Polytope of Type {76,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {76,8}*1216b
if this polytope has a name.
Group : SmallGroup(1216,718)
Rank : 3
Schlafli Type : {76,8}
Number of vertices, edges, etc : 76, 304, 8
Order of s0s1s2 : 152
Order of s0s1s2s1 : 4
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
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}*64b
38-fold quotients : {4,4}*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)( 77,248)( 78,266)( 79,265)( 80,264)
( 81,263)( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)( 88,256)
( 89,255)( 90,254)( 91,253)( 92,252)( 93,251)( 94,250)( 95,249)( 96,229)
( 97,247)( 98,246)( 99,245)(100,244)(101,243)(102,242)(103,241)(104,240)
(105,239)(106,238)(107,237)(108,236)(109,235)(110,234)(111,233)(112,232)
(113,231)(114,230)(115,286)(116,304)(117,303)(118,302)(119,301)(120,300)
(121,299)(122,298)(123,297)(124,296)(125,295)(126,294)(127,293)(128,292)
(129,291)(130,290)(131,289)(132,288)(133,287)(134,267)(135,285)(136,284)
(137,283)(138,282)(139,281)(140,280)(141,279)(142,278)(143,277)(144,276)
(145,275)(146,274)(147,273)(148,272)(149,271)(150,270)(151,269)(152,268)
(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)(381,552)(382,570)(383,569)(384,568)
(385,567)(386,566)(387,565)(388,564)(389,563)(390,562)(391,561)(392,560)
(393,559)(394,558)(395,557)(396,556)(397,555)(398,554)(399,553)(400,533)
(401,551)(402,550)(403,549)(404,548)(405,547)(406,546)(407,545)(408,544)
(409,543)(410,542)(411,541)(412,540)(413,539)(414,538)(415,537)(416,536)
(417,535)(418,534)(419,590)(420,608)(421,607)(422,606)(423,605)(424,604)
(425,603)(426,602)(427,601)(428,600)(429,599)(430,598)(431,597)(432,596)
(433,595)(434,594)(435,593)(436,592)(437,591)(438,571)(439,589)(440,588)
(441,587)(442,586)(443,585)(444,584)(445,583)(446,582)(447,581)(448,580)
(449,579)(450,578)(451,577)(452,576)(453,575)(454,574)(455,573)(456,572);;
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)(457,591)(458,590)(459,608)(460,607)(461,606)(462,605)
(463,604)(464,603)(465,602)(466,601)(467,600)(468,599)(469,598)(470,597)
(471,596)(472,595)(473,594)(474,593)(475,592)(476,572)(477,571)(478,589)
(479,588)(480,587)(481,586)(482,585)(483,584)(484,583)(485,582)(486,581)
(487,580)(488,579)(489,578)(490,577)(491,576)(492,575)(493,574)(494,573)
(495,553)(496,552)(497,570)(498,569)(499,568)(500,567)(501,566)(502,565)
(503,564)(504,563)(505,562)(506,561)(507,560)(508,559)(509,558)(510,557)
(511,556)(512,555)(513,554)(514,534)(515,533)(516,551)(517,550)(518,549)
(519,548)(520,547)(521,546)(522,545)(523,544)(524,543)(525,542)(526,541)
(527,540)(528,539)(529,538)(530,537)(531,536)(532,535);;
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)( 39,362)( 40,363)
( 41,364)( 42,365)( 43,366)( 44,367)( 45,368)( 46,369)( 47,370)( 48,371)
( 49,372)( 50,373)( 51,374)( 52,375)( 53,376)( 54,377)( 55,378)( 56,379)
( 57,380)( 58,343)( 59,344)( 60,345)( 61,346)( 62,347)( 63,348)( 64,349)
( 65,350)( 66,351)( 67,352)( 68,353)( 69,354)( 70,355)( 71,356)( 72,357)
( 73,358)( 74,359)( 75,360)( 76,361)( 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)(115,419)(116,420)(117,421)(118,422)(119,423)(120,424)
(121,425)(122,426)(123,427)(124,428)(125,429)(126,430)(127,431)(128,432)
(129,433)(130,434)(131,435)(132,436)(133,437)(134,438)(135,439)(136,440)
(137,441)(138,442)(139,443)(140,444)(141,445)(142,446)(143,447)(144,448)
(145,449)(146,450)(147,451)(148,452)(149,453)(150,454)(151,455)(152,456)
(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)(191,514)(192,515)
(193,516)(194,517)(195,518)(196,519)(197,520)(198,521)(199,522)(200,523)
(201,524)(202,525)(203,526)(204,527)(205,528)(206,529)(207,530)(208,531)
(209,532)(210,495)(211,496)(212,497)(213,498)(214,499)(215,500)(216,501)
(217,502)(218,503)(219,504)(220,505)(221,506)(222,507)(223,508)(224,509)
(225,510)(226,511)(227,512)(228,513)(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)(267,571)(268,572)(269,573)(270,574)(271,575)(272,576)
(273,577)(274,578)(275,579)(276,580)(277,581)(278,582)(279,583)(280,584)
(281,585)(282,586)(283,587)(284,588)(285,589)(286,590)(287,591)(288,592)
(289,593)(290,594)(291,595)(292,596)(293,597)(294,598)(295,599)(296,600)
(297,601)(298,602)(299,603)(300,604)(301,605)(302,606)(303,607)(304,608);;
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*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*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)( 77,248)( 78,266)( 79,265)
( 80,264)( 81,263)( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)
( 88,256)( 89,255)( 90,254)( 91,253)( 92,252)( 93,251)( 94,250)( 95,249)
( 96,229)( 97,247)( 98,246)( 99,245)(100,244)(101,243)(102,242)(103,241)
(104,240)(105,239)(106,238)(107,237)(108,236)(109,235)(110,234)(111,233)
(112,232)(113,231)(114,230)(115,286)(116,304)(117,303)(118,302)(119,301)
(120,300)(121,299)(122,298)(123,297)(124,296)(125,295)(126,294)(127,293)
(128,292)(129,291)(130,290)(131,289)(132,288)(133,287)(134,267)(135,285)
(136,284)(137,283)(138,282)(139,281)(140,280)(141,279)(142,278)(143,277)
(144,276)(145,275)(146,274)(147,273)(148,272)(149,271)(150,270)(151,269)
(152,268)(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)(381,552)(382,570)(383,569)
(384,568)(385,567)(386,566)(387,565)(388,564)(389,563)(390,562)(391,561)
(392,560)(393,559)(394,558)(395,557)(396,556)(397,555)(398,554)(399,553)
(400,533)(401,551)(402,550)(403,549)(404,548)(405,547)(406,546)(407,545)
(408,544)(409,543)(410,542)(411,541)(412,540)(413,539)(414,538)(415,537)
(416,536)(417,535)(418,534)(419,590)(420,608)(421,607)(422,606)(423,605)
(424,604)(425,603)(426,602)(427,601)(428,600)(429,599)(430,598)(431,597)
(432,596)(433,595)(434,594)(435,593)(436,592)(437,591)(438,571)(439,589)
(440,588)(441,587)(442,586)(443,585)(444,584)(445,583)(446,582)(447,581)
(448,580)(449,579)(450,578)(451,577)(452,576)(453,575)(454,574)(455,573)
(456,572);
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)(457,591)(458,590)(459,608)(460,607)(461,606)
(462,605)(463,604)(464,603)(465,602)(466,601)(467,600)(468,599)(469,598)
(470,597)(471,596)(472,595)(473,594)(474,593)(475,592)(476,572)(477,571)
(478,589)(479,588)(480,587)(481,586)(482,585)(483,584)(484,583)(485,582)
(486,581)(487,580)(488,579)(489,578)(490,577)(491,576)(492,575)(493,574)
(494,573)(495,553)(496,552)(497,570)(498,569)(499,568)(500,567)(501,566)
(502,565)(503,564)(504,563)(505,562)(506,561)(507,560)(508,559)(509,558)
(510,557)(511,556)(512,555)(513,554)(514,534)(515,533)(516,551)(517,550)
(518,549)(519,548)(520,547)(521,546)(522,545)(523,544)(524,543)(525,542)
(526,541)(527,540)(528,539)(529,538)(530,537)(531,536)(532,535);
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)( 39,362)
( 40,363)( 41,364)( 42,365)( 43,366)( 44,367)( 45,368)( 46,369)( 47,370)
( 48,371)( 49,372)( 50,373)( 51,374)( 52,375)( 53,376)( 54,377)( 55,378)
( 56,379)( 57,380)( 58,343)( 59,344)( 60,345)( 61,346)( 62,347)( 63,348)
( 64,349)( 65,350)( 66,351)( 67,352)( 68,353)( 69,354)( 70,355)( 71,356)
( 72,357)( 73,358)( 74,359)( 75,360)( 76,361)( 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)(115,419)(116,420)(117,421)(118,422)(119,423)
(120,424)(121,425)(122,426)(123,427)(124,428)(125,429)(126,430)(127,431)
(128,432)(129,433)(130,434)(131,435)(132,436)(133,437)(134,438)(135,439)
(136,440)(137,441)(138,442)(139,443)(140,444)(141,445)(142,446)(143,447)
(144,448)(145,449)(146,450)(147,451)(148,452)(149,453)(150,454)(151,455)
(152,456)(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)(191,514)
(192,515)(193,516)(194,517)(195,518)(196,519)(197,520)(198,521)(199,522)
(200,523)(201,524)(202,525)(203,526)(204,527)(205,528)(206,529)(207,530)
(208,531)(209,532)(210,495)(211,496)(212,497)(213,498)(214,499)(215,500)
(216,501)(217,502)(218,503)(219,504)(220,505)(221,506)(222,507)(223,508)
(224,509)(225,510)(226,511)(227,512)(228,513)(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)(267,571)(268,572)(269,573)(270,574)(271,575)
(272,576)(273,577)(274,578)(275,579)(276,580)(277,581)(278,582)(279,583)
(280,584)(281,585)(282,586)(283,587)(284,588)(285,589)(286,590)(287,591)
(288,592)(289,593)(290,594)(291,595)(292,596)(293,597)(294,598)(295,599)
(296,600)(297,601)(298,602)(299,603)(300,604)(301,605)(302,606)(303,607)
(304,608);
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope