Polytope of Type {160,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {160,4}*1280a
Also Known As : {160,4|2}. if this polytope has another name.
Group : SmallGroup(1280,90209)
Rank : 3
Schlafli Type : {160,4}
Number of vertices, edges, etc : 160, 320, 4
Order of s0s1s2 : 160
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
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 : {80,4}*640a, {160,2}*640
4-fold quotients : {40,4}*320a, {80,2}*320
5-fold quotients : {32,4}*256a
8-fold quotients : {20,4}*160, {40,2}*160
10-fold quotients : {16,4}*128a, {32,2}*128
16-fold quotients : {20,2}*80, {10,4}*80
20-fold quotients : {8,4}*64a, {16,2}*64
32-fold quotients : {10,2}*40
40-fold quotients : {4,4}*32, {8,2}*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)( 21,351)( 22,355)( 23,354)( 24,353)
( 25,352)( 26,356)( 27,360)( 28,359)( 29,358)( 30,357)( 31,341)( 32,345)
( 33,344)( 34,343)( 35,342)( 36,346)( 37,350)( 38,349)( 39,348)( 40,347)
( 41,361)( 42,365)( 43,364)( 44,363)( 45,362)( 46,366)( 47,370)( 48,369)
( 49,368)( 50,367)( 51,376)( 52,380)( 53,379)( 54,378)( 55,377)( 56,371)
( 57,375)( 58,374)( 59,373)( 60,372)( 61,391)( 62,395)( 63,394)( 64,393)
( 65,392)( 66,396)( 67,400)( 68,399)( 69,398)( 70,397)( 71,381)( 72,385)
( 73,384)( 74,383)( 75,382)( 76,386)( 77,390)( 78,389)( 79,388)( 80,387)
( 81,421)( 82,425)( 83,424)( 84,423)( 85,422)( 86,426)( 87,430)( 88,429)
( 89,428)( 90,427)( 91,436)( 92,440)( 93,439)( 94,438)( 95,437)( 96,431)
( 97,435)( 98,434)( 99,433)(100,432)(101,401)(102,405)(103,404)(104,403)
(105,402)(106,406)(107,410)(108,409)(109,408)(110,407)(111,416)(112,420)
(113,419)(114,418)(115,417)(116,411)(117,415)(118,414)(119,413)(120,412)
(121,461)(122,465)(123,464)(124,463)(125,462)(126,466)(127,470)(128,469)
(129,468)(130,467)(131,476)(132,480)(133,479)(134,478)(135,477)(136,471)
(137,475)(138,474)(139,473)(140,472)(141,441)(142,445)(143,444)(144,443)
(145,442)(146,446)(147,450)(148,449)(149,448)(150,447)(151,456)(152,460)
(153,459)(154,458)(155,457)(156,451)(157,455)(158,454)(159,453)(160,452)
(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)(181,511)(182,515)(183,514)(184,513)
(185,512)(186,516)(187,520)(188,519)(189,518)(190,517)(191,501)(192,505)
(193,504)(194,503)(195,502)(196,506)(197,510)(198,509)(199,508)(200,507)
(201,521)(202,525)(203,524)(204,523)(205,522)(206,526)(207,530)(208,529)
(209,528)(210,527)(211,536)(212,540)(213,539)(214,538)(215,537)(216,531)
(217,535)(218,534)(219,533)(220,532)(221,551)(222,555)(223,554)(224,553)
(225,552)(226,556)(227,560)(228,559)(229,558)(230,557)(231,541)(232,545)
(233,544)(234,543)(235,542)(236,546)(237,550)(238,549)(239,548)(240,547)
(241,581)(242,585)(243,584)(244,583)(245,582)(246,586)(247,590)(248,589)
(249,588)(250,587)(251,596)(252,600)(253,599)(254,598)(255,597)(256,591)
(257,595)(258,594)(259,593)(260,592)(261,561)(262,565)(263,564)(264,563)
(265,562)(266,566)(267,570)(268,569)(269,568)(270,567)(271,576)(272,580)
(273,579)(274,578)(275,577)(276,571)(277,575)(278,574)(279,573)(280,572)
