Polytope of Type {16,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,20}*1280b
if this polytope has a name.
Group : SmallGroup(1280,81734)
Rank : 3
Schlafli Type : {16,20}
Number of vertices, edges, etc : 32, 320, 40
Order of s₀s₁s₂ : 80
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {8,20}*640a
   4-fold quotients : {4,20}*320, {8,20}*320a, {8,20}*320b
   5-fold quotients : {16,4}*256b
   8-fold quotients : {4,20}*160, {8,10}*160
   10-fold quotients : {8,4}*128a
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*32, {8,2}*32
   64-fold quotients : {2,5}*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)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)(  8,328)
(  9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)( 16,336)
( 17,337)( 18,338)( 19,339)( 20,340)( 21,346)( 22,347)( 23,348)( 24,349)
( 25,350)( 26,341)( 27,342)( 28,343)( 29,344)( 30,345)( 31,356)( 32,357)
( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)( 40,355)
( 41,376)( 42,377)( 43,378)( 44,379)( 45,380)( 46,371)( 47,372)( 48,373)
( 49,374)( 50,375)( 51,366)( 52,367)( 53,368)( 54,369)( 55,370)( 56,361)
( 57,362)( 58,363)( 59,364)( 60,365)( 61,391)( 62,392)( 63,393)( 64,394)
( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)( 72,382)
( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)( 80,390)
( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)( 88,428)
( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)( 96,436)
( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)(104,404)
(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)(112,412)
(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)(120,420)
(121,476)(122,477)(123,478)(124,479)(125,480)(126,471)(127,472)(128,473)
(129,474)(130,475)(131,466)(132,467)(133,468)(134,469)(135,470)(136,461)
(137,462)(138,463)(139,464)(140,465)(141,456)(142,457)(143,458)(144,459)
(145,460)(146,451)(147,452)(148,453)(149,454)(150,455)(151,446)(152,447)
(153,448)(154,449)(155,450)(156,441)(157,442)(158,443)(159,444)(160,445)
(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)
(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)(176,496)
(177,497)(178,498)(179,499)(180,500)(181,506)(182,507)(183,508)(184,509)
(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(191,516)(192,517)
(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)(200,515)
(201,536)(202,537)(203,538)(204,539)(205,540)(206,531)(207,532)(208,533)
(209,534)(210,535)(211,526)(212,527)(213,528)(214,529)(215,530)(216,521)
(217,522)(218,523)(219,524)(220,525)(221,551)(222,552)(223,553)(224,554)
(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)(232,542)
(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)(240,550)
(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)(248,588)
(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)(256,596)
(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)(264,564)
(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)(272,572)
(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)(280,580)
(281,636)(282,637)(283,638)(284,639)(285,640)(286,631)(287,632)(288,633)
(289,634)(290,635)(291,626)(292,627)(293,628)(294,629)(295,630)(296,621)
(297,622)(298,623)(299,624)(300,625)(301,616)(302,617)(303,618)(304,619)
(305,620)(306,611)(307,612)(308,613)(309,614)(310,615)(311,606)(312,607)
(313,608)(314,609)(315,610)(316,601)(317,602)(318,603)(319,604)(320,605);;
s1 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 11, 16)( 12, 20)( 13, 19)( 14, 18)
( 15, 17)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)
( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 56)( 52, 60)
( 53, 59)( 54, 58)( 55, 57)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)
( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 81,101)( 82,105)( 83,104)( 84,103)
( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,116)( 92,120)
( 93,119)( 94,118)( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)
