Polytope of Type {78,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {78,4}*1248
if this polytope has a name.
Group : SmallGroup(1248,1441)
Rank : 3
Schlafli Type : {78,4}
Number of vertices, edges, etc : 156, 312, 8
Order of s0s1s2 : 78
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {39,4}*624, {78,4}*624b, {78,4}*624c
4-fold quotients : {39,4}*312, {78,2}*312
8-fold quotients : {39,2}*156
12-fold quotients : {26,2}*104
13-fold quotients : {6,4}*96
24-fold quotients : {13,2}*52
26-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
52-fold quotients : {3,4}*24, {6,2}*24
104-fold quotients : {3,2}*12
156-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 49)( 6, 50)( 7, 52)( 8, 51)( 9, 45)( 10, 46)( 11, 48)
( 12, 47)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)( 19, 40)
( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 29)( 26, 30)( 27, 32)
( 28, 31)( 53,105)( 54,106)( 55,108)( 56,107)( 57,153)( 58,154)( 59,156)
( 60,155)( 61,149)( 62,150)( 63,152)( 64,151)( 65,145)( 66,146)( 67,148)
( 68,147)( 69,141)( 70,142)( 71,144)( 72,143)( 73,137)( 74,138)( 75,140)
( 76,139)( 77,133)( 78,134)( 79,136)( 80,135)( 81,129)( 82,130)( 83,132)
( 84,131)( 85,125)( 86,126)( 87,128)( 88,127)( 89,121)( 90,122)( 91,124)
( 92,123)( 93,117)( 94,118)( 95,120)( 96,119)( 97,113)( 98,114)( 99,116)
(100,115)(101,109)(102,110)(103,112)(104,111)(159,160)(161,205)(162,206)
(163,208)(164,207)(165,201)(166,202)(167,204)(168,203)(169,197)(170,198)
(171,200)(172,199)(173,193)(174,194)(175,196)(176,195)(177,189)(178,190)
(179,192)(180,191)(181,185)(182,186)(183,188)(184,187)(209,261)(210,262)
(211,264)(212,263)(213,309)(214,310)(215,312)(216,311)(217,305)(218,306)
(219,308)(220,307)(221,301)(222,302)(223,304)(224,303)(225,297)(226,298)
(227,300)(228,299)(229,293)(230,294)(231,296)(232,295)(233,289)(234,290)
(235,292)(236,291)(237,285)(238,286)(239,288)(240,287)(241,281)(242,282)
(243,284)(244,283)(245,277)(246,278)(247,280)(248,279)(249,273)(250,274)
(251,276)(252,275)(253,269)(254,270)(255,272)(256,271)(257,265)(258,266)
(259,268)(260,267)(315,316)(317,361)(318,362)(319,364)(320,363)(321,357)
(322,358)(323,360)(324,359)(325,353)(326,354)(327,356)(328,355)(329,349)
(330,350)(331,352)(332,351)(333,345)(334,346)(335,348)(336,347)(337,341)
(338,342)(339,344)(340,343)(365,417)(366,418)(367,420)(368,419)(369,465)
(370,466)(371,468)(372,467)(373,461)(374,462)(375,464)(376,463)(377,457)
(378,458)(379,460)(380,459)(381,453)(382,454)(383,456)(384,455)(385,449)
(386,450)(387,452)(388,451)(389,445)(390,446)(391,448)(392,447)(393,441)
(394,442)(395,444)(396,443)(397,437)(398,438)(399,440)(400,439)(401,433)
(402,434)(403,436)(404,435)(405,429)(406,430)(407,432)(408,431)(409,425)
(410,426)(411,428)(412,427)(413,421)(414,422)(415,424)(416,423)(471,472)
(473,517)(474,518)(475,520)(476,519)(477,513)(478,514)(479,516)(480,515)
(481,509)(482,510)(483,512)(484,511)(485,505)(486,506)(487,508)(488,507)
(489,501)(490,502)(491,504)(492,503)(493,497)(494,498)(495,500)(496,499)
(521,573)(522,574)(523,576)(524,575)(525,621)(526,622)(527,624)(528,623)
(529,617)(530,618)(531,620)(532,619)(533,613)(534,614)(535,616)(536,615)
(537,609)(538,610)(539,612)(540,611)(541,605)(542,606)(543,608)(544,607)
(545,601)(546,602)(547,604)(548,603)(549,597)(550,598)(551,600)(552,599)
(553,593)(554,594)(555,596)(556,595)(557,589)(558,590)(559,592)(560,591)
(561,585)(562,586)(563,588)(564,587)(565,581)(566,582)(567,584)(568,583)
(569,577)(570,578)(571,580)(572,579);;
s1 := ( 1,369)( 2,372)( 3,371)( 4,370)( 5,365)( 6,368)( 7,367)( 8,366)
( 9,413)( 10,416)( 11,415)( 12,414)( 13,409)( 14,412)( 15,411)( 16,410)
( 17,405)( 18,408)( 19,407)( 20,406)( 21,401)( 22,404)( 23,403)( 24,402)
( 25,397)( 26,400)( 27,399)( 28,398)( 29,393)( 30,396)( 31,395)( 32,394)
( 33,389)( 34,392)( 35,391)( 36,390)( 37,385)( 38,388)( 39,387)( 40,386)
( 41,381)( 42,384)( 43,383)( 44,382)( 45,377)( 46,380)( 47,379)( 48,378)
( 49,373)( 50,376)( 51,375)( 52,374)( 53,317)( 54,320)( 55,319)( 56,318)
( 57,313)( 58,316)( 59,315)( 60,314)( 61,361)( 62,364)( 63,363)( 64,362)
( 65,357)( 66,360)( 67,359)( 68,358)( 69,353)( 70,356)( 71,355)( 72,354)
( 73,349)( 74,352)( 75,351)( 76,350)( 77,345)( 78,348)( 79,347)( 80,346)
( 81,341)( 82,344)( 83,343)( 84,342)( 85,337)( 86,340)( 87,339)( 88,338)
( 89,333)( 90,336)( 91,335)( 92,334)( 93,329)( 94,332)( 95,331)( 96,330)
( 97,325)( 98,328)( 99,327)(100,326)(101,321)(102,324)(103,323)(104,322)
(105,421)(106,424)(107,423)(108,422)(109,417)(110,420)(111,419)(112,418)
(113,465)(114,468)(115,467)(116,466)(117,461)(118,464)(119,463)(120,462)
(121,457)(122,460)(123,459)(124,458)(125,453)(126,456)(127,455)(128,454)
(129,449)(130,452)(131,451)(132,450)(133,445)(134,448)(135,447)(136,446)
(137,441)(138,444)(139,443)(140,442)(141,437)(142,440)(143,439)(144,438)
(145,433)(146,436)(147,435)(148,434)(149,429)(150,432)(151,431)(152,430)
(153,425)(154,428)(155,427)(156,426)(157,525)(158,528)(159,527)(160,526)
(161,521)(162,524)(163,523)(164,522)(165,569)(166,572)(167,571)(168,570)
(169,565)(170,568)(171,567)(172,566)(173,561)(174,564)(175,563)(176,562)
(177,557)(178,560)(179,559)(180,558)(181,553)(182,556)(183,555)(184,554)
(185,549)(186,552)(187,551)(188,550)(189,545)(190,548)(191,547)(192,546)
(193,541)(194,544)(195,543)(196,542)(197,537)(198,540)(199,539)(200,538)
(201,533)(202,536)(203,535)(204,534)(205,529)(206,532)(207,531)(208,530)
(209,473)(210,476)(211,475)(212,474)(213,469)(214,472)(215,471)(216,470)
(217,517)(218,520)(219,519)(220,518)(221,513)(222,516)(223,515)(224,514)
(225,509)(226,512)(227,511)(228,510)(229,505)(230,508)(231,507)(232,506)
(233,501)(234,504)(235,503)(236,502)(237,497)(238,500)(239,499)(240,498)
(241,493)(242,496)(243,495)(244,494)(245,489)(246,492)(247,491)(248,490)
(249,485)(250,488)(251,487)(252,486)(253,481)(254,484)(255,483)(256,482)
(257,477)(258,480)(259,479)(260,478)(261,577)(262,580)(263,579)(264,578)
(265,573)(266,576)(267,575)(268,574)(269,621)(270,624)(271,623)(272,622)
(273,617)(274,620)(275,619)(276,618)(277,613)(278,616)(279,615)(280,614)
(281,609)(282,612)(283,611)(284,610)(285,605)(286,608)(287,607)(288,606)
(289,601)(290,604)(291,603)(292,602)(293,597)(294,600)(295,599)(296,598)
(297,593)(298,596)(299,595)(300,594)(301,589)(302,592)(303,591)(304,590)
(305,585)(306,588)(307,587)(308,586)(309,581)(310,584)(311,583)(312,582);;
s2 := ( 1,158)( 2,157)( 3,160)( 4,159)( 5,162)( 6,161)( 7,164)( 8,163)
( 9,166)( 10,165)( 11,168)( 12,167)( 13,170)( 14,169)( 15,172)( 16,171)
( 17,174)( 18,173)( 19,176)( 20,175)( 21,178)( 22,177)( 23,180)( 24,179)
( 25,182)( 26,181)( 27,184)( 28,183)( 29,186)( 30,185)( 31,188)( 32,187)
( 33,190)( 34,189)( 35,192)( 36,191)( 37,194)( 38,193)( 39,196)( 40,195)
( 41,198)( 42,197)( 43,200)( 44,199)( 45,202)( 46,201)( 47,204)( 48,203)
( 49,206)( 50,205)( 51,208)( 52,207)( 53,210)( 54,209)( 55,212)( 56,211)
( 57,214)( 58,213)( 59,216)( 60,215)( 61,218)( 62,217)( 63,220)( 64,219)
( 65,222)( 66,221)( 67,224)( 68,223)( 69,226)( 70,225)( 71,228)( 72,227)
( 73,230)( 74,229)( 75,232)( 76,231)( 77,234)( 78,233)( 79,236)( 80,235)
( 81,238)( 82,237)( 83,240)( 84,239)( 85,242)( 86,241)( 87,244)( 88,243)
( 89,246)( 90,245)( 91,248)( 92,247)( 93,250)( 94,249)( 95,252)( 96,251)
( 97,254)( 98,253)( 99,256)(100,255)(101,258)(102,257)(103,260)(104,259)
(105,262)(106,261)(107,264)(108,263)(109,266)(110,265)(111,268)(112,267)
(113,270)(114,269)(115,272)(116,271)(117,274)(118,273)(119,276)(120,275)
(121,278)(122,277)(123,280)(124,279)(125,282)(126,281)(127,284)(128,283)
(129,286)(130,285)(131,288)(132,287)(133,290)(134,289)(135,292)(136,291)
(137,294)(138,293)(139,296)(140,295)(141,298)(142,297)(143,300)(144,299)
(145,302)(146,301)(147,304)(148,303)(149,306)(150,305)(151,308)(152,307)
(153,310)(154,309)(155,312)(156,311)(313,470)(314,469)(315,472)(316,471)
(317,474)(318,473)(319,476)(320,475)(321,478)(322,477)(323,480)(324,479)
(325,482)(326,481)(327,484)(328,483)(329,486)(330,485)(331,488)(332,487)
(333,490)(334,489)(335,492)(336,491)(337,494)(338,493)(339,496)(340,495)
(341,498)(342,497)(343,500)(344,499)(345,502)(346,501)(347,504)(348,503)
(349,506)(350,505)(351,508)(352,507)(353,510)(354,509)(355,512)(356,511)
(357,514)(358,513)(359,516)(360,515)(361,518)(362,517)(363,520)(364,519)
(365,522)(366,521)(367,524)(368,523)(369,526)(370,525)(371,528)(372,527)
(373,530)(374,529)(375,532)(376,531)(377,534)(378,533)(379,536)(380,535)
(381,538)(382,537)(383,540)(384,539)(385,542)(386,541)(387,544)(388,543)
(389,546)(390,545)(391,548)(392,547)(393,550)(394,549)(395,552)(396,551)
(397,554)(398,553)(399,556)(400,555)(401,558)(402,557)(403,560)(404,559)
(405,562)(406,561)(407,564)(408,563)(409,566)(410,565)(411,568)(412,567)
(413,570)(414,569)(415,572)(416,571)(417,574)(418,573)(419,576)(420,575)
(421,578)(422,577)(423,580)(424,579)(425,582)(426,581)(427,584)(428,583)
(429,586)(430,585)(431,588)(432,587)(433,590)(434,589)(435,592)(436,591)
(437,594)(438,593)(439,596)(440,595)(441,598)(442,597)(443,600)(444,599)
(445,602)(446,601)(447,604)(448,603)(449,606)(450,605)(451,608)(452,607)
(453,610)(454,609)(455,612)(456,611)(457,614)(458,613)(459,616)(460,615)
(461,618)(462,617)(463,620)(464,619)(465,622)(466,621)(467,624)(468,623);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(624)!( 3, 4)( 5, 49)( 6, 50)( 7, 52)( 8, 51)( 9, 45)( 10, 46)
( 11, 48)( 12, 47)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)
( 19, 40)( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 29)( 26, 30)
( 27, 32)( 28, 31)( 53,105)( 54,106)( 55,108)( 56,107)( 57,153)( 58,154)
( 59,156)( 60,155)( 61,149)( 62,150)( 63,152)( 64,151)( 65,145)( 66,146)
( 67,148)( 68,147)( 69,141)( 70,142)( 71,144)( 72,143)( 73,137)( 74,138)
( 75,140)( 76,139)( 77,133)( 78,134)( 79,136)( 80,135)( 81,129)( 82,130)
( 83,132)( 84,131)( 85,125)( 86,126)( 87,128)( 88,127)( 89,121)( 90,122)
( 91,124)( 92,123)( 93,117)( 94,118)( 95,120)( 96,119)( 97,113)( 98,114)
( 99,116)(100,115)(101,109)(102,110)(103,112)(104,111)(159,160)(161,205)
(162,206)(163,208)(164,207)(165,201)(166,202)(167,204)(168,203)(169,197)
(170,198)(171,200)(172,199)(173,193)(174,194)(175,196)(176,195)(177,189)
(178,190)(179,192)(180,191)(181,185)(182,186)(183,188)(184,187)(209,261)
(210,262)(211,264)(212,263)(213,309)(214,310)(215,312)(216,311)(217,305)
(218,306)(219,308)(220,307)(221,301)(222,302)(223,304)(224,303)(225,297)
(226,298)(227,300)(228,299)(229,293)(230,294)(231,296)(232,295)(233,289)
(234,290)(235,292)(236,291)(237,285)(238,286)(239,288)(240,287)(241,281)
(242,282)(243,284)(244,283)(245,277)(246,278)(247,280)(248,279)(249,273)
(250,274)(251,276)(252,275)(253,269)(254,270)(255,272)(256,271)(257,265)
(258,266)(259,268)(260,267)(315,316)(317,361)(318,362)(319,364)(320,363)
(321,357)(322,358)(323,360)(324,359)(325,353)(326,354)(327,356)(328,355)
(329,349)(330,350)(331,352)(332,351)(333,345)(334,346)(335,348)(336,347)
(337,341)(338,342)(339,344)(340,343)(365,417)(366,418)(367,420)(368,419)
(369,465)(370,466)(371,468)(372,467)(373,461)(374,462)(375,464)(376,463)
(377,457)(378,458)(379,460)(380,459)(381,453)(382,454)(383,456)(384,455)
(385,449)(386,450)(387,452)(388,451)(389,445)(390,446)(391,448)(392,447)
(393,441)(394,442)(395,444)(396,443)(397,437)(398,438)(399,440)(400,439)
(401,433)(402,434)(403,436)(404,435)(405,429)(406,430)(407,432)(408,431)
(409,425)(410,426)(411,428)(412,427)(413,421)(414,422)(415,424)(416,423)
(471,472)(473,517)(474,518)(475,520)(476,519)(477,513)(478,514)(479,516)
(480,515)(481,509)(482,510)(483,512)(484,511)(485,505)(486,506)(487,508)
(488,507)(489,501)(490,502)(491,504)(492,503)(493,497)(494,498)(495,500)
(496,499)(521,573)(522,574)(523,576)(524,575)(525,621)(526,622)(527,624)
(528,623)(529,617)(530,618)(531,620)(532,619)(533,613)(534,614)(535,616)
(536,615)(537,609)(538,610)(539,612)(540,611)(541,605)(542,606)(543,608)
(544,607)(545,601)(546,602)(547,604)(548,603)(549,597)(550,598)(551,600)
(552,599)(553,593)(554,594)(555,596)(556,595)(557,589)(558,590)(559,592)
(560,591)(561,585)(562,586)(563,588)(564,587)(565,581)(566,582)(567,584)
(568,583)(569,577)(570,578)(571,580)(572,579);
s1 := Sym(624)!( 1,369)( 2,372)( 3,371)( 4,370)( 5,365)( 6,368)( 7,367)
( 8,366)( 9,413)( 10,416)( 11,415)( 12,414)( 13,409)( 14,412)( 15,411)
( 16,410)( 17,405)( 18,408)( 19,407)( 20,406)( 21,401)( 22,404)( 23,403)
( 24,402)( 25,397)( 26,400)( 27,399)( 28,398)( 29,393)( 30,396)( 31,395)
( 32,394)( 33,389)( 34,392)( 35,391)( 36,390)( 37,385)( 38,388)( 39,387)
( 40,386)( 41,381)( 42,384)( 43,383)( 44,382)( 45,377)( 46,380)( 47,379)
( 48,378)( 49,373)( 50,376)( 51,375)( 52,374)( 53,317)( 54,320)( 55,319)
( 56,318)( 57,313)( 58,316)( 59,315)( 60,314)( 61,361)( 62,364)( 63,363)
( 64,362)( 65,357)( 66,360)( 67,359)( 68,358)( 69,353)( 70,356)( 71,355)
( 72,354)( 73,349)( 74,352)( 75,351)( 76,350)( 77,345)( 78,348)( 79,347)
( 80,346)( 81,341)( 82,344)( 83,343)( 84,342)( 85,337)( 86,340)( 87,339)
( 88,338)( 89,333)( 90,336)( 91,335)( 92,334)( 93,329)( 94,332)( 95,331)
( 96,330)( 97,325)( 98,328)( 99,327)(100,326)(101,321)(102,324)(103,323)
(104,322)(105,421)(106,424)(107,423)(108,422)(109,417)(110,420)(111,419)
(112,418)(113,465)(114,468)(115,467)(116,466)(117,461)(118,464)(119,463)
(120,462)(121,457)(122,460)(123,459)(124,458)(125,453)(126,456)(127,455)
(128,454)(129,449)(130,452)(131,451)(132,450)(133,445)(134,448)(135,447)
(136,446)(137,441)(138,444)(139,443)(140,442)(141,437)(142,440)(143,439)
(144,438)(145,433)(146,436)(147,435)(148,434)(149,429)(150,432)(151,431)
(152,430)(153,425)(154,428)(155,427)(156,426)(157,525)(158,528)(159,527)
(160,526)(161,521)(162,524)(163,523)(164,522)(165,569)(166,572)(167,571)
(168,570)(169,565)(170,568)(171,567)(172,566)(173,561)(174,564)(175,563)
(176,562)(177,557)(178,560)(179,559)(180,558)(181,553)(182,556)(183,555)
(184,554)(185,549)(186,552)(187,551)(188,550)(189,545)(190,548)(191,547)
(192,546)(193,541)(194,544)(195,543)(196,542)(197,537)(198,540)(199,539)
(200,538)(201,533)(202,536)(203,535)(204,534)(205,529)(206,532)(207,531)
(208,530)(209,473)(210,476)(211,475)(212,474)(213,469)(214,472)(215,471)
(216,470)(217,517)(218,520)(219,519)(220,518)(221,513)(222,516)(223,515)
(224,514)(225,509)(226,512)(227,511)(228,510)(229,505)(230,508)(231,507)
(232,506)(233,501)(234,504)(235,503)(236,502)(237,497)(238,500)(239,499)
(240,498)(241,493)(242,496)(243,495)(244,494)(245,489)(246,492)(247,491)
(248,490)(249,485)(250,488)(251,487)(252,486)(253,481)(254,484)(255,483)
(256,482)(257,477)(258,480)(259,479)(260,478)(261,577)(262,580)(263,579)
(264,578)(265,573)(266,576)(267,575)(268,574)(269,621)(270,624)(271,623)
(272,622)(273,617)(274,620)(275,619)(276,618)(277,613)(278,616)(279,615)
(280,614)(281,609)(282,612)(283,611)(284,610)(285,605)(286,608)(287,607)
(288,606)(289,601)(290,604)(291,603)(292,602)(293,597)(294,600)(295,599)
(296,598)(297,593)(298,596)(299,595)(300,594)(301,589)(302,592)(303,591)
(304,590)(305,585)(306,588)(307,587)(308,586)(309,581)(310,584)(311,583)
(312,582);
s2 := Sym(624)!( 1,158)( 2,157)( 3,160)( 4,159)( 5,162)( 6,161)( 7,164)
( 8,163)( 9,166)( 10,165)( 11,168)( 12,167)( 13,170)( 14,169)( 15,172)
( 16,171)( 17,174)( 18,173)( 19,176)( 20,175)( 21,178)( 22,177)( 23,180)
( 24,179)( 25,182)( 26,181)( 27,184)( 28,183)( 29,186)( 30,185)( 31,188)
( 32,187)( 33,190)( 34,189)( 35,192)( 36,191)( 37,194)( 38,193)( 39,196)
( 40,195)( 41,198)( 42,197)( 43,200)( 44,199)( 45,202)( 46,201)( 47,204)
( 48,203)( 49,206)( 50,205)( 51,208)( 52,207)( 53,210)( 54,209)( 55,212)
( 56,211)( 57,214)( 58,213)( 59,216)( 60,215)( 61,218)( 62,217)( 63,220)
( 64,219)( 65,222)( 66,221)( 67,224)( 68,223)( 69,226)( 70,225)( 71,228)
( 72,227)( 73,230)( 74,229)( 75,232)( 76,231)( 77,234)( 78,233)( 79,236)
( 80,235)( 81,238)( 82,237)( 83,240)( 84,239)( 85,242)( 86,241)( 87,244)
( 88,243)( 89,246)( 90,245)( 91,248)( 92,247)( 93,250)( 94,249)( 95,252)
( 96,251)( 97,254)( 98,253)( 99,256)(100,255)(101,258)(102,257)(103,260)
(104,259)(105,262)(106,261)(107,264)(108,263)(109,266)(110,265)(111,268)
(112,267)(113,270)(114,269)(115,272)(116,271)(117,274)(118,273)(119,276)
(120,275)(121,278)(122,277)(123,280)(124,279)(125,282)(126,281)(127,284)
(128,283)(129,286)(130,285)(131,288)(132,287)(133,290)(134,289)(135,292)
(136,291)(137,294)(138,293)(139,296)(140,295)(141,298)(142,297)(143,300)
(144,299)(145,302)(146,301)(147,304)(148,303)(149,306)(150,305)(151,308)
(152,307)(153,310)(154,309)(155,312)(156,311)(313,470)(314,469)(315,472)
(316,471)(317,474)(318,473)(319,476)(320,475)(321,478)(322,477)(323,480)
(324,479)(325,482)(326,481)(327,484)(328,483)(329,486)(330,485)(331,488)
(332,487)(333,490)(334,489)(335,492)(336,491)(337,494)(338,493)(339,496)
(340,495)(341,498)(342,497)(343,500)(344,499)(345,502)(346,501)(347,504)
(348,503)(349,506)(350,505)(351,508)(352,507)(353,510)(354,509)(355,512)
(356,511)(357,514)(358,513)(359,516)(360,515)(361,518)(362,517)(363,520)
(364,519)(365,522)(366,521)(367,524)(368,523)(369,526)(370,525)(371,528)
(372,527)(373,530)(374,529)(375,532)(376,531)(377,534)(378,533)(379,536)
(380,535)(381,538)(382,537)(383,540)(384,539)(385,542)(386,541)(387,544)
(388,543)(389,546)(390,545)(391,548)(392,547)(393,550)(394,549)(395,552)
(396,551)(397,554)(398,553)(399,556)(400,555)(401,558)(402,557)(403,560)
(404,559)(405,562)(406,561)(407,564)(408,563)(409,566)(410,565)(411,568)
(412,567)(413,570)(414,569)(415,572)(416,571)(417,574)(418,573)(419,576)
(420,575)(421,578)(422,577)(423,580)(424,579)(425,582)(426,581)(427,584)
(428,583)(429,586)(430,585)(431,588)(432,587)(433,590)(434,589)(435,592)
(436,591)(437,594)(438,593)(439,596)(440,595)(441,598)(442,597)(443,600)
(444,599)(445,602)(446,601)(447,604)(448,603)(449,606)(450,605)(451,608)
(452,607)(453,610)(454,609)(455,612)(456,611)(457,614)(458,613)(459,616)
(460,615)(461,618)(462,617)(463,620)(464,619)(465,622)(466,621)(467,624)
(468,623);
poly := sub<Sym(624)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*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*s0*s1 >;
References : None.
to this polytope