Polytope of Type {8,36}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,36}*1152e
if this polytope has a name.
Group : SmallGroup(1152,154256)
Rank : 3
Schlafli Type : {8,36}
Number of vertices, edges, etc : 16, 288, 72
Order of s0s1s2 : 36
Order of s0s1s2s1 : 8
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 : {4,36}*576b, {8,18}*576b
3-fold quotients : {8,12}*384e
4-fold quotients : {4,36}*288b, {4,36}*288c, {8,9}*288, {4,18}*288
6-fold quotients : {4,12}*192b, {8,6}*192b
8-fold quotients : {2,36}*144, {4,9}*144, {4,18}*144b, {4,18}*144c
12-fold quotients : {4,12}*96b, {4,12}*96c, {8,3}*96, {4,6}*96
16-fold quotients : {4,9}*72, {2,18}*72
24-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
32-fold quotients : {2,9}*36
48-fold quotients : {4,3}*24, {2,6}*24
72-fold quotients : {2,4}*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 := ( 1,293)( 2,294)( 3,296)( 4,295)( 5,290)( 6,289)( 7,291)( 8,292)
( 9,301)( 10,302)( 11,304)( 12,303)( 13,298)( 14,297)( 15,299)( 16,300)
( 17,309)( 18,310)( 19,312)( 20,311)( 21,306)( 22,305)( 23,307)( 24,308)
( 25,317)( 26,318)( 27,320)( 28,319)( 29,314)( 30,313)( 31,315)( 32,316)
( 33,325)( 34,326)( 35,328)( 36,327)( 37,322)( 38,321)( 39,323)( 40,324)
( 41,333)( 42,334)( 43,336)( 44,335)( 45,330)( 46,329)( 47,331)( 48,332)
( 49,341)( 50,342)( 51,344)( 52,343)( 53,338)( 54,337)( 55,339)( 56,340)
( 57,349)( 58,350)( 59,352)( 60,351)( 61,346)( 62,345)( 63,347)( 64,348)
( 65,357)( 66,358)( 67,360)( 68,359)( 69,354)( 70,353)( 71,355)( 72,356)
( 73,365)( 74,366)( 75,368)( 76,367)( 77,362)( 78,361)( 79,363)( 80,364)
( 81,373)( 82,374)( 83,376)( 84,375)( 85,370)( 86,369)( 87,371)( 88,372)
( 89,381)( 90,382)( 91,384)( 92,383)( 93,378)( 94,377)( 95,379)( 96,380)
( 97,389)( 98,390)( 99,392)(100,391)(101,386)(102,385)(103,387)(104,388)
(105,397)(106,398)(107,400)(108,399)(109,394)(110,393)(111,395)(112,396)
(113,405)(114,406)(115,408)(116,407)(117,402)(118,401)(119,403)(120,404)
(121,413)(122,414)(123,416)(124,415)(125,410)(126,409)(127,411)(128,412)
(129,421)(130,422)(131,424)(132,423)(133,418)(134,417)(135,419)(136,420)
(137,429)(138,430)(139,432)(140,431)(141,426)(142,425)(143,427)(144,428)
(145,437)(146,438)(147,440)(148,439)(149,434)(150,433)(151,435)(152,436)
(153,445)(154,446)(155,448)(156,447)(157,442)(158,441)(159,443)(160,444)
(161,453)(162,454)(163,456)(164,455)(165,450)(166,449)(167,451)(168,452)
(169,461)(170,462)(171,464)(172,463)(173,458)(174,457)(175,459)(176,460)
(177,469)(178,470)(179,472)(180,471)(181,466)(182,465)(183,467)(184,468)
(185,477)(186,478)(187,480)(188,479)(189,474)(190,473)(191,475)(192,476)
(193,485)(194,486)(195,488)(196,487)(197,482)(198,481)(199,483)(200,484)
(201,493)(202,494)(203,496)(204,495)(205,490)(206,489)(207,491)(208,492)
(209,501)(210,502)(211,504)(212,503)(213,498)(214,497)(215,499)(216,500)
(217,509)(218,510)(219,512)(220,511)(221,506)(222,505)(223,507)(224,508)
(225,517)(226,518)(227,520)(228,519)(229,514)(230,513)(231,515)(232,516)
(233,525)(234,526)(235,528)(236,527)(237,522)(238,521)(239,523)(240,524)
(241,533)(242,534)(243,536)(244,535)(245,530)(246,529)(247,531)(248,532)
(249,541)(250,542)(251,544)(252,543)(253,538)(254,537)(255,539)(256,540)
(257,549)(258,550)(259,552)(260,551)(261,546)(262,545)(263,547)(264,548)
(265,557)(266,558)(267,560)(268,559)(269,554)(270,553)(271,555)(272,556)
(273,565)(274,566)(275,568)(276,567)(277,562)(278,561)(279,563)(280,564)
(281,573)(282,574)(283,576)(284,575)(285,570)(286,569)(287,571)(288,572);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)
( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)
( 38, 64)( 39, 61)( 40, 62)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 55)
( 46, 56)( 47, 53)( 48, 54)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)
( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,137)( 98,138)
( 99,140)(100,139)(101,143)(102,144)(103,141)(104,142)(105,129)(106,130)
(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)(113,121)(114,122)
(115,124)(116,123)(117,127)(118,128)(119,125)(120,126)(145,217)(146,218)
(147,220)(148,219)(149,223)(150,224)(151,221)(152,222)(153,233)(154,234)
(155,236)(156,235)(157,239)(158,240)(159,237)(160,238)(161,225)(162,226)
(163,228)(164,227)(165,231)(166,232)(167,229)(168,230)(169,281)(170,282)
(171,284)(172,283)(173,287)(174,288)(175,285)(176,286)(177,273)(178,274)
(179,276)(180,275)(181,279)(182,280)(183,277)(184,278)(185,265)(186,266)
(187,268)(188,267)(189,271)(190,272)(191,269)(192,270)(193,257)(194,258)
(195,260)(196,259)(197,263)(198,264)(199,261)(200,262)(201,249)(202,250)
(203,252)(204,251)(205,255)(206,256)(207,253)(208,254)(209,241)(210,242)
(211,244)(212,243)(213,247)(214,248)(215,245)(216,246)(289,290)(293,296)
(294,295)(297,306)(298,305)(299,307)(300,308)(301,312)(302,311)(303,310)
(304,309)(313,354)(314,353)(315,355)(316,356)(317,360)(318,359)(319,358)
(320,357)(321,346)(322,345)(323,347)(324,348)(325,352)(326,351)(327,350)
(328,349)(329,338)(330,337)(331,339)(332,340)(333,344)(334,343)(335,342)
(336,341)(361,362)(365,368)(366,367)(369,378)(370,377)(371,379)(372,380)
(373,384)(374,383)(375,382)(376,381)(385,426)(386,425)(387,427)(388,428)
(389,432)(390,431)(391,430)(392,429)(393,418)(394,417)(395,419)(396,420)
(397,424)(398,423)(399,422)(400,421)(401,410)(402,409)(403,411)(404,412)
(405,416)(406,415)(407,414)(408,413)(433,506)(434,505)(435,507)(436,508)
(437,512)(438,511)(439,510)(440,509)(441,522)(442,521)(443,523)(444,524)
(445,528)(446,527)(447,526)(448,525)(449,514)(450,513)(451,515)(452,516)
(453,520)(454,519)(455,518)(456,517)(457,570)(458,569)(459,571)(460,572)
(461,576)(462,575)(463,574)(464,573)(465,562)(466,561)(467,563)(468,564)
(469,568)(470,567)(471,566)(472,565)(473,554)(474,553)(475,555)(476,556)
(477,560)(478,559)(479,558)(480,557)(481,546)(482,545)(483,547)(484,548)
(485,552)(486,551)(487,550)(488,549)(489,538)(490,537)(491,539)(492,540)
(493,544)(494,543)(495,542)(496,541)(497,530)(498,529)(499,531)(500,532)
(501,536)(502,535)(503,534)(504,533);;
s2 := ( 1,169)( 2,170)( 3,175)( 4,176)( 5,174)( 6,173)( 7,171)( 8,172)
( 9,185)( 10,186)( 11,191)( 12,192)( 13,190)( 14,189)( 15,187)( 16,188)
( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)( 24,180)
( 25,145)( 26,146)( 27,151)( 28,152)( 29,150)( 30,149)( 31,147)( 32,148)
( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)( 40,164)
( 41,153)( 42,154)( 43,159)( 44,160)( 45,158)( 46,157)( 47,155)( 48,156)
( 49,209)( 50,210)( 51,215)( 52,216)( 53,214)( 54,213)( 55,211)( 56,212)
( 57,201)( 58,202)( 59,207)( 60,208)( 61,206)( 62,205)( 63,203)( 64,204)
( 65,193)( 66,194)( 67,199)( 68,200)( 69,198)( 70,197)( 71,195)( 72,196)
( 73,241)( 74,242)( 75,247)( 76,248)( 77,246)( 78,245)( 79,243)( 80,244)
( 81,257)( 82,258)( 83,263)( 84,264)( 85,262)( 86,261)( 87,259)( 88,260)
( 89,249)( 90,250)( 91,255)( 92,256)( 93,254)( 94,253)( 95,251)( 96,252)
( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)(104,220)
(105,233)(106,234)(107,239)(108,240)(109,238)(110,237)(111,235)(112,236)
(113,225)(114,226)(115,231)(116,232)(117,230)(118,229)(119,227)(120,228)
(121,281)(122,282)(123,287)(124,288)(125,286)(126,285)(127,283)(128,284)
(129,273)(130,274)(131,279)(132,280)(133,278)(134,277)(135,275)(136,276)
(137,265)(138,266)(139,271)(140,272)(141,270)(142,269)(143,267)(144,268)
(289,458)(290,457)(291,464)(292,463)(293,461)(294,462)(295,460)(296,459)
(297,474)(298,473)(299,480)(300,479)(301,477)(302,478)(303,476)(304,475)
(305,466)(306,465)(307,472)(308,471)(309,469)(310,470)(311,468)(312,467)
(313,434)(314,433)(315,440)(316,439)(317,437)(318,438)(319,436)(320,435)
(321,450)(322,449)(323,456)(324,455)(325,453)(326,454)(327,452)(328,451)
(329,442)(330,441)(331,448)(332,447)(333,445)(334,446)(335,444)(336,443)
(337,498)(338,497)(339,504)(340,503)(341,501)(342,502)(343,500)(344,499)
(345,490)(346,489)(347,496)(348,495)(349,493)(350,494)(351,492)(352,491)
(353,482)(354,481)(355,488)(356,487)(357,485)(358,486)(359,484)(360,483)
(361,530)(362,529)(363,536)(364,535)(365,533)(366,534)(367,532)(368,531)
(369,546)(370,545)(371,552)(372,551)(373,549)(374,550)(375,548)(376,547)
(377,538)(378,537)(379,544)(380,543)(381,541)(382,542)(383,540)(384,539)
(385,506)(386,505)(387,512)(388,511)(389,509)(390,510)(391,508)(392,507)
(393,522)(394,521)(395,528)(396,527)(397,525)(398,526)(399,524)(400,523)
(401,514)(402,513)(403,520)(404,519)(405,517)(406,518)(407,516)(408,515)
(409,570)(410,569)(411,576)(412,575)(413,573)(414,574)(415,572)(416,571)
(417,562)(418,561)(419,568)(420,567)(421,565)(422,566)(423,564)(424,563)
(425,554)(426,553)(427,560)(428,559)(429,557)(430,558)(431,556)(432,555);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,293)( 2,294)( 3,296)( 4,295)( 5,290)( 6,289)( 7,291)
( 8,292)( 9,301)( 10,302)( 11,304)( 12,303)( 13,298)( 14,297)( 15,299)
( 16,300)( 17,309)( 18,310)( 19,312)( 20,311)( 21,306)( 22,305)( 23,307)
( 24,308)( 25,317)( 26,318)( 27,320)( 28,319)( 29,314)( 30,313)( 31,315)
( 32,316)( 33,325)( 34,326)( 35,328)( 36,327)( 37,322)( 38,321)( 39,323)
( 40,324)( 41,333)( 42,334)( 43,336)( 44,335)( 45,330)( 46,329)( 47,331)
( 48,332)( 49,341)( 50,342)( 51,344)( 52,343)( 53,338)( 54,337)( 55,339)
( 56,340)( 57,349)( 58,350)( 59,352)( 60,351)( 61,346)( 62,345)( 63,347)
( 64,348)( 65,357)( 66,358)( 67,360)( 68,359)( 69,354)( 70,353)( 71,355)
( 72,356)( 73,365)( 74,366)( 75,368)( 76,367)( 77,362)( 78,361)( 79,363)
( 80,364)( 81,373)( 82,374)( 83,376)( 84,375)( 85,370)( 86,369)( 87,371)
( 88,372)( 89,381)( 90,382)( 91,384)( 92,383)( 93,378)( 94,377)( 95,379)
( 96,380)( 97,389)( 98,390)( 99,392)(100,391)(101,386)(102,385)(103,387)
(104,388)(105,397)(106,398)(107,400)(108,399)(109,394)(110,393)(111,395)
(112,396)(113,405)(114,406)(115,408)(116,407)(117,402)(118,401)(119,403)
(120,404)(121,413)(122,414)(123,416)(124,415)(125,410)(126,409)(127,411)
(128,412)(129,421)(130,422)(131,424)(132,423)(133,418)(134,417)(135,419)
(136,420)(137,429)(138,430)(139,432)(140,431)(141,426)(142,425)(143,427)
(144,428)(145,437)(146,438)(147,440)(148,439)(149,434)(150,433)(151,435)
(152,436)(153,445)(154,446)(155,448)(156,447)(157,442)(158,441)(159,443)
(160,444)(161,453)(162,454)(163,456)(164,455)(165,450)(166,449)(167,451)
(168,452)(169,461)(170,462)(171,464)(172,463)(173,458)(174,457)(175,459)
(176,460)(177,469)(178,470)(179,472)(180,471)(181,466)(182,465)(183,467)
(184,468)(185,477)(186,478)(187,480)(188,479)(189,474)(190,473)(191,475)
(192,476)(193,485)(194,486)(195,488)(196,487)(197,482)(198,481)(199,483)
(200,484)(201,493)(202,494)(203,496)(204,495)(205,490)(206,489)(207,491)
(208,492)(209,501)(210,502)(211,504)(212,503)(213,498)(214,497)(215,499)
(216,500)(217,509)(218,510)(219,512)(220,511)(221,506)(222,505)(223,507)
(224,508)(225,517)(226,518)(227,520)(228,519)(229,514)(230,513)(231,515)
(232,516)(233,525)(234,526)(235,528)(236,527)(237,522)(238,521)(239,523)
(240,524)(241,533)(242,534)(243,536)(244,535)(245,530)(246,529)(247,531)
(248,532)(249,541)(250,542)(251,544)(252,543)(253,538)(254,537)(255,539)
(256,540)(257,549)(258,550)(259,552)(260,551)(261,546)(262,545)(263,547)
(264,548)(265,557)(266,558)(267,560)(268,559)(269,554)(270,553)(271,555)
(272,556)(273,565)(274,566)(275,568)(276,567)(277,562)(278,561)(279,563)
(280,564)(281,573)(282,574)(283,576)(284,575)(285,570)(286,569)(287,571)
(288,572);
s1 := Sym(576)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 25, 65)( 26, 66)( 27, 68)( 28, 67)
( 29, 71)( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)
( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 41, 49)( 42, 50)( 43, 52)( 44, 51)
( 45, 55)( 46, 56)( 47, 53)( 48, 54)( 75, 76)( 77, 79)( 78, 80)( 81, 89)
( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,137)
( 98,138)( 99,140)(100,139)(101,143)(102,144)(103,141)(104,142)(105,129)
(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)(113,121)
(114,122)(115,124)(116,123)(117,127)(118,128)(119,125)(120,126)(145,217)
(146,218)(147,220)(148,219)(149,223)(150,224)(151,221)(152,222)(153,233)
(154,234)(155,236)(156,235)(157,239)(158,240)(159,237)(160,238)(161,225)
(162,226)(163,228)(164,227)(165,231)(166,232)(167,229)(168,230)(169,281)
(170,282)(171,284)(172,283)(173,287)(174,288)(175,285)(176,286)(177,273)
(178,274)(179,276)(180,275)(181,279)(182,280)(183,277)(184,278)(185,265)
(186,266)(187,268)(188,267)(189,271)(190,272)(191,269)(192,270)(193,257)
(194,258)(195,260)(196,259)(197,263)(198,264)(199,261)(200,262)(201,249)
(202,250)(203,252)(204,251)(205,255)(206,256)(207,253)(208,254)(209,241)
(210,242)(211,244)(212,243)(213,247)(214,248)(215,245)(216,246)(289,290)
(293,296)(294,295)(297,306)(298,305)(299,307)(300,308)(301,312)(302,311)
(303,310)(304,309)(313,354)(314,353)(315,355)(316,356)(317,360)(318,359)
(319,358)(320,357)(321,346)(322,345)(323,347)(324,348)(325,352)(326,351)
(327,350)(328,349)(329,338)(330,337)(331,339)(332,340)(333,344)(334,343)
(335,342)(336,341)(361,362)(365,368)(366,367)(369,378)(370,377)(371,379)
(372,380)(373,384)(374,383)(375,382)(376,381)(385,426)(386,425)(387,427)
(388,428)(389,432)(390,431)(391,430)(392,429)(393,418)(394,417)(395,419)
(396,420)(397,424)(398,423)(399,422)(400,421)(401,410)(402,409)(403,411)
(404,412)(405,416)(406,415)(407,414)(408,413)(433,506)(434,505)(435,507)
(436,508)(437,512)(438,511)(439,510)(440,509)(441,522)(442,521)(443,523)
(444,524)(445,528)(446,527)(447,526)(448,525)(449,514)(450,513)(451,515)
(452,516)(453,520)(454,519)(455,518)(456,517)(457,570)(458,569)(459,571)
(460,572)(461,576)(462,575)(463,574)(464,573)(465,562)(466,561)(467,563)
(468,564)(469,568)(470,567)(471,566)(472,565)(473,554)(474,553)(475,555)
(476,556)(477,560)(478,559)(479,558)(480,557)(481,546)(482,545)(483,547)
(484,548)(485,552)(486,551)(487,550)(488,549)(489,538)(490,537)(491,539)
(492,540)(493,544)(494,543)(495,542)(496,541)(497,530)(498,529)(499,531)
(500,532)(501,536)(502,535)(503,534)(504,533);
s2 := Sym(576)!( 1,169)( 2,170)( 3,175)( 4,176)( 5,174)( 6,173)( 7,171)
( 8,172)( 9,185)( 10,186)( 11,191)( 12,192)( 13,190)( 14,189)( 15,187)
( 16,188)( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)
( 24,180)( 25,145)( 26,146)( 27,151)( 28,152)( 29,150)( 30,149)( 31,147)
( 32,148)( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)
( 40,164)( 41,153)( 42,154)( 43,159)( 44,160)( 45,158)( 46,157)( 47,155)
( 48,156)( 49,209)( 50,210)( 51,215)( 52,216)( 53,214)( 54,213)( 55,211)
( 56,212)( 57,201)( 58,202)( 59,207)( 60,208)( 61,206)( 62,205)( 63,203)
( 64,204)( 65,193)( 66,194)( 67,199)( 68,200)( 69,198)( 70,197)( 71,195)
( 72,196)( 73,241)( 74,242)( 75,247)( 76,248)( 77,246)( 78,245)( 79,243)
( 80,244)( 81,257)( 82,258)( 83,263)( 84,264)( 85,262)( 86,261)( 87,259)
( 88,260)( 89,249)( 90,250)( 91,255)( 92,256)( 93,254)( 94,253)( 95,251)
( 96,252)( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)
(104,220)(105,233)(106,234)(107,239)(108,240)(109,238)(110,237)(111,235)
(112,236)(113,225)(114,226)(115,231)(116,232)(117,230)(118,229)(119,227)
(120,228)(121,281)(122,282)(123,287)(124,288)(125,286)(126,285)(127,283)
(128,284)(129,273)(130,274)(131,279)(132,280)(133,278)(134,277)(135,275)
(136,276)(137,265)(138,266)(139,271)(140,272)(141,270)(142,269)(143,267)
(144,268)(289,458)(290,457)(291,464)(292,463)(293,461)(294,462)(295,460)
(296,459)(297,474)(298,473)(299,480)(300,479)(301,477)(302,478)(303,476)
(304,475)(305,466)(306,465)(307,472)(308,471)(309,469)(310,470)(311,468)
(312,467)(313,434)(314,433)(315,440)(316,439)(317,437)(318,438)(319,436)
(320,435)(321,450)(322,449)(323,456)(324,455)(325,453)(326,454)(327,452)
(328,451)(329,442)(330,441)(331,448)(332,447)(333,445)(334,446)(335,444)
(336,443)(337,498)(338,497)(339,504)(340,503)(341,501)(342,502)(343,500)
(344,499)(345,490)(346,489)(347,496)(348,495)(349,493)(350,494)(351,492)
(352,491)(353,482)(354,481)(355,488)(356,487)(357,485)(358,486)(359,484)
(360,483)(361,530)(362,529)(363,536)(364,535)(365,533)(366,534)(367,532)
(368,531)(369,546)(370,545)(371,552)(372,551)(373,549)(374,550)(375,548)
(376,547)(377,538)(378,537)(379,544)(380,543)(381,541)(382,542)(383,540)
(384,539)(385,506)(386,505)(387,512)(388,511)(389,509)(390,510)(391,508)
(392,507)(393,522)(394,521)(395,528)(396,527)(397,525)(398,526)(399,524)
(400,523)(401,514)(402,513)(403,520)(404,519)(405,517)(406,518)(407,516)
(408,515)(409,570)(410,569)(411,576)(412,575)(413,573)(414,574)(415,572)
(416,571)(417,562)(418,561)(419,568)(420,567)(421,565)(422,566)(423,564)
(424,563)(425,554)(426,553)(427,560)(428,559)(429,557)(430,558)(431,556)
(432,555);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*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 >;
References : None.
to this polytope