Polytope of Type {64,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {64,10}*1280
Also Known As : {64,10|2}. if this polytope has another name.
Group : SmallGroup(1280,90609)
Rank : 3
Schlafli Type : {64,10}
Number of vertices, edges, etc : 64, 320, 10
Order of s₀s₁s₂ : 320
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 : {32,10}*640
   4-fold quotients : {16,10}*320
   5-fold quotients : {64,2}*256
   8-fold quotients : {8,10}*160
   10-fold quotients : {32,2}*128
   16-fold quotients : {4,10}*80
   20-fold quotients : {16,2}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {8,2}*32
   64-fold quotients : {2,5}*20
   80-fold quotients : {4,2}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 21, 31)( 22, 32)( 23, 33)
( 24, 34)( 25, 35)( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)( 41, 61)
( 42, 62)( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)( 49, 69)
( 50, 70)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 71)( 57, 72)
( 58, 73)( 59, 74)( 60, 75)( 81,121)( 82,122)( 83,123)( 84,124)( 85,125)
( 86,126)( 87,127)( 88,128)( 89,129)( 90,130)( 91,136)( 92,137)( 93,138)
( 94,139)( 95,140)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,151)
(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)
(110,160)(111,141)(112,142)(113,143)(114,144)(115,145)(116,146)(117,147)
(118,148)(119,149)(120,150)(171,176)(172,177)(173,178)(174,179)(175,180)
(181,191)(182,192)(183,193)(184,194)(185,195)(186,196)(187,197)(188,198)
(189,199)(190,200)(201,221)(202,222)(203,223)(204,224)(205,225)(206,226)
(207,227)(208,228)(209,229)(210,230)(211,236)(212,237)(213,238)(214,239)
(215,240)(216,231)(217,232)(218,233)(219,234)(220,235)(241,281)(242,282)
(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)
(251,296)(252,297)(253,298)(254,299)(255,300)(256,291)(257,292)(258,293)
(259,294)(260,295)(261,311)(262,312)(263,313)(264,314)(265,315)(266,316)
(267,317)(268,318)(269,319)(270,320)(271,301)(272,302)(273,303)(274,304)
(275,305)(276,306)(277,307)(278,308)(279,309)(280,310)(321,401)(322,402)
(323,403)(324,404)(325,405)(326,406)(327,407)(328,408)(329,409)(330,410)
(331,416)(332,417)(333,418)(334,419)(335,420)(336,411)(337,412)(338,413)
(339,414)(340,415)(341,431)(342,432)(343,433)(344,434)(345,435)(346,436)
(347,437)(348,438)(349,439)(350,440)(351,421)(352,422)(353,423)(354,424)
(355,425)(356,426)(357,427)(358,428)(359,429)(360,430)(361,461)(362,462)
(363,463)(364,464)(365,465)(366,466)(367,467)(368,468)(369,469)(370,470)
(371,476)(372,477)(373,478)(374,479)(375,480)(376,471)(377,472)(378,473)
(379,474)(380,475)(381,441)(382,442)(383,443)(384,444)(385,445)(386,446)
(387,447)(388,448)(389,449)(390,450)(391,456)(392,457)(393,458)(394,459)
(395,460)(396,451)(397,452)(398,453)(399,454)(400,455)(481,561)(482,562)
(483,563)(484,564)(485,565)(486,566)(487,567)(488,568)(489,569)(490,570)
(491,576)(492,577)(493,578)(494,579)(495,580)(496,571)(497,572)(498,573)
(499,574)(500,575)(501,591)(502,592)(503,593)(504,594)(505,595)(506,596)
(507,597)(508,598)(509,599)(510,600)(511,581)(512,582)(513,583)(514,584)
(515,585)(516,586)(517,587)(518,588)(519,589)(520,590)(521,621)(522,622)
(523,623)(524,624)(525,625)(526,626)(527,627)(528,628)(529,629)(530,630)
(531,636)(532,637)(533,638)(534,639)(535,640)(536,631)(537,632)(538,633)
(539,634)(540,635)(541,601)(542,602)(543,603)(544,604)(545,605)(546,606)
(547,607)(548,608)(549,609)(550,610)(551,616)(552,617)(553,618)(554,619)
(555,620)(556,611)(557,612)(558,613)(559,614)(560,615);;
s1 := (  1,481)(  2,485)(  3,484)(  4,483)(  5,482)(  6,486)(  7,490)(  8,489)
(  9,488)( 10,487)( 11,496)( 12,500)( 13,499)( 14,498)( 15,497)( 16,491)
( 17,495)( 18,494)( 19,493)( 20,492)( 21,511)( 22,515)( 23,514)( 24,513)
( 25,512)( 26,516)( 27,520)( 28,519)( 29,518)( 30,517)( 31,501)( 32,505)
( 33,504)( 34,503)( 35,502)( 36,506)( 37,510)( 38,509)( 39,508)( 40,507)
( 41,541)( 42,545)( 43,544)( 44,543)( 45,542)( 46,546)( 47,550)( 48,549)
( 49,548)( 50,547)( 51,556)( 52,560)( 53,559)( 54,558)( 55,557)( 56,551)
( 57,555)( 58,554)( 59,553)( 60,552)( 61,521)( 62,525)( 63,524)( 64,523)
( 65,522)( 66,526)( 67,530)( 68,529)( 69,528)( 70,527)( 71,536)( 72,540)
( 73,539)( 74,538)( 75,537)( 76,531)( 77,535)( 78,534)( 79,533)( 80,532)
( 81,601)( 82,605)( 83,604)( 84,603)( 85,602)( 86,606)( 87,610)( 88,609)
( 89,608)( 90,607)( 91,616)( 92,620)( 93,619)( 94,618)( 95,617)( 96,611)
( 97,615)( 98,614)( 99,613)(100,612)(101,631)(102,635)(103,634)(104,633)
(105,632)(106,636)(107,640)(108,639)(109,638)(110,637)(111,621)(112,625)
(113,624)(114,623)(115,622)(116,626)(117,630)(118,629)(119,628)(120,627)
(121,561)(122,565)(123,564)(124,563)(125,562)(126,566)(127,570)(128,569)
(129,568)(130,567)(131,576)(132,580)(133,579)(134,578)(135,577)(136,571)
(137,575)(138,574)(139,573)(140,572)(141,591)(142,595)(143,594)(144,593)
(145,592)(146,596)(147,600)(148,599)(149,598)(150,597)(151,581)(152,585)
(153,584)(154,583)(155,582)(156,586)(157,590)(158,589)(159,588)(160,587)
(161,321)(162,325)(163,324)(164,323)(165,322)(166,326)(167,330)(168,329)
(169,328)(170,327)(171,336)(172,340)(173,339)(174,338)(175,337)(176,331)
(177,335)(178,334)(179,333)(180,332)(181,351)(182,355)(183,354)(184,353)
(185,352)(186,356)(187,360)(188,359)(189,358)(190,357)(191,341)(192,345)
(193,344)(194,343)(195,342)(196,346)(197,350)(198,349)(199,348)(200,347)
(201,381)(202,385)(203,384)(204,383)(205,382)(206,386)(207,390)(208,389)
(209,388)(210,387)(211,396)(212,400)(213,399)(214,398)(215,397)(216,391)
(217,395)(218,394)(219,393)(220,392)(221,361)(222,365)(223,364)(224,363)
(225,362)(226,366)(227,370)(228,369)(229,368)(230,367)(231,376)(232,380)
(233,379)(234,378)(235,377)(236,371)(237,375)(238,374)(239,373)(240,372)
(241,441)(242,445)(243,444)(244,443)(245,442)(246,446)(247,450)(248,449)
(249,448)(250,447)(251,456)(252,460)(253,459)(254,458)(255,457)(256,451)
(257,455)(258,454)(259,453)(260,452)(261,471)(262,475)(263,474)(264,473)
(265,472)(266,476)(267,480)(268,479)(269,478)(270,477)(271,461)(272,465)
(273,464)(274,463)(275,462)(276,466)(277,470)(278,469)(279,468)(280,467)
(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)(288,409)
(289,408)(290,407)(291,416)(292,420)(293,419)(294,418)(295,417)(296,411)
(297,415)(298,414)(299,413)(300,412)(301,431)(302,435)(303,434)(304,433)
(305,432)(306,436)(307,440)(308,439)(309,438)(310,437)(311,421)(312,425)
(313,424)(314,423)(315,422)(316,426)(317,430)(318,429)(319,428)(320,427);;
s2 := (  1,163)(  2,162)(  3,161)(  4,165)(  5,164)(  6,168)(  7,167)(  8,166)
(  9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)( 16,178)
( 17,177)( 18,176)( 19,180)( 20,179)( 21,183)( 22,182)( 23,181)( 24,185)
( 25,184)( 26,188)( 27,187)( 28,186)( 29,190)( 30,189)( 31,193)( 32,192)
( 33,191)( 34,195)( 35,194)( 36,198)( 37,197)( 38,196)( 39,200)( 40,199)
( 41,203)( 42,202)( 43,201)( 44,205)( 45,204)( 46,208)( 47,207)( 48,206)
( 49,210)( 50,209)( 51,213)( 52,212)( 53,211)( 54,215)( 55,214)( 56,218)
( 57,217)( 58,216)( 59,220)( 60,219)( 61,223)( 62,222)( 63,221)( 64,225)
( 65,224)( 66,228)( 67,227)( 68,226)( 69,230)( 70,229)( 71,233)( 72,232)
( 73,231)( 74,235)( 75,234)( 76,238)( 77,237)( 78,236)( 79,240)( 80,239)
( 81,243)( 82,242)( 83,241)( 84,245)( 85,244)( 86,248)( 87,247)( 88,246)
( 89,250)( 90,249)( 91,253)( 92,252)( 93,251)( 94,255)( 95,254)( 96,258)
( 97,257)( 98,256)( 99,260)(100,259)(101,263)(102,262)(103,261)(104,265)
(105,264)(106,268)(107,267)(108,266)(109,270)(110,269)(111,273)(112,272)
(113,271)(114,275)(115,274)(116,278)(117,277)(118,276)(119,280)(120,279)
(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)(128,286)
(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)(136,298)
(137,297)(138,296)(139,300)(140,299)(141,303)(142,302)(143,301)(144,305)
(145,304)(146,308)(147,307)(148,306)(149,310)(150,309)(151,313)(152,312)
(153,311)(154,315)(155,314)(156,318)(157,317)(158,316)(159,320)(160,319)
(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)(328,486)
(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)(336,498)
(337,497)(338,496)(339,500)(340,499)(341,503)(342,502)(343,501)(344,505)
(345,504)(346,508)(347,507)(348,506)(349,510)(350,509)(351,513)(352,512)
(353,511)(354,515)(355,514)(356,518)(357,517)(358,516)(359,520)(360,519)
(361,523)(362,522)(363,521)(364,525)(365,524)(366,528)(367,527)(368,526)
(369,530)(370,529)(371,533)(372,532)(373,531)(374,535)(375,534)(376,538)
(377,537)(378,536)(379,540)(380,539)(381,543)(382,542)(383,541)(384,545)
(385,544)(386,548)(387,547)(388,546)(389,550)(390,549)(391,553)(392,552)
(393,551)(394,555)(395,554)(396,558)(397,557)(398,556)(399,560)(400,559)
(401,563)(402,562)(403,561)(404,565)(405,564)(406,568)(407,567)(408,566)
(409,570)(410,569)(411,573)(412,572)(413,571)(414,575)(415,574)(416,578)
(417,577)(418,576)(419,580)(420,579)(421,583)(422,582)(423,581)(424,585)
(425,584)(426,588)(427,587)(428,586)(429,590)(430,589)(431,593)(432,592)
(433,591)(434,595)(435,594)(436,598)(437,597)(438,596)(439,600)(440,599)
(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)(448,606)
(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)(456,618)
(457,617)(458,616)(459,620)(460,619)(461,623)(462,622)(463,621)(464,625)
(465,624)(466,628)(467,627)(468,626)(469,630)(470,629)(471,633)(472,632)
(473,631)(474,635)(475,634)(476,638)(477,637)(478,636)(479,640)(480,639);;
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*s1*s2*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(640)!( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 21, 31)( 22, 32)
( 23, 33)( 24, 34)( 25, 35)( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)
( 41, 61)( 42, 62)( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)
( 49, 69)( 50, 70)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 71)
( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 81,121)( 82,122)( 83,123)( 84,124)
( 85,125)( 86,126)( 87,127)( 88,128)( 89,129)( 90,130)( 91,136)( 92,137)
( 93,138)( 94,139)( 95,140)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)
(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)
(109,159)(110,160)(111,141)(112,142)(113,143)(114,144)(115,145)(116,146)
(117,147)(118,148)(119,149)(120,150)(171,176)(172,177)(173,178)(174,179)
(175,180)(181,191)(182,192)(183,193)(184,194)(185,195)(186,196)(187,197)
(188,198)(189,199)(190,200)(201,221)(202,222)(203,223)(204,224)(205,225)
(206,226)(207,227)(208,228)(209,229)(210,230)(211,236)(212,237)(213,238)
(214,239)(215,240)(216,231)(217,232)(218,233)(219,234)(220,235)(241,281)
(242,282)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)
(250,290)(251,296)(252,297)(253,298)(254,299)(255,300)(256,291)(257,292)
(258,293)(259,294)(260,295)(261,311)(262,312)(263,313)(264,314)(265,315)
(266,316)(267,317)(268,318)(269,319)(270,320)(271,301)(272,302)(273,303)
(274,304)(275,305)(276,306)(277,307)(278,308)(279,309)(280,310)(321,401)
(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)(328,408)(329,409)
(330,410)(331,416)(332,417)(333,418)(334,419)(335,420)(336,411)(337,412)
(338,413)(339,414)(340,415)(341,431)(342,432)(343,433)(344,434)(345,435)
(346,436)(347,437)(348,438)(349,439)(350,440)(351,421)(352,422)(353,423)
(354,424)(355,425)(356,426)(357,427)(358,428)(359,429)(360,430)(361,461)
(362,462)(363,463)(364,464)(365,465)(366,466)(367,467)(368,468)(369,469)
(370,470)(371,476)(372,477)(373,478)(374,479)(375,480)(376,471)(377,472)
(378,473)(379,474)(380,475)(381,441)(382,442)(383,443)(384,444)(385,445)
(386,446)(387,447)(388,448)(389,449)(390,450)(391,456)(392,457)(393,458)
(394,459)(395,460)(396,451)(397,452)(398,453)(399,454)(400,455)(481,561)
(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)(488,568)(489,569)
(490,570)(491,576)(492,577)(493,578)(494,579)(495,580)(496,571)(497,572)
(498,573)(499,574)(500,575)(501,591)(502,592)(503,593)(504,594)(505,595)
(506,596)(507,597)(508,598)(509,599)(510,600)(511,581)(512,582)(513,583)
(514,584)(515,585)(516,586)(517,587)(518,588)(519,589)(520,590)(521,621)
(522,622)(523,623)(524,624)(525,625)(526,626)(527,627)(528,628)(529,629)
(530,630)(531,636)(532,637)(533,638)(534,639)(535,640)(536,631)(537,632)
(538,633)(539,634)(540,635)(541,601)(542,602)(543,603)(544,604)(545,605)
(546,606)(547,607)(548,608)(549,609)(550,610)(551,616)(552,617)(553,618)
(554,619)(555,620)(556,611)(557,612)(558,613)(559,614)(560,615);
s1 := Sym(640)!(  1,481)(  2,485)(  3,484)(  4,483)(  5,482)(  6,486)(  7,490)
(  8,489)(  9,488)( 10,487)( 11,496)( 12,500)( 13,499)( 14,498)( 15,497)
( 16,491)( 17,495)( 18,494)( 19,493)( 20,492)( 21,511)( 22,515)( 23,514)
( 24,513)( 25,512)( 26,516)( 27,520)( 28,519)( 29,518)( 30,517)( 31,501)
( 32,505)( 33,504)( 34,503)( 35,502)( 36,506)( 37,510)( 38,509)( 39,508)
( 40,507)( 41,541)( 42,545)( 43,544)( 44,543)( 45,542)( 46,546)( 47,550)
( 48,549)( 49,548)( 50,547)( 51,556)( 52,560)( 53,559)( 54,558)( 55,557)
( 56,551)( 57,555)( 58,554)( 59,553)( 60,552)( 61,521)( 62,525)( 63,524)
( 64,523)( 65,522)( 66,526)( 67,530)( 68,529)( 69,528)( 70,527)( 71,536)
( 72,540)( 73,539)( 74,538)( 75,537)( 76,531)( 77,535)( 78,534)( 79,533)
( 80,532)( 81,601)( 82,605)( 83,604)( 84,603)( 85,602)( 86,606)( 87,610)
( 88,609)( 89,608)( 90,607)( 91,616)( 92,620)( 93,619)( 94,618)( 95,617)
( 96,611)( 97,615)( 98,614)( 99,613)(100,612)(101,631)(102,635)(103,634)
(104,633)(105,632)(106,636)(107,640)(108,639)(109,638)(110,637)(111,621)
(112,625)(113,624)(114,623)(115,622)(116,626)(117,630)(118,629)(119,628)
(120,627)(121,561)(122,565)(123,564)(124,563)(125,562)(126,566)(127,570)
(128,569)(129,568)(130,567)(131,576)(132,580)(133,579)(134,578)(135,577)
(136,571)(137,575)(138,574)(139,573)(140,572)(141,591)(142,595)(143,594)
(144,593)(145,592)(146,596)(147,600)(148,599)(149,598)(150,597)(151,581)
(152,585)(153,584)(154,583)(155,582)(156,586)(157,590)(158,589)(159,588)
(160,587)(161,321)(162,325)(163,324)(164,323)(165,322)(166,326)(167,330)
(168,329)(169,328)(170,327)(171,336)(172,340)(173,339)(174,338)(175,337)
(176,331)(177,335)(178,334)(179,333)(180,332)(181,351)(182,355)(183,354)
(184,353)(185,352)(186,356)(187,360)(188,359)(189,358)(190,357)(191,341)
(192,345)(193,344)(194,343)(195,342)(196,346)(197,350)(198,349)(199,348)
(200,347)(201,381)(202,385)(203,384)(204,383)(205,382)(206,386)(207,390)
(208,389)(209,388)(210,387)(211,396)(212,400)(213,399)(214,398)(215,397)
(216,391)(217,395)(218,394)(219,393)(220,392)(221,361)(222,365)(223,364)
(224,363)(225,362)(226,366)(227,370)(228,369)(229,368)(230,367)(231,376)
(232,380)(233,379)(234,378)(235,377)(236,371)(237,375)(238,374)(239,373)
(240,372)(241,441)(242,445)(243,444)(244,443)(245,442)(246,446)(247,450)
(248,449)(249,448)(250,447)(251,456)(252,460)(253,459)(254,458)(255,457)
(256,451)(257,455)(258,454)(259,453)(260,452)(261,471)(262,475)(263,474)
(264,473)(265,472)(266,476)(267,480)(268,479)(269,478)(270,477)(271,461)
(272,465)(273,464)(274,463)(275,462)(276,466)(277,470)(278,469)(279,468)
(280,467)(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)
(288,409)(289,408)(290,407)(291,416)(292,420)(293,419)(294,418)(295,417)
(296,411)(297,415)(298,414)(299,413)(300,412)(301,431)(302,435)(303,434)
(304,433)(305,432)(306,436)(307,440)(308,439)(309,438)(310,437)(311,421)
(312,425)(313,424)(314,423)(315,422)(316,426)(317,430)(318,429)(319,428)
(320,427);
s2 := Sym(640)!(  1,163)(  2,162)(  3,161)(  4,165)(  5,164)(  6,168)(  7,167)
(  8,166)(  9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)
( 16,178)( 17,177)( 18,176)( 19,180)( 20,179)( 21,183)( 22,182)( 23,181)
( 24,185)( 25,184)( 26,188)( 27,187)( 28,186)( 29,190)( 30,189)( 31,193)
( 32,192)( 33,191)( 34,195)( 35,194)( 36,198)( 37,197)( 38,196)( 39,200)
( 40,199)( 41,203)( 42,202)( 43,201)( 44,205)( 45,204)( 46,208)( 47,207)
( 48,206)( 49,210)( 50,209)( 51,213)( 52,212)( 53,211)( 54,215)( 55,214)
( 56,218)( 57,217)( 58,216)( 59,220)( 60,219)( 61,223)( 62,222)( 63,221)
( 64,225)( 65,224)( 66,228)( 67,227)( 68,226)( 69,230)( 70,229)( 71,233)
( 72,232)( 73,231)( 74,235)( 75,234)( 76,238)( 77,237)( 78,236)( 79,240)
( 80,239)( 81,243)( 82,242)( 83,241)( 84,245)( 85,244)( 86,248)( 87,247)
( 88,246)( 89,250)( 90,249)( 91,253)( 92,252)( 93,251)( 94,255)( 95,254)
( 96,258)( 97,257)( 98,256)( 99,260)(100,259)(101,263)(102,262)(103,261)
(104,265)(105,264)(106,268)(107,267)(108,266)(109,270)(110,269)(111,273)
(112,272)(113,271)(114,275)(115,274)(116,278)(117,277)(118,276)(119,280)
(120,279)(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)
(128,286)(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)
(136,298)(137,297)(138,296)(139,300)(140,299)(141,303)(142,302)(143,301)
(144,305)(145,304)(146,308)(147,307)(148,306)(149,310)(150,309)(151,313)
(152,312)(153,311)(154,315)(155,314)(156,318)(157,317)(158,316)(159,320)
(160,319)(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)
(328,486)(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)
(336,498)(337,497)(338,496)(339,500)(340,499)(341,503)(342,502)(343,501)
(344,505)(345,504)(346,508)(347,507)(348,506)(349,510)(350,509)(351,513)
(352,512)(353,511)(354,515)(355,514)(356,518)(357,517)(358,516)(359,520)
(360,519)(361,523)(362,522)(363,521)(364,525)(365,524)(366,528)(367,527)
(368,526)(369,530)(370,529)(371,533)(372,532)(373,531)(374,535)(375,534)
(376,538)(377,537)(378,536)(379,540)(380,539)(381,543)(382,542)(383,541)
(384,545)(385,544)(386,548)(387,547)(388,546)(389,550)(390,549)(391,553)
(392,552)(393,551)(394,555)(395,554)(396,558)(397,557)(398,556)(399,560)
(400,559)(401,563)(402,562)(403,561)(404,565)(405,564)(406,568)(407,567)
(408,566)(409,570)(410,569)(411,573)(412,572)(413,571)(414,575)(415,574)
(416,578)(417,577)(418,576)(419,580)(420,579)(421,583)(422,582)(423,581)
(424,585)(425,584)(426,588)(427,587)(428,586)(429,590)(430,589)(431,593)
(432,592)(433,591)(434,595)(435,594)(436,598)(437,597)(438,596)(439,600)
(440,599)(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)
(448,606)(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)
(456,618)(457,617)(458,616)(459,620)(460,619)(461,623)(462,622)(463,621)
(464,625)(465,624)(466,628)(467,627)(468,626)(469,630)(470,629)(471,633)
(472,632)(473,631)(474,635)(475,634)(476,638)(477,637)(478,636)(479,640)
(480,639);
poly := sub<Sym(640)|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*s1*s2*s1*s2*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 >;

References : None.
to this polytope