Polytope of Type {4,156}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,156}*1248c
if this polytope has a name.
Group : SmallGroup(1248,1233)
Rank : 3
Schlafli Type : {4,156}
Number of vertices, edges, etc : 4, 312, 156
Order of s0s1s2 : 156
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-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 : {4,78}*624b
4-fold quotients : {4,39}*312
13-fold quotients : {4,12}*96c
26-fold quotients : {4,6}*48c
52-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,159)( 2,160)( 3,157)( 4,158)( 5,163)( 6,164)( 7,161)( 8,162)
( 9,167)( 10,168)( 11,165)( 12,166)( 13,171)( 14,172)( 15,169)( 16,170)
( 17,175)( 18,176)( 19,173)( 20,174)( 21,179)( 22,180)( 23,177)( 24,178)
( 25,183)( 26,184)( 27,181)( 28,182)( 29,187)( 30,188)( 31,185)( 32,186)
( 33,191)( 34,192)( 35,189)( 36,190)( 37,195)( 38,196)( 39,193)( 40,194)
( 41,199)( 42,200)( 43,197)( 44,198)( 45,203)( 46,204)( 47,201)( 48,202)
( 49,207)( 50,208)( 51,205)( 52,206)( 53,211)( 54,212)( 55,209)( 56,210)
( 57,215)( 58,216)( 59,213)( 60,214)( 61,219)( 62,220)( 63,217)( 64,218)
( 65,223)( 66,224)( 67,221)( 68,222)( 69,227)( 70,228)( 71,225)( 72,226)
( 73,231)( 74,232)( 75,229)( 76,230)( 77,235)( 78,236)( 79,233)( 80,234)
( 81,239)( 82,240)( 83,237)( 84,238)( 85,243)( 86,244)( 87,241)( 88,242)
( 89,247)( 90,248)( 91,245)( 92,246)( 93,251)( 94,252)( 95,249)( 96,250)
( 97,255)( 98,256)( 99,253)(100,254)(101,259)(102,260)(103,257)(104,258)
(105,263)(106,264)(107,261)(108,262)(109,267)(110,268)(111,265)(112,266)
(113,271)(114,272)(115,269)(116,270)(117,275)(118,276)(119,273)(120,274)
(121,279)(122,280)(123,277)(124,278)(125,283)(126,284)(127,281)(128,282)
(129,287)(130,288)(131,285)(132,286)(133,291)(134,292)(135,289)(136,290)
(137,295)(138,296)(139,293)(140,294)(141,299)(142,300)(143,297)(144,298)
(145,303)(146,304)(147,301)(148,302)(149,307)(150,308)(151,305)(152,306)
(153,311)(154,312)(155,309)(156,310)(313,471)(314,472)(315,469)(316,470)
(317,475)(318,476)(319,473)(320,474)(321,479)(322,480)(323,477)(324,478)
(325,483)(326,484)(327,481)(328,482)(329,487)(330,488)(331,485)(332,486)
(333,491)(334,492)(335,489)(336,490)(337,495)(338,496)(339,493)(340,494)
(341,499)(342,500)(343,497)(344,498)(345,503)(346,504)(347,501)(348,502)
(349,507)(350,508)(351,505)(352,506)(353,511)(354,512)(355,509)(356,510)
(357,515)(358,516)(359,513)(360,514)(361,519)(362,520)(363,517)(364,518)
(365,523)(366,524)(367,521)(368,522)(369,527)(370,528)(371,525)(372,526)
(373,531)(374,532)(375,529)(376,530)(377,535)(378,536)(379,533)(380,534)
(381,539)(382,540)(383,537)(384,538)(385,543)(386,544)(387,541)(388,542)
(389,547)(390,548)(391,545)(392,546)(393,551)(394,552)(395,549)(396,550)
(397,555)(398,556)(399,553)(400,554)(401,559)(402,560)(403,557)(404,558)
(405,563)(406,564)(407,561)(408,562)(409,567)(410,568)(411,565)(412,566)
(413,571)(414,572)(415,569)(416,570)(417,575)(418,576)(419,573)(420,574)
(421,579)(422,580)(423,577)(424,578)(425,583)(426,584)(427,581)(428,582)
(429,587)(430,588)(431,585)(432,586)(433,591)(434,592)(435,589)(436,590)
(437,595)(438,596)(439,593)(440,594)(441,599)(442,600)(443,597)(444,598)
(445,603)(446,604)(447,601)(448,602)(449,607)(450,608)(451,605)(452,606)
(453,611)(454,612)(455,609)(456,610)(457,615)(458,616)(459,613)(460,614)
(461,619)(462,620)(463,617)(464,618)(465,623)(466,624)(467,621)(468,622);;
s1 := ( 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)(313,469)(314,470)(315,472)(316,471)(317,517)(318,518)
(319,520)(320,519)(321,513)(322,514)(323,516)(324,515)(325,509)(326,510)
(327,512)(328,511)(329,505)(330,506)(331,508)(332,507)(333,501)(334,502)
(335,504)(336,503)(337,497)(338,498)(339,500)(340,499)(341,493)(342,494)
(343,496)(344,495)(345,489)(346,490)(347,492)(348,491)(349,485)(350,486)
(351,488)(352,487)(353,481)(354,482)(355,484)(356,483)(357,477)(358,478)
(359,480)(360,479)(361,473)(362,474)(363,476)(364,475)(365,573)(366,574)
(367,576)(368,575)(369,621)(370,622)(371,624)(372,623)(373,617)(374,618)
(375,620)(376,619)(377,613)(378,614)(379,616)(380,615)(381,609)(382,610)
(383,612)(384,611)(385,605)(386,606)(387,608)(388,607)(389,601)(390,602)
(391,604)(392,603)(393,597)(394,598)(395,600)(396,599)(397,593)(398,594)
(399,596)(400,595)(401,589)(402,590)(403,592)(404,591)(405,585)(406,586)
(407,588)(408,587)(409,581)(410,582)(411,584)(412,583)(413,577)(414,578)
(415,580)(416,579)(417,521)(418,522)(419,524)(420,523)(421,569)(422,570)
(423,572)(424,571)(425,565)(426,566)(427,568)(428,567)(429,561)(430,562)
(431,564)(432,563)(433,557)(434,558)(435,560)(436,559)(437,553)(438,554)
(439,556)(440,555)(441,549)(442,550)(443,552)(444,551)(445,545)(446,546)
(447,548)(448,547)(449,541)(450,542)(451,544)(452,543)(453,537)(454,538)
(455,540)(456,539)(457,533)(458,534)(459,536)(460,535)(461,529)(462,530)
(463,532)(464,531)(465,525)(466,526)(467,528)(468,527);;
s2 := ( 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);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*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(624)!( 1,159)( 2,160)( 3,157)( 4,158)( 5,163)( 6,164)( 7,161)
( 8,162)( 9,167)( 10,168)( 11,165)( 12,166)( 13,171)( 14,172)( 15,169)
( 16,170)( 17,175)( 18,176)( 19,173)( 20,174)( 21,179)( 22,180)( 23,177)
( 24,178)( 25,183)( 26,184)( 27,181)( 28,182)( 29,187)( 30,188)( 31,185)
( 32,186)( 33,191)( 34,192)( 35,189)( 36,190)( 37,195)( 38,196)( 39,193)
( 40,194)( 41,199)( 42,200)( 43,197)( 44,198)( 45,203)( 46,204)( 47,201)
( 48,202)( 49,207)( 50,208)( 51,205)( 52,206)( 53,211)( 54,212)( 55,209)
( 56,210)( 57,215)( 58,216)( 59,213)( 60,214)( 61,219)( 62,220)( 63,217)
( 64,218)( 65,223)( 66,224)( 67,221)( 68,222)( 69,227)( 70,228)( 71,225)
( 72,226)( 73,231)( 74,232)( 75,229)( 76,230)( 77,235)( 78,236)( 79,233)
( 80,234)( 81,239)( 82,240)( 83,237)( 84,238)( 85,243)( 86,244)( 87,241)
( 88,242)( 89,247)( 90,248)( 91,245)( 92,246)( 93,251)( 94,252)( 95,249)
( 96,250)( 97,255)( 98,256)( 99,253)(100,254)(101,259)(102,260)(103,257)
(104,258)(105,263)(106,264)(107,261)(108,262)(109,267)(110,268)(111,265)
(112,266)(113,271)(114,272)(115,269)(116,270)(117,275)(118,276)(119,273)
(120,274)(121,279)(122,280)(123,277)(124,278)(125,283)(126,284)(127,281)
(128,282)(129,287)(130,288)(131,285)(132,286)(133,291)(134,292)(135,289)
(136,290)(137,295)(138,296)(139,293)(140,294)(141,299)(142,300)(143,297)
(144,298)(145,303)(146,304)(147,301)(148,302)(149,307)(150,308)(151,305)
(152,306)(153,311)(154,312)(155,309)(156,310)(313,471)(314,472)(315,469)
(316,470)(317,475)(318,476)(319,473)(320,474)(321,479)(322,480)(323,477)
(324,478)(325,483)(326,484)(327,481)(328,482)(329,487)(330,488)(331,485)
(332,486)(333,491)(334,492)(335,489)(336,490)(337,495)(338,496)(339,493)
(340,494)(341,499)(342,500)(343,497)(344,498)(345,503)(346,504)(347,501)
(348,502)(349,507)(350,508)(351,505)(352,506)(353,511)(354,512)(355,509)
(356,510)(357,515)(358,516)(359,513)(360,514)(361,519)(362,520)(363,517)
(364,518)(365,523)(366,524)(367,521)(368,522)(369,527)(370,528)(371,525)
(372,526)(373,531)(374,532)(375,529)(376,530)(377,535)(378,536)(379,533)
(380,534)(381,539)(382,540)(383,537)(384,538)(385,543)(386,544)(387,541)
(388,542)(389,547)(390,548)(391,545)(392,546)(393,551)(394,552)(395,549)
(396,550)(397,555)(398,556)(399,553)(400,554)(401,559)(402,560)(403,557)
(404,558)(405,563)(406,564)(407,561)(408,562)(409,567)(410,568)(411,565)
(412,566)(413,571)(414,572)(415,569)(416,570)(417,575)(418,576)(419,573)
(420,574)(421,579)(422,580)(423,577)(424,578)(425,583)(426,584)(427,581)
(428,582)(429,587)(430,588)(431,585)(432,586)(433,591)(434,592)(435,589)
(436,590)(437,595)(438,596)(439,593)(440,594)(441,599)(442,600)(443,597)
(444,598)(445,603)(446,604)(447,601)(448,602)(449,607)(450,608)(451,605)
(452,606)(453,611)(454,612)(455,609)(456,610)(457,615)(458,616)(459,613)
(460,614)(461,619)(462,620)(463,617)(464,618)(465,623)(466,624)(467,621)
(468,622);
s1 := 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)(313,469)(314,470)(315,472)(316,471)(317,517)
(318,518)(319,520)(320,519)(321,513)(322,514)(323,516)(324,515)(325,509)
(326,510)(327,512)(328,511)(329,505)(330,506)(331,508)(332,507)(333,501)
(334,502)(335,504)(336,503)(337,497)(338,498)(339,500)(340,499)(341,493)
(342,494)(343,496)(344,495)(345,489)(346,490)(347,492)(348,491)(349,485)
(350,486)(351,488)(352,487)(353,481)(354,482)(355,484)(356,483)(357,477)
(358,478)(359,480)(360,479)(361,473)(362,474)(363,476)(364,475)(365,573)
(366,574)(367,576)(368,575)(369,621)(370,622)(371,624)(372,623)(373,617)
(374,618)(375,620)(376,619)(377,613)(378,614)(379,616)(380,615)(381,609)
(382,610)(383,612)(384,611)(385,605)(386,606)(387,608)(388,607)(389,601)
(390,602)(391,604)(392,603)(393,597)(394,598)(395,600)(396,599)(397,593)
(398,594)(399,596)(400,595)(401,589)(402,590)(403,592)(404,591)(405,585)
(406,586)(407,588)(408,587)(409,581)(410,582)(411,584)(412,583)(413,577)
(414,578)(415,580)(416,579)(417,521)(418,522)(419,524)(420,523)(421,569)
(422,570)(423,572)(424,571)(425,565)(426,566)(427,568)(428,567)(429,561)
(430,562)(431,564)(432,563)(433,557)(434,558)(435,560)(436,559)(437,553)
(438,554)(439,556)(440,555)(441,549)(442,550)(443,552)(444,551)(445,545)
(446,546)(447,548)(448,547)(449,541)(450,542)(451,544)(452,543)(453,537)
(454,538)(455,540)(456,539)(457,533)(458,534)(459,536)(460,535)(461,529)
(462,530)(463,532)(464,531)(465,525)(466,526)(467,528)(468,527);
s2 := 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);
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*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