Polytope of Type {8,36}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,36}*1152a
if this polytope has a name.
Group : SmallGroup(1152,11996)
Rank : 3
Schlafli Type : {8,36}
Number of vertices, edges, etc : 16, 288, 72
Order of s0s1s2 : 72
Order of s0s1s2s1 : 4
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}*576a, {8,36}*576a, {8,36}*576b
3-fold quotients : {8,12}*384a
4-fold quotients : {4,36}*288a, {8,18}*288
6-fold quotients : {4,12}*192a, {8,12}*192a, {8,12}*192b
8-fold quotients : {2,36}*144, {4,18}*144a
9-fold quotients : {8,4}*128a
12-fold quotients : {4,12}*96a, {8,6}*96
16-fold quotients : {2,18}*72
18-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
24-fold quotients : {2,12}*48, {4,6}*48a
32-fold quotients : {2,9}*36
36-fold quotients : {4,4}*32, {8,2}*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 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)
( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)( 40,337)
( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)
( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)( 56,353)
( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)
( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)
( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)( 80,386)
( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)( 88,394)
( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)( 96,366)
( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)(104,374)
(105,375)(106,376)(107,377)(108,378)(109,424)(110,425)(111,426)(112,427)
(113,428)(114,429)(115,430)(116,431)(117,432)(118,415)(119,416)(120,417)
(121,418)(122,419)(123,420)(124,421)(125,422)(126,423)(127,406)(128,407)
(129,408)(130,409)(131,410)(132,411)(133,412)(134,413)(135,414)(136,397)
(137,398)(138,399)(139,400)(140,401)(141,402)(142,403)(143,404)(144,405)
(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)
(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)
(161,449)(162,450)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)
(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)
(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)(184,481)
(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)
(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,496)(200,497)
(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)
(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)
(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)(224,530)
(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)(232,538)
(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)(240,510)
(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)(248,518)
(249,519)(250,520)(251,521)(252,522)(253,568)(254,569)(255,570)(256,571)
(257,572)(258,573)(259,574)(260,575)(261,576)(262,559)(263,560)(264,561)
(265,562)(266,563)(267,564)(268,565)(269,566)(270,567)(271,550)(272,551)
(273,552)(274,553)(275,554)(276,555)(277,556)(278,557)(279,558)(280,541)
(281,542)(282,543)(283,544)(284,545)(285,546)(286,547)(287,548)(288,549);;
s1 := ( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)
( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)( 33, 34)
( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)( 51, 52)
( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 65, 66)( 67, 72)( 68, 71)( 69, 70)
( 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)(163,199)(164,201)
(165,200)(166,207)(167,206)(168,205)(169,204)(170,203)(171,202)(172,208)
(173,210)(174,209)(175,216)(176,215)(177,214)(178,213)(179,212)(180,211)
(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)(307,379)(308,381)
(309,380)(310,387)(311,386)(312,385)(313,384)(314,383)(315,382)(316,388)
(317,390)(318,389)(319,396)(320,395)(321,394)(322,393)(323,392)(324,391)
(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)(343,415)(344,417)(345,416)(346,423)(347,422)(348,421)
(349,420)(350,419)(351,418)(352,424)(353,426)(354,425)(355,432)(356,431)
(357,430)(358,429)(359,428)(360,427)(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)(451,568)(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)
(469,514)(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)(487,532)(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 := ( 1,148)( 2,150)( 3,149)( 4,145)( 5,147)( 6,146)( 7,153)( 8,152)
( 9,151)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,162)
( 17,161)( 18,160)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)
( 25,171)( 26,170)( 27,169)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)
( 33,173)( 34,180)( 35,179)( 36,178)( 37,184)( 38,186)( 39,185)( 40,181)
( 41,183)( 42,182)( 43,189)( 44,188)( 45,187)( 46,193)( 47,195)( 48,194)
( 49,190)( 50,192)( 51,191)( 52,198)( 53,197)( 54,196)( 55,202)( 56,204)
( 57,203)( 58,199)( 59,201)( 60,200)( 61,207)( 62,206)( 63,205)( 64,211)
( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,216)( 71,215)( 72,214)
( 73,229)( 74,231)( 75,230)( 76,226)( 77,228)( 78,227)( 79,234)( 80,233)
( 81,232)( 82,220)( 83,222)( 84,221)( 85,217)( 86,219)( 87,218)( 88,225)
( 89,224)( 90,223)( 91,247)( 92,249)( 93,248)( 94,244)( 95,246)( 96,245)
( 97,252)( 98,251)( 99,250)(100,238)(101,240)(102,239)(103,235)(104,237)
(105,236)(106,243)(107,242)(108,241)(109,265)(110,267)(111,266)(112,262)
(113,264)(114,263)(115,270)(116,269)(117,268)(118,256)(119,258)(120,257)
(121,253)(122,255)(123,254)(124,261)(125,260)(126,259)(127,283)(128,285)
(129,284)(130,280)(131,282)(132,281)(133,288)(134,287)(135,286)(136,274)
(137,276)(138,275)(139,271)(140,273)(141,272)(142,279)(143,278)(144,277)
(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,441)(296,440)
(297,439)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,450)
(305,449)(306,448)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)
(313,459)(314,458)(315,457)(316,463)(317,465)(318,464)(319,460)(320,462)
(321,461)(322,468)(323,467)(324,466)(325,472)(326,474)(327,473)(328,469)
(329,471)(330,470)(331,477)(332,476)(333,475)(334,481)(335,483)(336,482)
(337,478)(338,480)(339,479)(340,486)(341,485)(342,484)(343,490)(344,492)
(345,491)(346,487)(347,489)(348,488)(349,495)(350,494)(351,493)(352,499)
(353,501)(354,500)(355,496)(356,498)(357,497)(358,504)(359,503)(360,502)
(361,517)(362,519)(363,518)(364,514)(365,516)(366,515)(367,522)(368,521)
(369,520)(370,508)(371,510)(372,509)(373,505)(374,507)(375,506)(376,513)
(377,512)(378,511)(379,535)(380,537)(381,536)(382,532)(383,534)(384,533)
(385,540)(386,539)(387,538)(388,526)(389,528)(390,527)(391,523)(392,525)
(393,524)(394,531)(395,530)(396,529)(397,553)(398,555)(399,554)(400,550)
(401,552)(402,551)(403,558)(404,557)(405,556)(406,544)(407,546)(408,545)
(409,541)(410,543)(411,542)(412,549)(413,548)(414,547)(415,571)(416,573)
(417,572)(418,568)(419,570)(420,569)(421,576)(422,575)(423,574)(424,562)
(425,564)(426,563)(427,559)(428,561)(429,560)(430,567)(431,566)(432,565);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*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)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)
( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)
( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)
( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)
( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)
( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)
( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)
( 72,351)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)
( 80,386)( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)
( 88,394)( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)
( 96,366)( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)
(104,374)(105,375)(106,376)(107,377)(108,378)(109,424)(110,425)(111,426)
(112,427)(113,428)(114,429)(115,430)(116,431)(117,432)(118,415)(119,416)
(120,417)(121,418)(122,419)(123,420)(124,421)(125,422)(126,423)(127,406)
(128,407)(129,408)(130,409)(131,410)(132,411)(133,412)(134,413)(135,414)
(136,397)(137,398)(138,399)(139,400)(140,401)(141,402)(142,403)(143,404)
(144,405)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)
(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)
(160,448)(161,449)(162,450)(163,451)(164,452)(165,453)(166,454)(167,455)
(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)
(176,464)(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)
(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)
(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,496)
(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)
(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)
(216,495)(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)
(224,530)(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)
(232,538)(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)
(240,510)(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)
(248,518)(249,519)(250,520)(251,521)(252,522)(253,568)(254,569)(255,570)
(256,571)(257,572)(258,573)(259,574)(260,575)(261,576)(262,559)(263,560)
(264,561)(265,562)(266,563)(267,564)(268,565)(269,566)(270,567)(271,550)
(272,551)(273,552)(274,553)(275,554)(276,555)(277,556)(278,557)(279,558)
(280,541)(281,542)(282,543)(283,544)(284,545)(285,546)(286,547)(287,548)
(288,549);
s1 := Sym(576)!( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)
( 15, 16)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)
( 33, 34)( 38, 39)( 40, 45)( 41, 44)( 42, 43)( 47, 48)( 49, 54)( 50, 53)
( 51, 52)( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 65, 66)( 67, 72)( 68, 71)
( 69, 70)( 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)(163,199)
(164,201)(165,200)(166,207)(167,206)(168,205)(169,204)(170,203)(171,202)
(172,208)(173,210)(174,209)(175,216)(176,215)(177,214)(178,213)(179,212)
(180,211)(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)(307,379)
(308,381)(309,380)(310,387)(311,386)(312,385)(313,384)(314,383)(315,382)
(316,388)(317,390)(318,389)(319,396)(320,395)(321,394)(322,393)(323,392)
(324,391)(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)(343,415)(344,417)(345,416)(346,423)(347,422)
(348,421)(349,420)(350,419)(351,418)(352,424)(353,426)(354,425)(355,432)
(356,431)(357,430)(358,429)(359,428)(360,427)(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)(451,568)
(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)(469,514)(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)(487,532)(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)!( 1,148)( 2,150)( 3,149)( 4,145)( 5,147)( 6,146)( 7,153)
( 8,152)( 9,151)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)
( 16,162)( 17,161)( 18,160)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)
( 24,164)( 25,171)( 26,170)( 27,169)( 28,175)( 29,177)( 30,176)( 31,172)
( 32,174)( 33,173)( 34,180)( 35,179)( 36,178)( 37,184)( 38,186)( 39,185)
( 40,181)( 41,183)( 42,182)( 43,189)( 44,188)( 45,187)( 46,193)( 47,195)
( 48,194)( 49,190)( 50,192)( 51,191)( 52,198)( 53,197)( 54,196)( 55,202)
( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,207)( 62,206)( 63,205)
( 64,211)( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,216)( 71,215)
( 72,214)( 73,229)( 74,231)( 75,230)( 76,226)( 77,228)( 78,227)( 79,234)
( 80,233)( 81,232)( 82,220)( 83,222)( 84,221)( 85,217)( 86,219)( 87,218)
( 88,225)( 89,224)( 90,223)( 91,247)( 92,249)( 93,248)( 94,244)( 95,246)
( 96,245)( 97,252)( 98,251)( 99,250)(100,238)(101,240)(102,239)(103,235)
(104,237)(105,236)(106,243)(107,242)(108,241)(109,265)(110,267)(111,266)
(112,262)(113,264)(114,263)(115,270)(116,269)(117,268)(118,256)(119,258)
(120,257)(121,253)(122,255)(123,254)(124,261)(125,260)(126,259)(127,283)
(128,285)(129,284)(130,280)(131,282)(132,281)(133,288)(134,287)(135,286)
(136,274)(137,276)(138,275)(139,271)(140,273)(141,272)(142,279)(143,278)
(144,277)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,441)
(296,440)(297,439)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)
(304,450)(305,449)(306,448)(307,454)(308,456)(309,455)(310,451)(311,453)
(312,452)(313,459)(314,458)(315,457)(316,463)(317,465)(318,464)(319,460)
(320,462)(321,461)(322,468)(323,467)(324,466)(325,472)(326,474)(327,473)
(328,469)(329,471)(330,470)(331,477)(332,476)(333,475)(334,481)(335,483)
(336,482)(337,478)(338,480)(339,479)(340,486)(341,485)(342,484)(343,490)
(344,492)(345,491)(346,487)(347,489)(348,488)(349,495)(350,494)(351,493)
(352,499)(353,501)(354,500)(355,496)(356,498)(357,497)(358,504)(359,503)
(360,502)(361,517)(362,519)(363,518)(364,514)(365,516)(366,515)(367,522)
(368,521)(369,520)(370,508)(371,510)(372,509)(373,505)(374,507)(375,506)
(376,513)(377,512)(378,511)(379,535)(380,537)(381,536)(382,532)(383,534)
(384,533)(385,540)(386,539)(387,538)(388,526)(389,528)(390,527)(391,523)
(392,525)(393,524)(394,531)(395,530)(396,529)(397,553)(398,555)(399,554)
(400,550)(401,552)(402,551)(403,558)(404,557)(405,556)(406,544)(407,546)
(408,545)(409,541)(410,543)(411,542)(412,549)(413,548)(414,547)(415,571)
(416,573)(417,572)(418,568)(419,570)(420,569)(421,576)(422,575)(423,574)
(424,562)(425,564)(426,563)(427,559)(428,561)(429,560)(430,567)(431,566)
(432,565);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*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