Polytope of Type {4,160}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,160}*1280a
Also Known As : {4,160|2}. if this polytope has another name.
Group : SmallGroup(1280,90209)
Rank : 3
Schlafli Type : {4,160}
Number of vertices, edges, etc : 4, 320, 160
Order of s0s1s2 : 160
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 : {4,80}*640a, {2,160}*640
4-fold quotients : {4,40}*320a, {2,80}*320
5-fold quotients : {4,32}*256a
8-fold quotients : {4,20}*160, {2,40}*160
10-fold quotients : {4,16}*128a, {2,32}*128
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,8}*64a, {2,16}*64
32-fold quotients : {2,10}*40
40-fold quotients : {4,4}*32, {2,8}*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 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)
( 9,169)( 10,170)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)( 16,176)
( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)( 24,184)
( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 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)( 51,211)( 52,212)( 53,213)( 54,214)( 55,215)( 56,216)
( 57,217)( 58,218)( 59,219)( 60,220)( 61,221)( 62,222)( 63,223)( 64,224)
( 65,225)( 66,226)( 67,227)( 68,228)( 69,229)( 70,230)( 71,231)( 72,232)
( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)( 80,240)
( 81,241)( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)( 88,248)
( 89,249)( 90,250)( 91,251)( 92,252)( 93,253)( 94,254)( 95,255)( 96,256)
( 97,257)( 98,258)( 99,259)(100,260)(101,261)(102,262)(103,263)(104,264)
(105,265)(106,266)(107,267)(108,268)(109,269)(110,270)(111,271)(112,272)
(113,273)(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)
(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)(128,288)
(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)(136,296)
(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)(144,304)
(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)(152,312)
(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)(160,320)
(321,481)(322,482)(323,483)(324,484)(325,485)(326,486)(327,487)(328,488)
(329,489)(330,490)(331,491)(332,492)(333,493)(334,494)(335,495)(336,496)
(337,497)(338,498)(339,499)(340,500)(341,501)(342,502)(343,503)(344,504)
(345,505)(346,506)(347,507)(348,508)(349,509)(350,510)(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)(371,531)(372,532)(373,533)(374,534)(375,535)(376,536)
(377,537)(378,538)(379,539)(380,540)(381,541)(382,542)(383,543)(384,544)
(385,545)(386,546)(387,547)(388,548)(389,549)(390,550)(391,551)(392,552)
(393,553)(394,554)(395,555)(396,556)(397,557)(398,558)(399,559)(400,560)
(401,561)(402,562)(403,563)(404,564)(405,565)(406,566)(407,567)(408,568)
(409,569)(410,570)(411,571)(412,572)(413,573)(414,574)(415,575)(416,576)
(417,577)(418,578)(419,579)(420,580)(421,581)(422,582)(423,583)(424,584)
(425,585)(426,586)(427,587)(428,588)(429,589)(430,590)(431,591)(432,592)
(433,593)(434,594)(435,595)(436,596)(437,597)(438,598)(439,599)(440,600)
(441,601)(442,602)(443,603)(444,604)(445,605)(446,606)(447,607)(448,608)
(449,609)(450,610)(451,611)(452,612)(453,613)(454,614)(455,615)(456,616)
(457,617)(458,618)(459,619)(460,620)(461,621)(462,622)(463,623)(464,624)
(465,625)(466,626)(467,627)(468,628)(469,629)(470,630)(471,631)(472,632)
(473,633)(474,634)(475,635)(476,636)(477,637)(478,638)(479,639)(480,640);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 11, 16)( 12, 20)( 13, 19)( 14, 18)
( 15, 17)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)
( 28, 39)( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)( 62, 75)( 63, 74)( 64, 73)
( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 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)(181,231)(182,235)(183,234)(184,233)(185,232)(186,236)
(187,240)(188,239)(189,238)(190,237)(191,221)(192,225)(193,224)(194,223)
(195,222)(196,226)(197,230)(198,229)(199,228)(200,227)(241,301)(242,305)
(243,304)(244,303)(245,302)(246,306)(247,310)(248,309)(249,308)(250,307)
(251,316)(252,320)(253,319)(254,318)(255,317)(256,311)(257,315)(258,314)
(259,313)(260,312)(261,281)(262,285)(263,284)(264,283)(265,282)(266,286)
(267,290)(268,289)(269,288)(270,287)(271,296)(272,300)(273,299)(274,298)
(275,297)(276,291)(277,295)(278,294)(279,293)(280,292)(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)(341,431)(342,435)(343,434)(344,433)(345,432)(346,436)
(347,440)(348,439)(349,438)(350,437)(351,421)(352,425)(353,424)(354,423)
(355,422)(356,426)(357,430)(358,429)(359,428)(360,427)(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)(381,471)(382,475)(383,474)(384,473)(385,472)(386,476)
(387,480)(388,479)(389,478)(390,477)(391,461)(392,465)(393,464)(394,463)
(395,462)(396,466)(397,470)(398,469)(399,468)(400,467)(481,601)(482,605)
(483,604)(484,603)(485,602)(486,606)(487,610)(488,609)(489,608)(490,607)
(491,616)(492,620)(493,619)(494,618)(495,617)(496,611)(497,615)(498,614)
(499,613)(500,612)(501,631)(502,635)(503,634)(504,633)(505,632)(506,636)
(507,640)(508,639)(509,638)(510,637)(511,621)(512,625)(513,624)(514,623)
(515,622)(516,626)(517,630)(518,629)(519,628)(520,627)(521,561)(522,565)
(523,564)(524,563)(525,562)(526,566)(527,570)(528,569)(529,568)(530,567)
(531,576)(532,580)(533,579)(534,578)(535,577)(536,571)(537,575)(538,574)
(539,573)(540,572)(541,591)(542,595)(543,594)(544,593)(545,592)(546,596)
(547,600)(548,599)(549,598)(550,597)(551,581)(552,585)(553,584)(554,583)
(555,582)(556,586)(557,590)(558,589)(559,588)(560,587);;
s2 := ( 1,323)( 2,322)( 3,321)( 4,325)( 5,324)( 6,328)( 7,327)( 8,326)
( 9,330)( 10,329)( 11,338)( 12,337)( 13,336)( 14,340)( 15,339)( 16,333)
( 17,332)( 18,331)( 19,335)( 20,334)( 21,353)( 22,352)( 23,351)( 24,355)
( 25,354)( 26,358)( 27,357)( 28,356)( 29,360)( 30,359)( 31,343)( 32,342)
( 33,341)( 34,345)( 35,344)( 36,348)( 37,347)( 38,346)( 39,350)( 40,349)
( 41,363)( 42,362)( 43,361)( 44,365)( 45,364)( 46,368)( 47,367)( 48,366)
( 49,370)( 50,369)( 51,378)( 52,377)( 53,376)( 54,380)( 55,379)( 56,373)
( 57,372)( 58,371)( 59,375)( 60,374)( 61,393)( 62,392)( 63,391)( 64,395)
( 65,394)( 66,398)( 67,397)( 68,396)( 69,400)( 70,399)( 71,383)( 72,382)
( 73,381)( 74,385)( 75,384)( 76,388)( 77,387)( 78,386)( 79,390)( 80,389)
( 81,423)( 82,422)( 83,421)( 84,425)( 85,424)( 86,428)( 87,427)( 88,426)
( 89,430)( 90,429)( 91,438)( 92,437)( 93,436)( 94,440)( 95,439)( 96,433)
( 97,432)( 98,431)( 99,435)(100,434)(101,403)(102,402)(103,401)(104,405)
(105,404)(106,408)(107,407)(108,406)(109,410)(110,409)(111,418)(112,417)
(113,416)(114,420)(115,419)(116,413)(117,412)(118,411)(119,415)(120,414)
(121,463)(122,462)(123,461)(124,465)(125,464)(126,468)(127,467)(128,466)
(129,470)(130,469)(131,478)(132,477)(133,476)(134,480)(135,479)(136,473)
(137,472)(138,471)(139,475)(140,474)(141,443)(142,442)(143,441)(144,445)
(145,444)(146,448)(147,447)(148,446)(149,450)(150,449)(151,458)(152,457)
(153,456)(154,460)(155,459)(156,453)(157,452)(158,451)(159,455)(160,454)
(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)(168,486)
(169,490)(170,489)(171,498)(172,497)(173,496)(174,500)(175,499)(176,493)
(177,492)(178,491)(179,495)(180,494)(181,513)(182,512)(183,511)(184,515)
(185,514)(186,518)(187,517)(188,516)(189,520)(190,519)(191,503)(192,502)
(193,501)(194,505)(195,504)(196,508)(197,507)(198,506)(199,510)(200,509)
(201,523)(202,522)(203,521)(204,525)(205,524)(206,528)(207,527)(208,526)
(209,530)(210,529)(211,538)(212,537)(213,536)(214,540)(215,539)(216,533)
(217,532)(218,531)(219,535)(220,534)(221,553)(222,552)(223,551)(224,555)
(225,554)(226,558)(227,557)(228,556)(229,560)(230,559)(231,543)(232,542)
(233,541)(234,545)(235,544)(236,548)(237,547)(238,546)(239,550)(240,549)
(241,583)(242,582)(243,581)(244,585)(245,584)(246,588)(247,587)(248,586)
(249,590)(250,589)(251,598)(252,597)(253,596)(254,600)(255,599)(256,593)
(257,592)(258,591)(259,595)(260,594)(261,563)(262,562)(263,561)(264,565)
(265,564)(266,568)(267,567)(268,566)(269,570)(270,569)(271,578)(272,577)
(273,576)(274,580)(275,579)(276,573)(277,572)(278,571)(279,575)(280,574)
(281,623)(282,622)(283,621)(284,625)(285,624)(286,628)(287,627)(288,626)
(289,630)(290,629)(291,638)(292,637)(293,636)(294,640)(295,639)(296,633)
(297,632)(298,631)(299,635)(300,634)(301,603)(302,602)(303,601)(304,605)
(305,604)(306,608)(307,607)(308,606)(309,610)(310,609)(311,618)(312,617)
(313,616)(314,620)(315,619)(316,613)(317,612)(318,611)(319,615)(320,614);;
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*s0*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*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*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*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(640)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)
( 8,168)( 9,169)( 10,170)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)
( 16,176)( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)
( 24,184)( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 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)( 51,211)( 52,212)( 53,213)( 54,214)( 55,215)
( 56,216)( 57,217)( 58,218)( 59,219)( 60,220)( 61,221)( 62,222)( 63,223)
( 64,224)( 65,225)( 66,226)( 67,227)( 68,228)( 69,229)( 70,230)( 71,231)
( 72,232)( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)
( 80,240)( 81,241)( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)
( 88,248)( 89,249)( 90,250)( 91,251)( 92,252)( 93,253)( 94,254)( 95,255)
( 96,256)( 97,257)( 98,258)( 99,259)(100,260)(101,261)(102,262)(103,263)
(104,264)(105,265)(106,266)(107,267)(108,268)(109,269)(110,270)(111,271)
(112,272)(113,273)(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)
(120,280)(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)
(128,288)(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)
(136,296)(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)
(144,304)(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)
(152,312)(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)
(160,320)(321,481)(322,482)(323,483)(324,484)(325,485)(326,486)(327,487)
(328,488)(329,489)(330,490)(331,491)(332,492)(333,493)(334,494)(335,495)
(336,496)(337,497)(338,498)(339,499)(340,500)(341,501)(342,502)(343,503)
(344,504)(345,505)(346,506)(347,507)(348,508)(349,509)(350,510)(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)(371,531)(372,532)(373,533)(374,534)(375,535)
(376,536)(377,537)(378,538)(379,539)(380,540)(381,541)(382,542)(383,543)
(384,544)(385,545)(386,546)(387,547)(388,548)(389,549)(390,550)(391,551)
(392,552)(393,553)(394,554)(395,555)(396,556)(397,557)(398,558)(399,559)
(400,560)(401,561)(402,562)(403,563)(404,564)(405,565)(406,566)(407,567)
(408,568)(409,569)(410,570)(411,571)(412,572)(413,573)(414,574)(415,575)
(416,576)(417,577)(418,578)(419,579)(420,580)(421,581)(422,582)(423,583)
(424,584)(425,585)(426,586)(427,587)(428,588)(429,589)(430,590)(431,591)
(432,592)(433,593)(434,594)(435,595)(436,596)(437,597)(438,598)(439,599)
(440,600)(441,601)(442,602)(443,603)(444,604)(445,605)(446,606)(447,607)
(448,608)(449,609)(450,610)(451,611)(452,612)(453,613)(454,614)(455,615)
(456,616)(457,617)(458,618)(459,619)(460,620)(461,621)(462,622)(463,623)
(464,624)(465,625)(466,626)(467,627)(468,628)(469,629)(470,630)(471,631)
(472,632)(473,633)(474,634)(475,635)(476,636)(477,637)(478,638)(479,639)
(480,640);
s1 := Sym(640)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 11, 16)( 12, 20)( 13, 19)
( 14, 18)( 15, 17)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)
( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)( 62, 75)( 63, 74)
( 64, 73)( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 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)(181,231)(182,235)(183,234)(184,233)(185,232)
(186,236)(187,240)(188,239)(189,238)(190,237)(191,221)(192,225)(193,224)
(194,223)(195,222)(196,226)(197,230)(198,229)(199,228)(200,227)(241,301)
(242,305)(243,304)(244,303)(245,302)(246,306)(247,310)(248,309)(249,308)
(250,307)(251,316)(252,320)(253,319)(254,318)(255,317)(256,311)(257,315)
(258,314)(259,313)(260,312)(261,281)(262,285)(263,284)(264,283)(265,282)
(266,286)(267,290)(268,289)(269,288)(270,287)(271,296)(272,300)(273,299)
(274,298)(275,297)(276,291)(277,295)(278,294)(279,293)(280,292)(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)(341,431)(342,435)(343,434)(344,433)(345,432)
(346,436)(347,440)(348,439)(349,438)(350,437)(351,421)(352,425)(353,424)
(354,423)(355,422)(356,426)(357,430)(358,429)(359,428)(360,427)(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)(381,471)(382,475)(383,474)(384,473)(385,472)
(386,476)(387,480)(388,479)(389,478)(390,477)(391,461)(392,465)(393,464)
(394,463)(395,462)(396,466)(397,470)(398,469)(399,468)(400,467)(481,601)
(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)(488,609)(489,608)
(490,607)(491,616)(492,620)(493,619)(494,618)(495,617)(496,611)(497,615)
(498,614)(499,613)(500,612)(501,631)(502,635)(503,634)(504,633)(505,632)
(506,636)(507,640)(508,639)(509,638)(510,637)(511,621)(512,625)(513,624)
(514,623)(515,622)(516,626)(517,630)(518,629)(519,628)(520,627)(521,561)
(522,565)(523,564)(524,563)(525,562)(526,566)(527,570)(528,569)(529,568)
(530,567)(531,576)(532,580)(533,579)(534,578)(535,577)(536,571)(537,575)
(538,574)(539,573)(540,572)(541,591)(542,595)(543,594)(544,593)(545,592)
(546,596)(547,600)(548,599)(549,598)(550,597)(551,581)(552,585)(553,584)
(554,583)(555,582)(556,586)(557,590)(558,589)(559,588)(560,587);
s2 := Sym(640)!( 1,323)( 2,322)( 3,321)( 4,325)( 5,324)( 6,328)( 7,327)
( 8,326)( 9,330)( 10,329)( 11,338)( 12,337)( 13,336)( 14,340)( 15,339)
( 16,333)( 17,332)( 18,331)( 19,335)( 20,334)( 21,353)( 22,352)( 23,351)
( 24,355)( 25,354)( 26,358)( 27,357)( 28,356)( 29,360)( 30,359)( 31,343)
( 32,342)( 33,341)( 34,345)( 35,344)( 36,348)( 37,347)( 38,346)( 39,350)
( 40,349)( 41,363)( 42,362)( 43,361)( 44,365)( 45,364)( 46,368)( 47,367)
( 48,366)( 49,370)( 50,369)( 51,378)( 52,377)( 53,376)( 54,380)( 55,379)
( 56,373)( 57,372)( 58,371)( 59,375)( 60,374)( 61,393)( 62,392)( 63,391)
( 64,395)( 65,394)( 66,398)( 67,397)( 68,396)( 69,400)( 70,399)( 71,383)
( 72,382)( 73,381)( 74,385)( 75,384)( 76,388)( 77,387)( 78,386)( 79,390)
( 80,389)( 81,423)( 82,422)( 83,421)( 84,425)( 85,424)( 86,428)( 87,427)
( 88,426)( 89,430)( 90,429)( 91,438)( 92,437)( 93,436)( 94,440)( 95,439)
( 96,433)( 97,432)( 98,431)( 99,435)(100,434)(101,403)(102,402)(103,401)
(104,405)(105,404)(106,408)(107,407)(108,406)(109,410)(110,409)(111,418)
(112,417)(113,416)(114,420)(115,419)(116,413)(117,412)(118,411)(119,415)
(120,414)(121,463)(122,462)(123,461)(124,465)(125,464)(126,468)(127,467)
(128,466)(129,470)(130,469)(131,478)(132,477)(133,476)(134,480)(135,479)
(136,473)(137,472)(138,471)(139,475)(140,474)(141,443)(142,442)(143,441)
(144,445)(145,444)(146,448)(147,447)(148,446)(149,450)(150,449)(151,458)
(152,457)(153,456)(154,460)(155,459)(156,453)(157,452)(158,451)(159,455)
(160,454)(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)
(168,486)(169,490)(170,489)(171,498)(172,497)(173,496)(174,500)(175,499)
(176,493)(177,492)(178,491)(179,495)(180,494)(181,513)(182,512)(183,511)
(184,515)(185,514)(186,518)(187,517)(188,516)(189,520)(190,519)(191,503)
(192,502)(193,501)(194,505)(195,504)(196,508)(197,507)(198,506)(199,510)
(200,509)(201,523)(202,522)(203,521)(204,525)(205,524)(206,528)(207,527)
(208,526)(209,530)(210,529)(211,538)(212,537)(213,536)(214,540)(215,539)
(216,533)(217,532)(218,531)(219,535)(220,534)(221,553)(222,552)(223,551)
(224,555)(225,554)(226,558)(227,557)(228,556)(229,560)(230,559)(231,543)
(232,542)(233,541)(234,545)(235,544)(236,548)(237,547)(238,546)(239,550)
(240,549)(241,583)(242,582)(243,581)(244,585)(245,584)(246,588)(247,587)
(248,586)(249,590)(250,589)(251,598)(252,597)(253,596)(254,600)(255,599)
(256,593)(257,592)(258,591)(259,595)(260,594)(261,563)(262,562)(263,561)
(264,565)(265,564)(266,568)(267,567)(268,566)(269,570)(270,569)(271,578)
(272,577)(273,576)(274,580)(275,579)(276,573)(277,572)(278,571)(279,575)
(280,574)(281,623)(282,622)(283,621)(284,625)(285,624)(286,628)(287,627)
(288,626)(289,630)(290,629)(291,638)(292,637)(293,636)(294,640)(295,639)
(296,633)(297,632)(298,631)(299,635)(300,634)(301,603)(302,602)(303,601)
(304,605)(305,604)(306,608)(307,607)(308,606)(309,610)(310,609)(311,618)
(312,617)(313,616)(314,620)(315,619)(316,613)(317,612)(318,611)(319,615)
(320,614);
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*s0*s1*s0*s1*s0*s1,
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*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*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*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