(281,621)(282,625)(283,624)(284,623)(285,622)(286,626)(287,630)(288,629)
(289,628)(290,627)(291,636)(292,640)(293,639)(294,638)(295,637)(296,631)
(297,635)(298,634)(299,633)(300,632)(301,601)(302,605)(303,604)(304,603)
(305,602)(306,606)(307,610)(308,609)(309,608)(310,607)(311,616)(312,620)
(313,619)(314,618)(315,617)(316,611)(317,615)(318,614)(319,613)(320,612);;
s1 := ( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 18)( 12, 17)( 13, 16)( 14, 20)
( 15, 19)( 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, 58)
( 52, 57)( 53, 56)( 54, 60)( 55, 59)( 61, 73)( 62, 72)( 63, 71)( 64, 75)
( 65, 74)( 66, 78)( 67, 77)( 68, 76)( 69, 80)( 70, 79)( 81,103)( 82,102)
( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)
( 91,118)( 92,117)( 93,116)( 94,120)( 95,119)( 96,113)( 97,112)( 98,111)
( 99,115)(100,114)(121,143)(122,142)(123,141)(124,145)(125,144)(126,148)
(127,147)(128,146)(129,150)(130,149)(131,158)(132,157)(133,156)(134,160)
(135,159)(136,153)(137,152)(138,151)(139,155)(140,154)(161,203)(162,202)
(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)
(171,218)(172,217)(173,216)(174,220)(175,219)(176,213)(177,212)(178,211)
(179,215)(180,214)(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)(241,303)(242,302)
(243,301)(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)
(251,318)(252,317)(253,316)(254,320)(255,319)(256,313)(257,312)(258,311)
(259,315)(260,314)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)
(267,287)(268,286)(269,290)(270,289)(271,298)(272,297)(273,296)(274,300)
(275,299)(276,293)(277,292)(278,291)(279,295)(280,294)(321,403)(322,402)
(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)
(331,418)(332,417)(333,416)(334,420)(335,419)(336,413)(337,412)(338,411)
(339,415)(340,414)(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)
(371,458)(372,457)(373,456)(374,460)(375,459)(376,453)(377,452)(378,451)
(379,455)(380,454)(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)(481,603)(482,602)
(483,601)(484,605)(485,604)(486,608)(487,607)(488,606)(489,610)(490,609)
(491,618)(492,617)(493,616)(494,620)(495,619)(496,613)(497,612)(498,611)
(499,615)(500,614)(501,633)(502,632)(503,631)(504,635)(505,634)(506,638)
(507,637)(508,636)(509,640)(510,639)(511,623)(512,622)(513,621)(514,625)
(515,624)(516,628)(517,627)(518,626)(519,630)(520,629)(521,563)(522,562)
(523,561)(524,565)(525,564)(526,568)(527,567)(528,566)(529,570)(530,569)
(531,578)(532,577)(533,576)(534,580)(535,579)(536,573)(537,572)(538,571)
(539,575)(540,574)(541,593)(542,592)(543,591)(544,595)(545,594)(546,598)
(547,597)(548,596)(549,600)(550,599)(551,583)(552,582)(553,581)(554,585)
(555,584)(556,588)(557,587)(558,586)(559,590)(560,589);;
s2 := ( 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);;
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*s0*s1*s0*s1 ];;
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)( 21,351)( 22,355)( 23,354)
( 24,353)( 25,352)( 26,356)( 27,360)( 28,359)( 29,358)( 30,357)( 31,341)
( 32,345)( 33,344)( 34,343)( 35,342)( 36,346)( 37,350)( 38,349)( 39,348)