(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)(128,149)
(129,148)(130,147)(131,156)(132,160)(133,159)(134,158)(135,157)(136,151)
(137,155)(138,154)(139,153)(140,152)(161,201)(162,205)(163,204)(164,203)
(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,216)(172,220)
(173,219)(174,218)(175,217)(176,211)(177,215)(178,214)(179,213)(180,212)
(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)(187,225)(188,224)
(189,223)(190,222)(191,231)(192,235)(193,234)(194,233)(195,232)(196,236)
(197,240)(198,239)(199,238)(200,237)(241,306)(242,310)(243,309)(244,308)
(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)(251,311)(252,315)
(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)(260,317)
(261,286)(262,290)(263,289)(264,288)(265,287)(266,281)(267,285)(268,284)
(269,283)(270,282)(271,291)(272,295)(273,294)(274,293)(275,292)(276,296)
(277,300)(278,299)(279,298)(280,297)(321,401)(322,405)(323,404)(324,403)
(325,402)(326,406)(327,410)(328,409)(329,408)(330,407)(331,416)(332,420)
(333,419)(334,418)(335,417)(336,411)(337,415)(338,414)(339,413)(340,412)
(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)(347,425)(348,424)
(349,423)(350,422)(351,431)(352,435)(353,434)(354,433)(355,432)(356,436)
(357,440)(358,439)(359,438)(360,437)(361,441)(362,445)(363,444)(364,443)
(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,456)(372,460)
(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)(380,452)
(381,466)(382,470)(383,469)(384,468)(385,467)(386,461)(387,465)(388,464)
(389,463)(390,462)(391,471)(392,475)(393,474)(394,473)(395,472)(396,476)
(397,480)(398,479)(399,478)(400,477)(481,611)(482,615)(483,614)(484,613)
(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,606)(492,610)
(493,609)(494,608)(495,607)(496,601)(497,605)(498,604)(499,603)(500,602)
(501,636)(502,640)(503,639)(504,638)(505,637)(506,631)(507,635)(508,634)
(509,633)(510,632)(511,621)(512,625)(513,624)(514,623)(515,622)(516,626)
(517,630)(518,629)(519,628)(520,627)(521,571)(522,575)(523,574)(524,573)
(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,566)(532,570)
(533,569)(534,568)(535,567)(536,561)(537,565)(538,564)(539,563)(540,562)
(541,596)(542,600)(543,599)(544,598)(545,597)(546,591)(547,595)(548,594)
(549,593)(550,592)(551,581)(552,585)(553,584)(554,583)(555,582)(556,586)
(557,590)(558,589)(559,588)(560,587);;
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)
( 81,253)( 82,252)( 83,251)( 84,255)( 85,254)( 86,258)( 87,257)( 88,256)
( 89,260)( 90,259)( 91,243)( 92,242)( 93,241)( 94,245)( 95,244)( 96,248)
( 97,247)( 98,246)( 99,250)(100,249)(101,273)(102,272)(103,271)(104,275)
(105,274)(106,278)(107,277)(108,276)(109,280)(110,279)(111,263)(112,262)
(113,261)(114,265)(115,264)(116,268)(117,267)(118,266)(119,270)(120,269)
(121,293)(122,292)(123,291)(124,295)(125,294)(126,298)(127,297)(128,296)
(129,300)(130,299)(131,283)(132,282)(133,281)(134,285)(135,284)(136,288)
(137,287)(138,286)(139,290)(140,289)(141,313)(142,312)(143,311)(144,315)
(145,314)(146,318)(147,317)(148,316)(149,320)(150,319)(151,303)(152,302)
(153,301)(154,305)(155,304)(156,308)(157,307)(158,306)(159,310)(160,309)
(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)
(401,573)(402,572)(403,571)(404,575)(405,574)(406,578)(407,577)(408,576)
(409,580)(410,579)(411,563)(412,562)(413,561)(414,565)(415,564)(416,568)
(417,567)(418,566)(419,570)(420,569)(421,593)(422,592)(423,591)(424,595)
(425,594)(426,598)(427,597)(428,596)(429,600)(430,599)(431,583)(432,582)
(433,581)(434,585)(435,584)(436,588)(437,587)(438,586)(439,590)(440,589)
(441,613)(442,612)(443,611)(444,615)(445,614)(446,618)(447,617)(448,616)
(449,620)(450,619)(451,603)(452,602)(453,601)(454,605)(455,604)(456,608)
(457,607)(458,606)(459,610)(460,609)(461,633)(462,632)(463,631)(464,635)
(465,634)(466,638)(467,637)(468,636)(469,640)(470,639)(471,623)(472,622)
(473,621)(474,625)(475,624)(476,628)(477,627)(478,626)(479,630)(480,629);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope