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