Polytope of Type {40,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,4}*1280c
if this polytope has a name.
Group : SmallGroup(1280,90302)
Rank : 3
Schlafli Type : {40,4}
Number of vertices, edges, etc : 160, 320, 16
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {20,4}*640a
   4-fold quotients : {20,4}*320
   5-fold quotients : {8,4}*256c
   8-fold quotients : {20,4}*160
   10-fold quotients : {4,4}*128
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {4,4}*64
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32
   64-fold quotients : {5,2}*20
   80-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope