Polytope of Type {4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,16}*1152a
if this polytope has a name.
Group : SmallGroup(1152,32083)
Rank : 3
Schlafli Type : {4,16}
Number of vertices, edges, etc : 36, 288, 144
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 6
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 : {4,8}*576a
   4-fold quotients : {4,4}*288
   8-fold quotients : {4,4}*144
   9-fold quotients : {4,16}*128a
   16-fold quotients : {4,4}*72
   18-fold quotients : {4,8}*64a, {2,16}*64
   36-fold quotients : {4,4}*32, {2,8}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope