48,4}*384b
4-fold quotients : {36,4}*288a, {72,2}*288
6-fold quotients : {24,4}*192a
8-fold quotients : {36,2}*144, {18,4}*144a
9-fold quotients : {16,4}*128b
12-fold quotients : {12,4}*96a, {24,2}*96
16-fold quotients : {18,2}*72
18-fold quotients : {8,4}*64a
24-fold quotients : {12,2}*48, {6,4}*48a
32-fold quotients : {9,2}*36
36-fold quotients : {4,4}*32, {8,2}*32
48-fold quotients : {6,2}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {3,2}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,289)( 2,291)( 3,290)( 4,297)( 5,296)( 6,295)( 7,294)( 8,293)
( 9,292)( 10,298)( 11,300)( 12,299)( 13,306)( 14,305)( 15,304)( 16,303)
( 17,302)( 18,301)( 19,316)( 20,318)( 21,317)( 22,324)( 23,323)( 24,322)
( 25,321)( 26,320)( 27,319)( 28,307)( 29,309)( 30,308)( 31,315)( 32,314)
( 33,313)( 34,312)( 35,311)( 36,310)( 37,334)( 38,336)( 39,335)( 40,342)
( 41,341)( 42,340)( 43,339)( 44,338)( 45,337)( 46,325)( 47,327)( 48,326)
( 49,333)( 50,332)( 51,331)( 52,330)( 53,329)( 54,328)( 55,343)( 56,345)
( 57,344)( 58,351)( 59,350)( 60,349)( 61,348)( 62,347)( 63,346)( 64,352)
( 65,354)( 66,353)( 67,360)( 68,359)( 69,358)( 70,357)( 71,356)( 72,355)
( 73,379)( 74,381)( 75,380)( 76,387)( 77,386)( 78,385)( 79,384)( 80,383)
( 81,382)( 82,388)( 83,390)( 84,389)( 85,396)( 86,395)( 87,394)( 88,393)
( 89,392)( 90,391)( 91,361)( 92,363)( 93,362)( 94,369)( 95,368)( 96,367)
( 97,366)( 98,365)( 99,364)(100,370)(101,372)(102,371)(103,378)(104,377)
(105,376)(106,375)(107,374)(108,373)(109,424)(110,426)(111,425)(112,432)
(113,431)(114,430)(115,429)(116,428)(117,427)(118,415)(119,417)(120,416)
(121,423)(122,422)(123,421)(124,420)(125,419)(126,418)(127,406)(128,408)
(129,407)(130,414)(131,413)(132,412)(133,411)(134,410)(135,409)(136,397)
(137,399)(138,398)(139,405)(140,404)(141,403)(142,402)(143,401)(144,400)
(145,433)(146,435)(147,434)(148,441)(149,440)(150,439)(151,438)(152,437)
(153,436)(154,442)(155,444)(156,443)(157,450)(158,449)(159,448)(160,447)
(161,446)(162,445)(163,460)(164,462)(165,461)(166,468)(167,467)(168,466)
(169,465)(170,464)(171,463)(172,451)(173,453)(174,452)(175,459)(176,458)
(177,457)(178,456)(179,455)(180,454)(181,478)(182,480)(183,479)(184,486)
(185,485)(186,484)(187,483)(188,482)(189,481)(190,469)(191,471)(192,470)
(193,477)(194,476)(195,475)(196,474)(197,473)(198,472)(199,487)(200,489)
(201,488)(202,495)(203,494)(204,493)(205,492)(206,491)(207,490)(208,496)
(209,498)(210,497)(211,504)(212,503)(213,502)(214,501)(215,500)(216,499)
(217,523)(218,525)(219,524)(220,531)(221,530)(222,529)(223,528)(224,527)
(225,526)(226,532)(227,534)(228,533)(229,540)(230,539)(231,538)(232,537)
(233,536)(234,535)(235,505)(236,507)(237,506)(238,513)(239,512)(240,511)
(241,510)(242,509)(243,508)(244,514)(245,516)(246,515)(247,522)(248,521)
(249,520)(250,519)(251,518)(252,517)(253,568)(254,570)(255,569)(256,576)
(257,575)(258,574)(259,573)(260,572)(261,571)(262,559)(263,561)(264,560)
(265,567)(266,566)(267,565)(268,564)(269,563)(270,562)(271,550)(272,552)
(273,551)(274,558)(275,557)(276,556)(277,555)(278,554)(279,553)(280,541)
(281,543)(282,542)(283,549)(284,548)(285,547)(286,546)(287,545)(288,544);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)
( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)( 26, 35)
( 27, 34)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)( 48, 50)
( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)
( 62, 71)( 63, 70)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)
( 79, 99)( 80, 98)( 81, 97)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)
( 87,101)( 88,108)( 89,107)( 90,106)(109,130)(110,132)(111,131)(112,127)
(113,129)(114,128)(115,135)(116,134)(117,133)(118,139)(119,141)(120,140)
(121,136)(122,138)(123,137)(124,144)(125,143)(126,142)(145,184)(146,186)
(147,185)(148,181)(149,183)(150,182)(151,189)(152,188)(153,187)(154,193)
(155,195)(156,194)(157,190)(158,192)(159,191)(160,198)(161,197)(162,196)
(163,211)(164,213)(165,212)(166,208)(167,210)(168,209)(169,216)(170,215)
(171,214)(172,202)(173,204)(174,203)(175,199)(176,201)(177,200)(178,207)
(179,206)(180,205)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)
(223,279)(224,278)(225,277)(226,283)(227,285)(228,284)(229,280)(230,282)
(231,281)(232,288)(233,287)(234,286)(235,256)(236,258)(237,257)(238,253)
(239,255)(240,254)(241,261)(242,260)(243,259)(244,265)(245,267)(246,266)
(247,262)(248,264)(249,263)(250,270)(251,269)(252,268)(289,364)(290,366)
(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)(297,367)(298,373)
(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)(305,377)(306,376)
(307,391)(308,393)(309,392)(310,388)(311,390)(312,389)(313,396)(314,395)
(315,394)(316,382)(317,384)(318,383)(319,379)(320,381)(321,380)(322,387)
(323,386)(324,385)(325,400)(326,402)(327,401)(328,397)(329,399)(330,398)
(331,405)(332,404)(333,403)(334,409)(335,411)(336,410)(337,406)(338,408)
(339,407)(340,414)(341,413)(342,412)(343,427)(344,429)(345,428)(346,424)
(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)(354,419)
(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(433,553)(434,555)
(435,554)(436,550)(437,552)(438,551)(439,558)(440,557)(441,556)(442,544)
(443,546)(444,545)(445,541)(446,543)(447,542)(448,549)(449,548)(450,547)
(451,562)(452,564)(453,563)(454,559)(455,561)(456,560)(457,567)(458,566)
(459,565)(460,571)(461,573)(462,572)(463,568)(464,570)(465,569)(466,576)
(467,575)(468,574)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)
(475,522)(476,521)(477,520)(478,508)(479,510)(480,509)(481,505)(482,507)
(483,506)(484,513)(485,512)(486,511)(487,526)(488,528)(489,527)(490,523)
(491,525)(492,524)(493,531)(494,530)(495,529)(496,535)(497,537)(498,536)
(499,532)(500,534)(501,533)(502,540)(503,539)(504,538);;
s2 := ( 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);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*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*s2*s1*s0*s1*s0*s2*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*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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,289)( 2,291)( 3,290)( 4,297)( 5,296)( 6,295)( 7,294)
( 8,293)( 9,292)( 10,298)( 11,300)( 12,299)( 13,306)( 14,305)( 15,304)
( 16,303)( 17,302)( 18,301)( 19,316)( 20,318)( 21,317)( 22,324)( 23,323)
( 24,322)( 25,321)( 26,320)( 27,319)( 28,307)( 29,309)( 30,308)( 31,315)
( 32,314)( 33,313)( 34,312)( 35,311)( 36,310)( 37,334)( 38,336)( 39,335)
( 40,342)( 41,341)( 42,340)( 43,339)( 44,338)( 45,337)( 46,325)( 47,327)
( 48,326)( 49,333)( 50,332)( 51,331)( 52,330)( 53,329)( 54,328)( 55,343)
( 56,345)( 57,344)( 58,351)( 59,350)( 60,349)( 61,348)( 62,347)( 63,346)
( 64,352)( 65,354)( 66,353)( 67,360)( 68,359)( 69,358)( 70,357)( 71,356)
( 72,355)( 73,379)( 74,381)( 75,380)( 76,387)( 77,386)( 78,385)( 79,384)
( 80,383)( 81,382)( 82,388)( 83,390)( 84,389)( 85,396)( 86,395)( 87,394)
( 88,393)( 89,392)( 90,391)( 91,361)( 92,363)( 93,362)( 94,369)( 95,368)
( 96,367)( 97,366)( 98,365)( 99,364)(100,370)(101,372)(102,371)(103,378)
(104,377)(105,376)(106,375)(107,374)(108,373)(109,424)(110,426)(111,425)
(112,432)(113,431)(114,430)(115,429)(116,428)(117,427)(118,415)(119,417)
(120,416)(121,423)(122,422)(123,421)(124,420)(125,419)(126,418)(127,406)
(128,408)(129,407)(130,414)(131,413)(132,412)(133,411)(134,410)(135,409)
(136,397)(137,399)(138,398)(139,405)(140,404)(141,403)(142,402)(143,401)
(144,400)(145,433)(146,435)(147,434)(148,441)(149,440)(150,439)(151,438)
(152,437)(153,436)(154,442)(155,444)(156,443)(157,450)(158,449)(159,448)
(160,447)(161,446)(162,445)(163,460)(164,462)(165,461)(166,468)(167,467)
(168,466)(169,465)(170,464)(171,463)(172,451)(173,453)(174,452)(175,459)
(176,458)(177,457)(178,456)(179,455)(180,454)(181,478)(182,480)(183,479)
(184,486)(185,485)(186,484)(187,483)(188,482)(189,481)(190,469)(191,471)
(192,470)(193,477)(194,476)(195,475)(196,474)(197,473)(198,472)(199,487)
(200,489)(201,488)(202,495)(203,494)(204,493)(205,492)(206,491)(207,490)
(208,496)(209,498)(210,497)(211,504)(212,503)(213,502)(214,501)(215,500)
(216,499)(217,523)(218,525)(219,524)(220,531)(221,530)(222,529)(223,528)
(224,527)(225,526)(226,532)(227,534)(228,533)(229,540)(230,539)(231,538)
(232,537)(233,536)(234,535)(235,505)(236,507)(237,506)(238,513)(239,512)
(240,511)(241,510)(242,509)(243,508)(244,514)(245,516)(246,515)(247,522)
(248,521)(249,520)(250,519)(251,518)(252,517)(253,568)(254,570)(255,569)
(256,576)(257,575)(258,574)(259,573)(260,572)(261,571)(262,559)(263,561)
(264,560)(265,567)(266,566)(267,565)(268,564)(269,563)(270,562)(271,550)
(272,552)(273,551)(274,558)(275,557)(276,556)(277,555)(278,554)(279,553)
(280,541)(281,543)(282,542)(283,549)(284,548)(285,547)(286,546)(287,545)
(288,544);
s1 := Sym(576)!( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 13)( 11, 15)( 12, 14)
( 16, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)
( 26, 35)( 27, 34)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)
( 48, 50)( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)
( 61, 72)( 62, 71)( 63, 70)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)
( 78, 92)( 79, 99)( 80, 98)( 81, 97)( 82,103)( 83,105)( 84,104)( 85,100)
( 86,102)( 87,101)( 88,108)( 89,107)( 90,106)(109,130)(110,132)(111,131)
(112,127)(113,129)(114,128)(115,135)(116,134)(117,133)(118,139)(119,141)
(120,140)(121,136)(122,138)(123,137)(124,144)(125,143)(126,142)(145,184)
(146,186)(147,185)(148,181)(149,183)(150,182)(151,189)(152,188)(153,187)
(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,198)(161,197)
(162,196)(163,211)(164,213)(165,212)(166,208)(167,210)(168,209)(169,216)
(170,215)(171,214)(172,202)(173,204)(174,203)(175,199)(176,201)(177,200)
(178,207)(179,206)(180,205)(217,274)(218,276)(219,275)(220,271)(221,273)
(222,272)(223,279)(224,278)(225,277)(226,283)(227,285)(228,284)(229,280)
(230,282)(231,281)(232,288)(233,287)(234,286)(235,256)(236,258)(237,257)
(238,253)(239,255)(240,254)(241,261)(242,260)(243,259)(244,265)(245,267)
(246,266)(247,262)(248,264)(249,263)(250,270)(251,269)(252,268)(289,364)
(290,366)(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)(297,367)
(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)(305,377)
(306,376)(307,391)(308,393)(309,392)(310,388)(311,390)(312,389)(313,396)
(314,395)(315,394)(316,382)(317,384)(318,383)(319,379)(320,381)(321,380)
(322,387)(323,386)(324,385)(325,400)(326,402)(327,401)(328,397)(329,399)
(330,398)(331,405)(332,404)(333,403)(334,409)(335,411)(336,410)(337,406)
(338,408)(339,407)(340,414)(341,413)(342,412)(343,427)(344,429)(345,428)
(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)
(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(433,553)
(434,555)(435,554)(436,550)(437,552)(438,551)(439,558)(440,557)(441,556)
(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,549)(449,548)
(450,547)(451,562)(452,564)(453,563)(454,559)(455,561)(456,560)(457,567)
(458,566)(459,565)(460,571)(461,573)(462,572)(463,568)(464,570)(465,569)
(466,576)(467,575)(468,574)(469,517)(470,519)(471,518)(472,514)(473,516)
(474,515)(475,522)(476,521)(477,520)(478,508)(479,510)(480,509)(481,505)
(482,507)(483,506)(484,513)(485,512)(486,511)(487,526)(488,528)(489,527)
(490,523)(491,525)(492,524)(493,531)(494,530)(495,529)(496,535)(497,537)
(498,536)(499,532)(500,534)(501,533)(502,540)(503,539)(504,538);
s2 := 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);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*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*s2*s1*s0*s1*s0*s2*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*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*s0*s1*s0*s1 >;
References : None.
to this polytope