Polytope of Type {8,76}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,76}*1216a
Also Known As : {8,76|2}. if this polytope has another name.
Group : SmallGroup(1216,684)
Rank : 3
Schlafli Type : {8,76}
Number of vertices, edges, etc : 8, 304, 76
Order of s0s1s2 : 152
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 : {4,76}*608, {8,38}*608
4-fold quotients : {2,76}*304, {4,38}*304
8-fold quotients : {2,38}*152
16-fold quotients : {2,19}*76
19-fold quotients : {8,4}*64a
38-fold quotients : {4,4}*32, {8,2}*32
76-fold quotients : {2,4}*16, {4,2}*16
152-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,305)( 2,306)( 3,307)( 4,308)( 5,309)( 6,310)( 7,311)( 8,312)
( 9,313)( 10,314)( 11,315)( 12,316)( 13,317)( 14,318)( 15,319)( 16,320)
( 17,321)( 18,322)( 19,323)( 20,324)( 21,325)( 22,326)( 23,327)( 24,328)
( 25,329)( 26,330)( 27,331)( 28,332)( 29,333)( 30,334)( 31,335)( 32,336)
( 33,337)( 34,338)( 35,339)( 36,340)( 37,341)( 38,342)( 39,343)( 40,344)
( 41,345)( 42,346)( 43,347)( 44,348)( 45,349)( 46,350)( 47,351)( 48,352)
( 49,353)( 50,354)( 51,355)( 52,356)( 53,357)( 54,358)( 55,359)( 56,360)
( 57,361)( 58,362)( 59,363)( 60,364)( 61,365)( 62,366)( 63,367)( 64,368)
( 65,369)( 66,370)( 67,371)( 68,372)( 69,373)( 70,374)( 71,375)( 72,376)
( 73,377)( 74,378)( 75,379)( 76,380)( 77,400)( 78,401)( 79,402)( 80,403)
( 81,404)( 82,405)( 83,406)( 84,407)( 85,408)( 86,409)( 87,410)( 88,411)
( 89,412)( 90,413)( 91,414)( 92,415)( 93,416)( 94,417)( 95,418)( 96,381)
( 97,382)( 98,383)( 99,384)(100,385)(101,386)(102,387)(103,388)(104,389)
(105,390)(106,391)(107,392)(108,393)(109,394)(110,395)(111,396)(112,397)
(113,398)(114,399)(115,438)(116,439)(117,440)(118,441)(119,442)(120,443)
(121,444)(122,445)(123,446)(124,447)(125,448)(126,449)(127,450)(128,451)
(129,452)(130,453)(131,454)(132,455)(133,456)(134,419)(135,420)(136,421)
(137,422)(138,423)(139,424)(140,425)(141,426)(142,427)(143,428)(144,429)
(145,430)(146,431)(147,432)(148,433)(149,434)(150,435)(151,436)(152,437)
(153,457)(154,458)(155,459)(156,460)(157,461)(158,462)(159,463)(160,464)
(161,465)(162,466)(163,467)(164,468)(165,469)(166,470)(167,471)(168,472)
(169,473)(170,474)(171,475)(172,476)(173,477)(174,478)(175,479)(176,480)
(177,481)(178,482)(179,483)(180,484)(181,485)(182,486)(183,487)(184,488)
(185,489)(186,490)(187,491)(188,492)(189,493)(190,494)(191,495)(192,496)
(193,497)(194,498)(195,499)(196,500)(197,501)(198,502)(199,503)(200,504)
(201,505)(202,506)(203,507)(204,508)(205,509)(206,510)(207,511)(208,512)
(209,513)(210,514)(211,515)(212,516)(213,517)(214,518)(215,519)(216,520)
(217,521)(218,522)(219,523)(220,524)(221,525)(222,526)(223,527)(224,528)
(225,529)(226,530)(227,531)(228,532)(229,552)(230,553)(231,554)(232,555)
(233,556)(234,557)(235,558)(236,559)(237,560)(238,561)(239,562)(240,563)
(241,564)(242,565)(243,566)(244,567)(245,568)(246,569)(247,570)(248,533)
(249,534)(250,535)(251,536)(252,537)(253,538)(254,539)(255,540)(256,541)
(257,542)(258,543)(259,544)(260,545)(261,546)(262,547)(263,548)(264,549)
(265,550)(266,551)(267,590)(268,591)(269,592)(270,593)(271,594)(272,595)
(273,596)(274,597)(275,598)(276,599)(277,600)(278,601)(279,602)(280,603)
(281,604)(282,605)(283,606)(284,607)(285,608)(286,571)(287,572)(288,573)
(289,574)(290,575)(291,576)(292,577)(293,578)(294,579)(295,580)(296,581)
(297,582)(298,583)(299,584)(300,585)(301,586)(302,587)(303,588)(304,589);;
s1 := ( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)
( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)( 80,112)
( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)( 88,104)
( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)(115,134)
(116,152)(117,151)(118,150)(119,149)(120,148)(121,147)(122,146)(123,145)
(124,144)(125,143)(126,142)(127,141)(128,140)(129,139)(130,138)(131,137)
(132,136)(133,135)(153,191)(154,209)(155,208)(156,207)(157,206)(158,205)
(159,204)(160,203)(161,202)(162,201)(163,200)(164,199)(165,198)(166,197)
(167,196)(168,195)(169,194)(170,193)(171,192)(172,210)(173,228)(174,227)
(175,226)(176,225)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)
(183,218)(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)(190,211)
(229,286)(230,304)(231,303)(232,302)(233,301)(234,300)(235,299)(236,298)
(237,297)(238,296)(239,295)(240,294)(241,293)(242,292)(243,291)(244,290)
(245,289)(246,288)(247,287)(248,267)(249,285)(250,284)(251,283)(252,282)
(253,281)(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)(260,274)
(261,273)(262,272)(263,271)(264,270)(265,269)(266,268)(305,381)(306,399)
(307,398)(308,397)(309,396)(310,395)(311,394)(312,393)(313,392)(314,391)
(315,390)(316,389)(317,388)(318,387)(319,386)(320,385)(321,384)(322,383)
(323,382)(324,400)(325,418)(326,417)(327,416)(328,415)(329,414)(330,413)
(331,412)(332,411)(333,410)(334,409)(335,408)(336,407)(337,406)(338,405)
(339,404)(340,403)(341,402)(342,401)(343,419)(344,437)(345,436)(346,435)
(347,434)(348,433)(349,432)(350,431)(351,430)(352,429)(353,428)(354,427)
(355,426)(356,425)(357,424)(358,423)(359,422)(360,421)(361,420)(362,438)
(363,456)(364,455)(365,454)(366,453)(367,452)(368,451)(369,450)(370,449)
(371,448)(372,447)(373,446)(374,445)(375,444)(376,443)(377,442)(378,441)
(379,440)(380,439)(457,571)(458,589)(459,588)(460,587)(461,586)(462,585)
(463,584)(464,583)(465,582)(466,581)(467,580)(468,579)(469,578)(470,577)
(471,576)(472,575)(473,574)(474,573)(475,572)(476,590)(477,608)(478,607)
(479,606)(480,605)(481,604)(482,603)(483,602)(484,601)(485,600)(486,599)
(487,598)(488,597)(489,596)(490,595)(491,594)(492,593)(493,592)(494,591)
(495,533)(496,551)(497,550)(498,549)(499,548)(500,547)(501,546)(502,545)
(503,544)(504,543)(505,542)(506,541)(507,540)(508,539)(509,538)(510,537)
(511,536)(512,535)(513,534)(514,552)(515,570)(516,569)(517,568)(518,567)
(519,566)(520,565)(521,564)(522,563)(523,562)(524,561)(525,560)(526,559)
(527,558)(528,557)(529,556)(530,555)(531,554)(532,553);;
s2 := ( 1,154)( 2,153)( 3,171)( 4,170)( 5,169)( 6,168)( 7,167)( 8,166)
( 9,165)( 10,164)( 11,163)( 12,162)( 13,161)( 14,160)( 15,159)( 16,158)
( 17,157)( 18,156)( 19,155)( 20,173)( 21,172)( 22,190)( 23,189)( 24,188)
( 25,187)( 26,186)( 27,185)( 28,184)( 29,183)( 30,182)( 31,181)( 32,180)
( 33,179)( 34,178)( 35,177)( 36,176)( 37,175)( 38,174)( 39,192)( 40,191)
( 41,209)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)( 48,202)
( 49,201)( 50,200)( 51,199)( 52,198)( 53,197)( 54,196)( 55,195)( 56,194)
( 57,193)( 58,211)( 59,210)( 60,228)( 61,227)( 62,226)( 63,225)( 64,224)
( 65,223)( 66,222)( 67,221)( 68,220)( 69,219)( 70,218)( 71,217)( 72,216)
( 73,215)( 74,214)( 75,213)( 76,212)( 77,230)( 78,229)( 79,247)( 80,246)
( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)( 88,238)
( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)( 96,249)
( 97,248)( 98,266)( 99,265)(100,264)(101,263)(102,262)(103,261)(104,260)
(105,259)(106,258)(107,257)(108,256)(109,255)(110,254)(111,253)(112,252)
(113,251)(114,250)(115,268)(116,267)(117,285)(118,284)(119,283)(120,282)
(121,281)(122,280)(123,279)(124,278)(125,277)(126,276)(127,275)(128,274)
(129,273)(130,272)(131,271)(132,270)(133,269)(134,287)(135,286)(136,304)
(137,303)(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)(144,296)
(145,295)(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)(152,288)
(305,458)(306,457)(307,475)(308,474)(309,473)(310,472)(311,471)(312,470)
(313,469)(314,468)(315,467)(316,466)(317,465)(318,464)(319,463)(320,462)
(321,461)(322,460)(323,459)(324,477)(325,476)(326,494)(327,493)(328,492)
(329,491)(330,490)(331,489)(332,488)(333,487)(334,486)(335,485)(336,484)
(337,483)(338,482)(339,481)(340,480)(341,479)(342,478)(343,496)(344,495)
(345,513)(346,512)(347,511)(348,510)(349,509)(350,508)(351,507)(352,506)
(353,505)(354,504)(355,503)(356,502)(357,501)(358,500)(359,499)(360,498)
(361,497)(362,515)(363,514)(364,532)(365,531)(366,530)(367,529)(368,528)
(369,527)(370,526)(371,525)(372,524)(373,523)(374,522)(375,521)(376,520)
(377,519)(378,518)(379,517)(380,516)(381,534)(382,533)(383,551)(384,550)
(385,549)(386,548)(387,547)(388,546)(389,545)(390,544)(391,543)(392,542)
(393,541)(394,540)(395,539)(396,538)(397,537)(398,536)(399,535)(400,553)
(401,552)(402,570)(403,569)(404,568)(405,567)(406,566)(407,565)(408,564)
(409,563)(410,562)(411,561)(412,560)(413,559)(414,558)(415,557)(416,556)
(417,555)(418,554)(419,572)(420,571)(421,589)(422,588)(423,587)(424,586)
(425,585)(426,584)(427,583)(428,582)(429,581)(430,580)(431,579)(432,578)
(433,577)(434,576)(435,575)(436,574)(437,573)(438,591)(439,590)(440,608)
(441,607)(442,606)(443,605)(444,604)(445,603)(446,602)(447,601)(448,600)
(449,599)(450,598)(451,597)(452,596)(453,595)(454,594)(455,593)(456,592);;
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*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(608)!( 1,305)( 2,306)( 3,307)( 4,308)( 5,309)( 6,310)( 7,311)
( 8,312)( 9,313)( 10,314)( 11,315)( 12,316)( 13,317)( 14,318)( 15,319)
( 16,320)( 17,321)( 18,322)( 19,323)( 20,324)( 21,325)( 22,326)( 23,327)
( 24,328)( 25,329)( 26,330)( 27,331)( 28,332)( 29,333)( 30,334)( 31,335)
( 32,336)( 33,337)( 34,338)( 35,339)( 36,340)( 37,341)( 38,342)( 39,343)
( 40,344)( 41,345)( 42,346)( 43,347)( 44,348)( 45,349)( 46,350)( 47,351)
( 48,352)( 49,353)( 50,354)( 51,355)( 52,356)( 53,357)( 54,358)( 55,359)
( 56,360)( 57,361)( 58,362)( 59,363)( 60,364)( 61,365)( 62,366)( 63,367)
( 64,368)( 65,369)( 66,370)( 67,371)( 68,372)( 69,373)( 70,374)( 71,375)
( 72,376)( 73,377)( 74,378)( 75,379)( 76,380)( 77,400)( 78,401)( 79,402)
( 80,403)( 81,404)( 82,405)( 83,406)( 84,407)( 85,408)( 86,409)( 87,410)
( 88,411)( 89,412)( 90,413)( 91,414)( 92,415)( 93,416)( 94,417)( 95,418)
( 96,381)( 97,382)( 98,383)( 99,384)(100,385)(101,386)(102,387)(103,388)
(104,389)(105,390)(106,391)(107,392)(108,393)(109,394)(110,395)(111,396)
(112,397)(113,398)(114,399)(115,438)(116,439)(117,440)(118,441)(119,442)
(120,443)(121,444)(122,445)(123,446)(124,447)(125,448)(126,449)(127,450)
(128,451)(129,452)(130,453)(131,454)(132,455)(133,456)(134,419)(135,420)
(136,421)(137,422)(138,423)(139,424)(140,425)(141,426)(142,427)(143,428)
(144,429)(145,430)(146,431)(147,432)(148,433)(149,434)(150,435)(151,436)
(152,437)(153,457)(154,458)(155,459)(156,460)(157,461)(158,462)(159,463)
(160,464)(161,465)(162,466)(163,467)(164,468)(165,469)(166,470)(167,471)
(168,472)(169,473)(170,474)(171,475)(172,476)(173,477)(174,478)(175,479)
(176,480)(177,481)(178,482)(179,483)(180,484)(181,485)(182,486)(183,487)
(184,488)(185,489)(186,490)(187,491)(188,492)(189,493)(190,494)(191,495)
(192,496)(193,497)(194,498)(195,499)(196,500)(197,501)(198,502)(199,503)
(200,504)(201,505)(202,506)(203,507)(204,508)(205,509)(206,510)(207,511)
(208,512)(209,513)(210,514)(211,515)(212,516)(213,517)(214,518)(215,519)
(216,520)(217,521)(218,522)(219,523)(220,524)(221,525)(222,526)(223,527)
(224,528)(225,529)(226,530)(227,531)(228,532)(229,552)(230,553)(231,554)
(232,555)(233,556)(234,557)(235,558)(236,559)(237,560)(238,561)(239,562)
(240,563)(241,564)(242,565)(243,566)(244,567)(245,568)(246,569)(247,570)
(248,533)(249,534)(250,535)(251,536)(252,537)(253,538)(254,539)(255,540)
(256,541)(257,542)(258,543)(259,544)(260,545)(261,546)(262,547)(263,548)
(264,549)(265,550)(266,551)(267,590)(268,591)(269,592)(270,593)(271,594)
(272,595)(273,596)(274,597)(275,598)(276,599)(277,600)(278,601)(279,602)
(280,603)(281,604)(282,605)(283,606)(284,607)(285,608)(286,571)(287,572)
(288,573)(289,574)(290,575)(291,576)(292,577)(293,578)(294,579)(295,580)
(296,581)(297,582)(298,583)(299,584)(300,585)(301,586)(302,587)(303,588)
(304,589);
s1 := Sym(608)!( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)
( 9, 12)( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)
( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)
( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)
(115,134)(116,152)(117,151)(118,150)(119,149)(120,148)(121,147)(122,146)
(123,145)(124,144)(125,143)(126,142)(127,141)(128,140)(129,139)(130,138)
(131,137)(132,136)(133,135)(153,191)(154,209)(155,208)(156,207)(157,206)
(158,205)(159,204)(160,203)(161,202)(162,201)(163,200)(164,199)(165,198)
(166,197)(167,196)(168,195)(169,194)(170,193)(171,192)(172,210)(173,228)
(174,227)(175,226)(176,225)(177,224)(178,223)(179,222)(180,221)(181,220)
(182,219)(183,218)(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)
(190,211)(229,286)(230,304)(231,303)(232,302)(233,301)(234,300)(235,299)
(236,298)(237,297)(238,296)(239,295)(240,294)(241,293)(242,292)(243,291)
(244,290)(245,289)(246,288)(247,287)(248,267)(249,285)(250,284)(251,283)
(252,282)(253,281)(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)
(260,274)(261,273)(262,272)(263,271)(264,270)(265,269)(266,268)(305,381)
(306,399)(307,398)(308,397)(309,396)(310,395)(311,394)(312,393)(313,392)
(314,391)(315,390)(316,389)(317,388)(318,387)(319,386)(320,385)(321,384)
(322,383)(323,382)(324,400)(325,418)(326,417)(327,416)(328,415)(329,414)
(330,413)(331,412)(332,411)(333,410)(334,409)(335,408)(336,407)(337,406)
(338,405)(339,404)(340,403)(341,402)(342,401)(343,419)(344,437)(345,436)
(346,435)(347,434)(348,433)(349,432)(350,431)(351,430)(352,429)(353,428)
(354,427)(355,426)(356,425)(357,424)(358,423)(359,422)(360,421)(361,420)
(362,438)(363,456)(364,455)(365,454)(366,453)(367,452)(368,451)(369,450)
(370,449)(371,448)(372,447)(373,446)(374,445)(375,444)(376,443)(377,442)
(378,441)(379,440)(380,439)(457,571)(458,589)(459,588)(460,587)(461,586)
(462,585)(463,584)(464,583)(465,582)(466,581)(467,580)(468,579)(469,578)
(470,577)(471,576)(472,575)(473,574)(474,573)(475,572)(476,590)(477,608)
(478,607)(479,606)(480,605)(481,604)(482,603)(483,602)(484,601)(485,600)
(486,599)(487,598)(488,597)(489,596)(490,595)(491,594)(492,593)(493,592)
(494,591)(495,533)(496,551)(497,550)(498,549)(499,548)(500,547)(501,546)
(502,545)(503,544)(504,543)(505,542)(506,541)(507,540)(508,539)(509,538)
(510,537)(511,536)(512,535)(513,534)(514,552)(515,570)(516,569)(517,568)
(518,567)(519,566)(520,565)(521,564)(522,563)(523,562)(524,561)(525,560)
(526,559)(527,558)(528,557)(529,556)(530,555)(531,554)(532,553);
s2 := Sym(608)!( 1,154)( 2,153)( 3,171)( 4,170)( 5,169)( 6,168)( 7,167)
( 8,166)( 9,165)( 10,164)( 11,163)( 12,162)( 13,161)( 14,160)( 15,159)
( 16,158)( 17,157)( 18,156)( 19,155)( 20,173)( 21,172)( 22,190)( 23,189)
( 24,188)( 25,187)( 26,186)( 27,185)( 28,184)( 29,183)( 30,182)( 31,181)
( 32,180)( 33,179)( 34,178)( 35,177)( 36,176)( 37,175)( 38,174)( 39,192)
( 40,191)( 41,209)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)
( 48,202)( 49,201)( 50,200)( 51,199)( 52,198)( 53,197)( 54,196)( 55,195)
( 56,194)( 57,193)( 58,211)( 59,210)( 60,228)( 61,227)( 62,226)( 63,225)
( 64,224)( 65,223)( 66,222)( 67,221)( 68,220)( 69,219)( 70,218)( 71,217)
( 72,216)( 73,215)( 74,214)( 75,213)( 76,212)( 77,230)( 78,229)( 79,247)
( 80,246)( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)
( 88,238)( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)
( 96,249)( 97,248)( 98,266)( 99,265)(100,264)(101,263)(102,262)(103,261)
(104,260)(105,259)(106,258)(107,257)(108,256)(109,255)(110,254)(111,253)
(112,252)(113,251)(114,250)(115,268)(116,267)(117,285)(118,284)(119,283)
(120,282)(121,281)(122,280)(123,279)(124,278)(125,277)(126,276)(127,275)
(128,274)(129,273)(130,272)(131,271)(132,270)(133,269)(134,287)(135,286)
(136,304)(137,303)(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)
(144,296)(145,295)(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)
(152,288)(305,458)(306,457)(307,475)(308,474)(309,473)(310,472)(311,471)
(312,470)(313,469)(314,468)(315,467)(316,466)(317,465)(318,464)(319,463)
(320,462)(321,461)(322,460)(323,459)(324,477)(325,476)(326,494)(327,493)
(328,492)(329,491)(330,490)(331,489)(332,488)(333,487)(334,486)(335,485)
(336,484)(337,483)(338,482)(339,481)(340,480)(341,479)(342,478)(343,496)
(344,495)(345,513)(346,512)(347,511)(348,510)(349,509)(350,508)(351,507)
(352,506)(353,505)(354,504)(355,503)(356,502)(357,501)(358,500)(359,499)
(360,498)(361,497)(362,515)(363,514)(364,532)(365,531)(366,530)(367,529)
(368,528)(369,527)(370,526)(371,525)(372,524)(373,523)(374,522)(375,521)
(376,520)(377,519)(378,518)(379,517)(380,516)(381,534)(382,533)(383,551)
(384,550)(385,549)(386,548)(387,547)(388,546)(389,545)(390,544)(391,543)
(392,542)(393,541)(394,540)(395,539)(396,538)(397,537)(398,536)(399,535)
(400,553)(401,552)(402,570)(403,569)(404,568)(405,567)(406,566)(407,565)
(408,564)(409,563)(410,562)(411,561)(412,560)(413,559)(414,558)(415,557)
(416,556)(417,555)(418,554)(419,572)(420,571)(421,589)(422,588)(423,587)
(424,586)(425,585)(426,584)(427,583)(428,582)(429,581)(430,580)(431,579)
(432,578)(433,577)(434,576)(435,575)(436,574)(437,573)(438,591)(439,590)
(440,608)(441,607)(442,606)(443,605)(444,604)(445,603)(446,602)(447,601)
(448,600)(449,599)(450,598)(451,597)(452,596)(453,595)(454,594)(455,593)
(456,592);
poly := sub<Sym(608)|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*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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