Polytope of Type {8,76}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,76}*1216b
if this polytope has a name.
Group : SmallGroup(1216,718)
Rank : 3
Schlafli Type : {8,76}
Number of vertices, edges, etc : 8, 304, 76
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 : {4,76}*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}*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 := ( 1,305)( 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);;
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)(457,590)(458,608)(459,607)(460,606)(461,605)(462,604)
(463,603)(464,602)(465,601)(466,600)(467,599)(468,598)(469,597)(470,596)
(471,595)(472,594)(473,593)(474,592)(475,591)(476,571)(477,589)(478,588)
(479,587)(480,586)(481,585)(482,584)(483,583)(484,582)(485,581)(486,580)
(487,579)(488,578)(489,577)(490,576)(491,575)(492,574)(493,573)(494,572)
(495,552)(496,570)(497,569)(498,568)(499,567)(500,566)(501,565)(502,564)
(503,563)(504,562)(505,561)(506,560)(507,559)(508,558)(509,557)(510,556)
(511,555)(512,554)(513,553)(514,533)(515,551)(516,550)(517,549)(518,548)
(519,547)(520,546)(521,545)(522,544)(523,543)(524,542)(525,541)(526,540)
(527,539)(528,538)(529,537)(530,536)(531,535)(532,534);;
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)( 77,249)( 78,248)( 79,266)( 80,265)
( 81,264)( 82,263)( 83,262)( 84,261)( 85,260)( 86,259)( 87,258)( 88,257)
( 89,256)( 90,255)( 91,254)( 92,253)( 93,252)( 94,251)( 95,250)( 96,230)
( 97,229)( 98,247)( 99,246)(100,245)(101,244)(102,243)(103,242)(104,241)
(105,240)(106,239)(107,238)(108,237)(109,236)(110,235)(111,234)(112,233)
(113,232)(114,231)(115,287)(116,286)(117,304)(118,303)(119,302)(120,301)
(121,300)(122,299)(123,298)(124,297)(125,296)(126,295)(127,294)(128,293)
(129,292)(130,291)(131,290)(132,289)(133,288)(134,268)(135,267)(136,285)
(137,284)(138,283)(139,282)(140,281)(141,280)(142,279)(143,278)(144,277)
(145,276)(146,275)(147,274)(148,273)(149,272)(150,271)(151,270)(152,269)
(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)(381,553)(382,552)(383,570)(384,569)
(385,568)(386,567)(387,566)(388,565)(389,564)(390,563)(391,562)(392,561)
(393,560)(394,559)(395,558)(396,557)(397,556)(398,555)(399,554)(400,534)
(401,533)(402,551)(403,550)(404,549)(405,548)(406,547)(407,546)(408,545)
(409,544)(410,543)(411,542)(412,541)(413,540)(414,539)(415,538)(416,537)
(417,536)(418,535)(419,591)(420,590)(421,608)(422,607)(423,606)(424,605)
(425,604)(426,603)(427,602)(428,601)(429,600)(430,599)(431,598)(432,597)
(433,596)(434,595)(435,594)(436,593)(437,592)(438,572)(439,571)(440,589)
(441,588)(442,587)(443,586)(444,585)(445,584)(446,583)(447,582)(448,581)
(449,580)(450,579)(451,578)(452,577)(453,576)(454,575)(455,574)(456,573);;
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*s0*s1*s2*s0*s1*s0*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)( 39,362)
( 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);
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)(457,590)(458,608)(459,607)(460,606)(461,605)
(462,604)(463,603)(464,602)(465,601)(466,600)(467,599)(468,598)(469,597)
(470,596)(471,595)(472,594)(473,593)(474,592)(475,591)(476,571)(477,589)
(478,588)(479,587)(480,586)(481,585)(482,584)(483,583)(484,582)(485,581)
(486,580)(487,579)(488,578)(489,577)(490,576)(491,575)(492,574)(493,573)
(494,572)(495,552)(496,570)(497,569)(498,568)(499,567)(500,566)(501,565)
(502,564)(503,563)(504,562)(505,561)(506,560)(507,559)(508,558)(509,557)
(510,556)(511,555)(512,554)(513,553)(514,533)(515,551)(516,550)(517,549)
(518,548)(519,547)(520,546)(521,545)(522,544)(523,543)(524,542)(525,541)
(526,540)(527,539)(528,538)(529,537)(530,536)(531,535)(532,534);
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)( 77,249)( 78,248)( 79,266)
( 80,265)( 81,264)( 82,263)( 83,262)( 84,261)( 85,260)( 86,259)( 87,258)
( 88,257)( 89,256)( 90,255)( 91,254)( 92,253)( 93,252)( 94,251)( 95,250)
( 96,230)( 97,229)( 98,247)( 99,246)(100,245)(101,244)(102,243)(103,242)
(104,241)(105,240)(106,239)(107,238)(108,237)(109,236)(110,235)(111,234)
(112,233)(113,232)(114,231)(115,287)(116,286)(117,304)(118,303)(119,302)
(120,301)(121,300)(122,299)(123,298)(124,297)(125,296)(126,295)(127,294)
(128,293)(129,292)(130,291)(131,290)(132,289)(133,288)(134,268)(135,267)
(136,285)(137,284)(138,283)(139,282)(140,281)(141,280)(142,279)(143,278)
(144,277)(145,276)(146,275)(147,274)(148,273)(149,272)(150,271)(151,270)
(152,269)(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)(381,553)(382,552)(383,570)
(384,569)(385,568)(386,567)(387,566)(388,565)(389,564)(390,563)(391,562)
(392,561)(393,560)(394,559)(395,558)(396,557)(397,556)(398,555)(399,554)
(400,534)(401,533)(402,551)(403,550)(404,549)(405,548)(406,547)(407,546)
(408,545)(409,544)(410,543)(411,542)(412,541)(413,540)(414,539)(415,538)
(416,537)(417,536)(418,535)(419,591)(420,590)(421,608)(422,607)(423,606)
(424,605)(425,604)(426,603)(427,602)(428,601)(429,600)(430,599)(431,598)
(432,597)(433,596)(434,595)(435,594)(436,593)(437,592)(438,572)(439,571)
(440,589)(441,588)(442,587)(443,586)(444,585)(445,584)(446,583)(447,582)
(448,581)(449,580)(450,579)(451,578)(452,577)(453,576)(454,575)(455,574)
(456,573);
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*s0*s1*s2*s0*s1*s0*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