Polytope of Type {158,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {158,4}*1264
Also Known As : {158,4|2}. if this polytope has another name.
Group : SmallGroup(1264,34)
Rank : 3
Schlafli Type : {158,4}
Number of vertices, edges, etc : 158, 316, 4
Order of s₀s₁s₂ : 316
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 : {158,2}*632
   4-fold quotients : {79,2}*316
   79-fold quotients : {2,4}*16
   158-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,159)(  2,237)(  3,236)(  4,235)(  5,234)(  6,233)(  7,232)(  8,231)
(  9,230)( 10,229)( 11,228)( 12,227)( 13,226)( 14,225)( 15,224)( 16,223)
( 17,222)( 18,221)( 19,220)( 20,219)( 21,218)( 22,217)( 23,216)( 24,215)
( 25,214)( 26,213)( 27,212)( 28,211)( 29,210)( 30,209)( 31,208)( 32,207)
( 33,206)( 34,205)( 35,204)( 36,203)( 37,202)( 38,201)( 39,200)( 40,199)
( 41,198)( 42,197)( 43,196)( 44,195)( 45,194)( 46,193)( 47,192)( 48,191)
( 49,190)( 50,189)( 51,188)( 52,187)( 53,186)( 54,185)( 55,184)( 56,183)
( 57,182)( 58,181)( 59,180)( 60,179)( 61,178)( 62,177)( 63,176)( 64,175)
( 65,174)( 66,173)( 67,172)( 68,171)( 69,170)( 70,169)( 71,168)( 72,167)
( 73,166)( 74,165)( 75,164)( 76,163)( 77,162)( 78,161)( 79,160)( 80,238)
( 81,316)( 82,315)( 83,314)( 84,313)( 85,312)( 86,311)( 87,310)( 88,309)
( 89,308)( 90,307)( 91,306)( 92,305)( 93,304)( 94,303)( 95,302)( 96,301)
( 97,300)( 98,299)( 99,298)(100,297)(101,296)(102,295)(103,294)(104,293)
(105,292)(106,291)(107,290)(108,289)(109,288)(110,287)(111,286)(112,285)
(113,284)(114,283)(115,282)(116,281)(117,280)(118,279)(119,278)(120,277)
(121,276)(122,275)(123,274)(124,273)(125,272)(126,271)(127,270)(128,269)
(129,268)(130,267)(131,266)(132,265)(133,264)(134,263)(135,262)(136,261)
(137,260)(138,259)(139,258)(140,257)(141,256)(142,255)(143,254)(144,253)
(145,252)(146,251)(147,250)(148,249)(149,248)(150,247)(151,246)(152,245)
(153,244)(154,243)(155,242)(156,241)(157,240)(158,239)(317,475)(318,553)
(319,552)(320,551)(321,550)(322,549)(323,548)(324,547)(325,546)(326,545)
(327,544)(328,543)(329,542)(330,541)(331,540)(332,539)(333,538)(334,537)
(335,536)(336,535)(337,534)(338,533)(339,532)(340,531)(341,530)(342,529)
(343,528)(344,527)(345,526)(346,525)(347,524)(348,523)(349,522)(350,521)
(351,520)(352,519)(353,518)(354,517)(355,516)(356,515)(357,514)(358,513)
(359,512)(360,511)(361,510)(362,509)(363,508)(364,507)(365,506)(366,505)
(367,504)(368,503)(369,502)(370,501)(371,500)(372,499)(373,498)(374,497)
(375,496)(376,495)(377,494)(378,493)(379,492)(380,491)(381,490)(382,489)
(383,488)(384,487)(385,486)(386,485)(387,484)(388,483)(389,482)(390,481)
(391,480)(392,479)(393,478)(394,477)(395,476)(396,554)(397,632)(398,631)
(399,630)(400,629)(401,628)(402,627)(403,626)(404,625)(405,624)(406,623)
(407,622)(408,621)(409,620)(410,619)(411,618)(412,617)(413,616)(414,615)
(415,614)(416,613)(417,612)(418,611)(419,610)(420,609)(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)(438,591)
(439,590)(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)(457,572)(458,571)(459,570)(460,569)(461,568)(462,567)
(463,566)(464,565)(465,564)(466,563)(467,562)(468,561)(469,560)(470,559)
(471,558)(472,557)(473,556)(474,555);;
s1 := (  1,160)(  2,159)(  3,237)(  4,236)(  5,235)(  6,234)(  7,233)(  8,232)
(  9,231)( 10,230)( 11,229)( 12,228)( 13,227)( 14,226)( 15,225)( 16,224)
( 17,223)( 18,222)( 19,221)( 20,220)( 21,219)( 22,218)( 23,217)( 24,216)
( 25,215)( 26,214)( 27,213)( 28,212)( 29,211)( 30,210)( 31,209)( 32,208)
( 33,207)( 34,206)( 35,205)( 36,204)( 37,203)( 38,202)( 39,201)( 40,200)
( 41,199)( 42,198)( 43,197)( 44,196)( 45,195)( 46,194)( 47,193)( 48,192)
( 49,191)( 50,190)( 51,189)( 52,188)( 53,187)( 54,186)( 55,185)( 56,184)
( 57,183)( 58,182)( 59,181)( 60,180)( 61,179)( 62,178)( 63,177)( 64,176)
( 65,175)( 66,174)( 67,173)( 68,172)( 69,171)( 70,170)( 71,169)( 72,168)
( 73,167)( 74,166)( 75,165)( 76,164)( 77,163)( 78,162)( 79,161)( 80,239)
( 81,238)( 82,316)( 83,315)( 84,314)( 85,313)( 86,312)( 87,311)( 88,310)
( 89,309)( 90,308)( 91,307)( 92,306)( 93,305)( 94,304)( 95,303)( 96,302)
( 97,301)( 98,300)( 99,299)(100,298)(101,297)(102,296)(103,295)(104,294)
(105,293)(106,292)(107,291)(108,290)(109,289)(110,288)(111,287)(112,286)
(113,285)(114,284)(115,283)(116,282)(117,281)(118,280)(119,279)(120,278)
(121,277)(122,276)(123,275)(124,274)(125,273)(126,272)(127,271)(128,270)
(129,269)(130,268)(131,267)(132,266)(133,265)(134,264)(135,263)(136,262)
(137,261)(138,260)(139,259)(140,258)(141,257)(142,256)(143,255)(144,254)
(145,253)(146,252)(147,251)(148,250)(149,249)(150,248)(151,247)(152,246)
(153,245)(154,244)(155,243)(156,242)(157,241)(158,240)(317,555)(318,554)
(319,632)(320,631)(321,630)(322,629)(323,628)(324,627)(325,626)(326,625)
(327,624)(328,623)(329,622)(330,621)(331,620)(332,619)(333,618)(334,617)
(335,616)(336,615)(337,614)(338,613)(339,612)(340,611)(341,610)(342,609)
(343,608)(344,607)(345,606)(346,605)(347,604)(348,603)(349,602)(350,601)
(351,600)(352,599)(353,598)(354,597)(355,596)(356,595)(357,594)(358,593)
(359,592)(360,591)(361,590)(362,589)(363,588)(364,587)(365,586)(366,585)
(367,584)(368,583)(369,582)(370,581)(371,580)(372,579)(373,578)(374,577)
(375,576)(376,575)(377,574)(378,573)(379,572)(380,571)(381,570)(382,569)
(383,568)(384,567)(385,566)(386,565)(387,564)(388,563)(389,562)(390,561)
(391,560)(392,559)(393,558)(394,557)(395,556)(396,476)(397,475)(398,553)
(399,552)(400,551)(401,550)(402,549)(403,548)(404,547)(405,546)(406,545)
(407,544)(408,543)(409,542)(410,541)(411,540)(412,539)(413,538)(414,537)
(415,536)(416,535)(417,534)(418,533)(419,532)(420,531)(421,530)(422,529)
(423,528)(424,527)(425,526)(426,525)(427,524)(428,523)(429,522)(430,521)
(431,520)(432,519)(433,518)(434,517)(435,516)(436,515)(437,514)(438,513)
(439,512)(440,511)(441,510)(442,509)(443,508)(444,507)(445,506)(446,505)
(447,504)(448,503)(449,502)(450,501)(451,500)(452,499)(453,498)(454,497)
(455,496)(456,495)(457,494)(458,493)(459,492)(460,491)(461,490)(462,489)
(463,488)(464,487)(465,486)(466,485)(467,484)(468,483)(469,482)(470,481)
(471,480)(472,479)(473,478)(474,477);;
s2 := (  1,317)(  2,318)(  3,319)(  4,320)(  5,321)(  6,322)(  7,323)(  8,324)
(  9,325)( 10,326)( 11,327)( 12,328)( 13,329)( 14,330)( 15,331)( 16,332)
( 17,333)( 18,334)( 19,335)( 20,336)( 21,337)( 22,338)( 23,339)( 24,340)
( 25,341)( 26,342)( 27,343)( 28,344)( 29,345)( 30,346)( 31,347)( 32,348)
( 33,349)( 34,350)( 35,351)( 36,352)( 37,353)( 38,354)( 39,355)( 40,356)
( 41,357)( 42,358)( 43,359)( 44,360)( 45,361)( 46,362)( 47,363)( 48,364)
( 49,365)( 50,366)( 51,367)( 52,368)( 53,369)( 54,370)( 55,371)( 56,372)
( 57,373)( 58,374)( 59,375)( 60,376)( 61,377)( 62,378)( 63,379)( 64,380)
( 65,381)( 66,382)( 67,383)( 68,384)( 69,385)( 70,386)( 71,387)( 72,388)
( 73,389)( 74,390)( 75,391)( 76,392)( 77,393)( 78,394)( 79,395)( 80,396)
( 81,397)( 82,398)( 83,399)( 84,400)( 85,401)( 86,402)( 87,403)( 88,404)
( 89,405)( 90,406)( 91,407)( 92,408)( 93,409)( 94,410)( 95,411)( 96,412)
( 97,413)( 98,414)( 99,415)(100,416)(101,417)(102,418)(103,419)(104,420)
(105,421)(106,422)(107,423)(108,424)(109,425)(110,426)(111,427)(112,428)
(113,429)(114,430)(115,431)(116,432)(117,433)(118,434)(119,435)(120,436)
(121,437)(122,438)(123,439)(124,440)(125,441)(126,442)(127,443)(128,444)
(129,445)(130,446)(131,447)(132,448)(133,449)(134,450)(135,451)(136,452)
(137,453)(138,454)(139,455)(140,456)(141,457)(142,458)(143,459)(144,460)
(145,461)(146,462)(147,463)(148,464)(149,465)(150,466)(151,467)(152,468)
(153,469)(154,470)(155,471)(156,472)(157,473)(158,474)(159,475)(160,476)
(161,477)(162,478)(163,479)(164,480)(165,481)(166,482)(167,483)(168,484)
(169,485)(170,486)(171,487)(172,488)(173,489)(174,490)(175,491)(176,492)
(177,493)(178,494)(179,495)(180,496)(181,497)(182,498)(183,499)(184,500)
(185,501)(186,502)(187,503)(188,504)(189,505)(190,506)(191,507)(192,508)
(193,509)(194,510)(195,511)(196,512)(197,513)(198,514)(199,515)(200,516)
(201,517)(202,518)(203,519)(204,520)(205,521)(206,522)(207,523)(208,524)
(209,525)(210,526)(211,527)(212,528)(213,529)(214,530)(215,531)(216,532)
(217,533)(218,534)(219,535)(220,536)(221,537)(222,538)(223,539)(224,540)
(225,541)(226,542)(227,543)(228,544)(229,545)(230,546)(231,547)(232,548)
(233,549)(234,550)(235,551)(236,552)(237,553)(238,554)(239,555)(240,556)
(241,557)(242,558)(243,559)(244,560)(245,561)(246,562)(247,563)(248,564)
(249,565)(250,566)(251,567)(252,568)(253,569)(254,570)(255,571)(256,572)
(257,573)(258,574)(259,575)(260,576)(261,577)(262,578)(263,579)(264,580)
(265,581)(266,582)(267,583)(268,584)(269,585)(270,586)(271,587)(272,588)
(273,589)(274,590)(275,591)(276,592)(277,593)(278,594)(279,595)(280,596)
(281,597)(282,598)(283,599)(284,600)(285,601)(286,602)(287,603)(288,604)
(289,605)(290,606)(291,607)(292,608)(293,609)(294,610)(295,611)(296,612)
(297,613)(298,614)(299,615)(300,616)(301,617)(302,618)(303,619)(304,620)
(305,621)(306,622)(307,623)(308,624)(309,625)(310,626)(311,627)(312,628)
(313,629)(314,630)(315,631)(316,632);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(632)!(  1,159)(  2,237)(  3,236)(  4,235)(  5,234)(  6,233)(  7,232)
(  8,231)(  9,230)( 10,229)( 11,228)( 12,227)( 13,226)( 14,225)( 15,224)
( 16,223)( 17,222)( 18,221)( 19,220)( 20,219)( 21,218)( 22,217)( 23,216)
( 24,215)( 25,214)( 26,213)( 27,212)( 28,211)( 29,210)( 30,209)( 31,208)
( 32,207)( 33,206)( 34,205)( 35,204)( 36,203)( 37,202)( 38,201)( 39,200)
( 40,199)( 41,198)( 42,197)( 43,196)( 44,195)( 45,194)( 46,193)( 47,192)
( 48,191)( 49,190)( 50,189)( 51,188)( 52,187)( 53,186)( 54,185)( 55,184)
( 56,183)( 57,182)( 58,181)( 59,180)( 60,179)( 61,178)( 62,177)( 63,176)
( 64,175)( 65,174)( 66,173)( 67,172)( 68,171)( 69,170)( 70,169)( 71,168)
( 72,167)( 73,166)( 74,165)( 75,164)( 76,163)( 77,162)( 78,161)( 79,160)
( 80,238)( 81,316)( 82,315)( 83,314)( 84,313)( 85,312)( 86,311)( 87,310)
( 88,309)( 89,308)( 90,307)( 91,306)( 92,305)( 93,304)( 94,303)( 95,302)
( 96,301)( 97,300)( 98,299)( 99,298)(100,297)(101,296)(102,295)(103,294)
(104,293)(105,292)(106,291)(107,290)(108,289)(109,288)(110,287)(111,286)
(112,285)(113,284)(114,283)(115,282)(116,281)(117,280)(118,279)(119,278)
(120,277)(121,276)(122,275)(123,274)(124,273)(125,272)(126,271)(127,270)
(128,269)(129,268)(130,267)(131,266)(132,265)(133,264)(134,263)(135,262)
(136,261)(137,260)(138,259)(139,258)(140,257)(141,256)(142,255)(143,254)
(144,253)(145,252)(146,251)(147,250)(148,249)(149,248)(150,247)(151,246)
(152,245)(153,244)(154,243)(155,242)(156,241)(157,240)(158,239)(317,475)
(318,553)(319,552)(320,551)(321,550)(322,549)(323,548)(324,547)(325,546)
(326,545)(327,544)(328,543)(329,542)(330,541)(331,540)(332,539)(333,538)
(334,537)(335,536)(336,535)(337,534)(338,533)(339,532)(340,531)(341,530)
(342,529)(343,528)(344,527)(345,526)(346,525)(347,524)(348,523)(349,522)
(350,521)(351,520)(352,519)(353,518)(354,517)(355,516)(356,515)(357,514)
(358,513)(359,512)(360,511)(361,510)(362,509)(363,508)(364,507)(365,506)
(366,505)(367,504)(368,503)(369,502)(370,501)(371,500)(372,499)(373,498)
(374,497)(375,496)(376,495)(377,494)(378,493)(379,492)(380,491)(381,490)
(382,489)(383,488)(384,487)(385,486)(386,485)(387,484)(388,483)(389,482)
(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,554)(397,632)
(398,631)(399,630)(400,629)(401,628)(402,627)(403,626)(404,625)(405,624)
(406,623)(407,622)(408,621)(409,620)(410,619)(411,618)(412,617)(413,616)
(414,615)(415,614)(416,613)(417,612)(418,611)(419,610)(420,609)(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)
(438,591)(439,590)(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)(457,572)(458,571)(459,570)(460,569)(461,568)
(462,567)(463,566)(464,565)(465,564)(466,563)(467,562)(468,561)(469,560)
(470,559)(471,558)(472,557)(473,556)(474,555);
s1 := Sym(632)!(  1,160)(  2,159)(  3,237)(  4,236)(  5,235)(  6,234)(  7,233)
(  8,232)(  9,231)( 10,230)( 11,229)( 12,228)( 13,227)( 14,226)( 15,225)
( 16,224)( 17,223)( 18,222)( 19,221)( 20,220)( 21,219)( 22,218)( 23,217)
( 24,216)( 25,215)( 26,214)( 27,213)( 28,212)( 29,211)( 30,210)( 31,209)
( 32,208)( 33,207)( 34,206)( 35,205)( 36,204)( 37,203)( 38,202)( 39,201)
( 40,200)( 41,199)( 42,198)( 43,197)( 44,196)( 45,195)( 46,194)( 47,193)
( 48,192)( 49,191)( 50,190)( 51,189)( 52,188)( 53,187)( 54,186)( 55,185)
( 56,184)( 57,183)( 58,182)( 59,181)( 60,180)( 61,179)( 62,178)( 63,177)
( 64,176)( 65,175)( 66,174)( 67,173)( 68,172)( 69,171)( 70,170)( 71,169)
( 72,168)( 73,167)( 74,166)( 75,165)( 76,164)( 77,163)( 78,162)( 79,161)
( 80,239)( 81,238)( 82,316)( 83,315)( 84,314)( 85,313)( 86,312)( 87,311)
( 88,310)( 89,309)( 90,308)( 91,307)( 92,306)( 93,305)( 94,304)( 95,303)
( 96,302)( 97,301)( 98,300)( 99,299)(100,298)(101,297)(102,296)(103,295)
(104,294)(105,293)(106,292)(107,291)(108,290)(109,289)(110,288)(111,287)
(112,286)(113,285)(114,284)(115,283)(116,282)(117,281)(118,280)(119,279)
(120,278)(121,277)(122,276)(123,275)(124,274)(125,273)(126,272)(127,271)
(128,270)(129,269)(130,268)(131,267)(132,266)(133,265)(134,264)(135,263)
(136,262)(137,261)(138,260)(139,259)(140,258)(141,257)(142,256)(143,255)
(144,254)(145,253)(146,252)(147,251)(148,250)(149,249)(150,248)(151,247)
(152,246)(153,245)(154,244)(155,243)(156,242)(157,241)(158,240)(317,555)
(318,554)(319,632)(320,631)(321,630)(322,629)(323,628)(324,627)(325,626)
(326,625)(327,624)(328,623)(329,622)(330,621)(331,620)(332,619)(333,618)
(334,617)(335,616)(336,615)(337,614)(338,613)(339,612)(340,611)(341,610)
(342,609)(343,608)(344,607)(345,606)(346,605)(347,604)(348,603)(349,602)
(350,601)(351,600)(352,599)(353,598)(354,597)(355,596)(356,595)(357,594)
(358,593)(359,592)(360,591)(361,590)(362,589)(363,588)(364,587)(365,586)
(366,585)(367,584)(368,583)(369,582)(370,581)(371,580)(372,579)(373,578)
(374,577)(375,576)(376,575)(377,574)(378,573)(379,572)(380,571)(381,570)
(382,569)(383,568)(384,567)(385,566)(386,565)(387,564)(388,563)(389,562)
(390,561)(391,560)(392,559)(393,558)(394,557)(395,556)(396,476)(397,475)
(398,553)(399,552)(400,551)(401,550)(402,549)(403,548)(404,547)(405,546)
(406,545)(407,544)(408,543)(409,542)(410,541)(411,540)(412,539)(413,538)
(414,537)(415,536)(416,535)(417,534)(418,533)(419,532)(420,531)(421,530)
(422,529)(423,528)(424,527)(425,526)(426,525)(427,524)(428,523)(429,522)
(430,521)(431,520)(432,519)(433,518)(434,517)(435,516)(436,515)(437,514)
(438,513)(439,512)(440,511)(441,510)(442,509)(443,508)(444,507)(445,506)
(446,505)(447,504)(448,503)(449,502)(450,501)(451,500)(452,499)(453,498)
(454,497)(455,496)(456,495)(457,494)(458,493)(459,492)(460,491)(461,490)
(462,489)(463,488)(464,487)(465,486)(466,485)(467,484)(468,483)(469,482)
(470,481)(471,480)(472,479)(473,478)(474,477);
s2 := Sym(632)!(  1,317)(  2,318)(  3,319)(  4,320)(  5,321)(  6,322)(  7,323)
(  8,324)(  9,325)( 10,326)( 11,327)( 12,328)( 13,329)( 14,330)( 15,331)
( 16,332)( 17,333)( 18,334)( 19,335)( 20,336)( 21,337)( 22,338)( 23,339)
( 24,340)( 25,341)( 26,342)( 27,343)( 28,344)( 29,345)( 30,346)( 31,347)
( 32,348)( 33,349)( 34,350)( 35,351)( 36,352)( 37,353)( 38,354)( 39,355)
( 40,356)( 41,357)( 42,358)( 43,359)( 44,360)( 45,361)( 46,362)( 47,363)
( 48,364)( 49,365)( 50,366)( 51,367)( 52,368)( 53,369)( 54,370)( 55,371)
( 56,372)( 57,373)( 58,374)( 59,375)( 60,376)( 61,377)( 62,378)( 63,379)
( 64,380)( 65,381)( 66,382)( 67,383)( 68,384)( 69,385)( 70,386)( 71,387)
( 72,388)( 73,389)( 74,390)( 75,391)( 76,392)( 77,393)( 78,394)( 79,395)
( 80,396)( 81,397)( 82,398)( 83,399)( 84,400)( 85,401)( 86,402)( 87,403)
( 88,404)( 89,405)( 90,406)( 91,407)( 92,408)( 93,409)( 94,410)( 95,411)
( 96,412)( 97,413)( 98,414)( 99,415)(100,416)(101,417)(102,418)(103,419)
(104,420)(105,421)(106,422)(107,423)(108,424)(109,425)(110,426)(111,427)
(112,428)(113,429)(114,430)(115,431)(116,432)(117,433)(118,434)(119,435)
(120,436)(121,437)(122,438)(123,439)(124,440)(125,441)(126,442)(127,443)
(128,444)(129,445)(130,446)(131,447)(132,448)(133,449)(134,450)(135,451)
(136,452)(137,453)(138,454)(139,455)(140,456)(141,457)(142,458)(143,459)
(144,460)(145,461)(146,462)(147,463)(148,464)(149,465)(150,466)(151,467)
(152,468)(153,469)(154,470)(155,471)(156,472)(157,473)(158,474)(159,475)
(160,476)(161,477)(162,478)(163,479)(164,480)(165,481)(166,482)(167,483)
(168,484)(169,485)(170,486)(171,487)(172,488)(173,489)(174,490)(175,491)
(176,492)(177,493)(178,494)(179,495)(180,496)(181,497)(182,498)(183,499)
(184,500)(185,501)(186,502)(187,503)(188,504)(189,505)(190,506)(191,507)
(192,508)(193,509)(194,510)(195,511)(196,512)(197,513)(198,514)(199,515)
(200,516)(201,517)(202,518)(203,519)(204,520)(205,521)(206,522)(207,523)
(208,524)(209,525)(210,526)(211,527)(212,528)(213,529)(214,530)(215,531)
(216,532)(217,533)(218,534)(219,535)(220,536)(221,537)(222,538)(223,539)
(224,540)(225,541)(226,542)(227,543)(228,544)(229,545)(230,546)(231,547)
(232,548)(233,549)(234,550)(235,551)(236,552)(237,553)(238,554)(239,555)
(240,556)(241,557)(242,558)(243,559)(244,560)(245,561)(246,562)(247,563)
(248,564)(249,565)(250,566)(251,567)(252,568)(253,569)(254,570)(255,571)
(256,572)(257,573)(258,574)(259,575)(260,576)(261,577)(262,578)(263,579)
(264,580)(265,581)(266,582)(267,583)(268,584)(269,585)(270,586)(271,587)
(272,588)(273,589)(274,590)(275,591)(276,592)(277,593)(278,594)(279,595)
(280,596)(281,597)(282,598)(283,599)(284,600)(285,601)(286,602)(287,603)
(288,604)(289,605)(290,606)(291,607)(292,608)(293,609)(294,610)(295,611)
(296,612)(297,613)(298,614)(299,615)(300,616)(301,617)(302,618)(303,619)
(304,620)(305,621)(306,622)(307,623)(308,624)(309,625)(310,626)(311,627)
(312,628)(313,629)(314,630)(315,631)(316,632);
poly := sub<Sym(632)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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