( 40,347)( 41,361)( 42,365)( 43,364)( 44,363)( 45,362)( 46,366)( 47,370)
( 48,369)( 49,368)( 50,367)( 51,376)( 52,380)( 53,379)( 54,378)( 55,377)
( 56,371)( 57,375)( 58,374)( 59,373)( 60,372)( 61,391)( 62,395)( 63,394)
( 64,393)( 65,392)( 66,396)( 67,400)( 68,399)( 69,398)( 70,397)( 71,381)
( 72,385)( 73,384)( 74,383)( 75,382)( 76,386)( 77,390)( 78,389)( 79,388)
( 80,387)( 81,421)( 82,425)( 83,424)( 84,423)( 85,422)( 86,426)( 87,430)
( 88,429)( 89,428)( 90,427)( 91,436)( 92,440)( 93,439)( 94,438)( 95,437)
( 96,431)( 97,435)( 98,434)( 99,433)(100,432)(101,401)(102,405)(103,404)
(104,403)(105,402)(106,406)(107,410)(108,409)(109,408)(110,407)(111,416)
(112,420)(113,419)(114,418)(115,417)(116,411)(117,415)(118,414)(119,413)
(120,412)(121,461)(122,465)(123,464)(124,463)(125,462)(126,466)(127,470)
(128,469)(129,468)(130,467)(131,476)(132,480)(133,479)(134,478)(135,477)
(136,471)(137,475)(138,474)(139,473)(140,472)(141,441)(142,445)(143,444)
(144,443)(145,442)(146,446)(147,450)(148,449)(149,448)(150,447)(151,456)
(152,460)(153,459)(154,458)(155,457)(156,451)(157,455)(158,454)(159,453)
(160,452)(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)(181,511)(182,515)(183,514)
(184,513)(185,512)(186,516)(187,520)(188,519)(189,518)(190,517)(191,501)
(192,505)(193,504)(194,503)(195,502)(196,506)(197,510)(198,509)(199,508)
(200,507)(201,521)(202,525)(203,524)(204,523)(205,522)(206,526)(207,530)
(208,529)(209,528)(210,527)(211,536)(212,540)(213,539)(214,538)(215,537)
(216,531)(217,535)(218,534)(219,533)(220,532)(221,551)(222,555)(223,554)
(224,553)(225,552)(226,556)(227,560)(228,559)(229,558)(230,557)(231,541)
(232,545)(233,544)(234,543)(235,542)(236,546)(237,550)(238,549)(239,548)
(240,547)(241,581)(242,585)(243,584)(244,583)(245,582)(246,586)(247,590)
(248,589)(249,588)(250,587)(251,596)(252,600)(253,599)(254,598)(255,597)
(256,591)(257,595)(258,594)(259,593)(260,592)(261,561)(262,565)(263,564)
(264,563)(265,562)(266,566)(267,570)(268,569)(269,568)(270,567)(271,576)
(272,580)(273,579)(274,578)(275,577)(276,571)(277,575)(278,574)(279,573)
(280,572)(281,621)(282,625)(283,624)(284,623)(285,622)(286,626)(287,630)
(288,629)(289,628)(290,627)(291,636)(292,640)(293,639)(294,638)(295,637)
(296,631)(297,635)(298,634)(299,633)(300,632)(301,601)(302,605)(303,604)
(304,603)(305,602)(306,606)(307,610)(308,609)(309,608)(310,607)(311,616)
(312,620)(313,619)(314,618)(315,617)(316,611)(317,615)(318,614)(319,613)
(320,612);
s1 := Sym(640)!( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 18)( 12, 17)( 13, 16)
( 14, 20)( 15, 19)( 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, 58)( 52, 57)( 53, 56)( 54, 60)( 55, 59)( 61, 73)( 62, 72)( 63, 71)
( 64, 75)( 65, 74)( 66, 78)( 67, 77)( 68, 76)( 69, 80)( 70, 79)( 81,103)
( 82,102)( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)
( 90,109)( 91,118)( 92,117)( 93,116)( 94,120)( 95,119)( 96,113)( 97,112)
( 98,111)( 99,115)(100,114)(121,143)(122,142)(123,141)(124,145)(125,144)
(126,148)(127,147)(128,146)(129,150)(130,149)(131,158)(132,157)(133,156)
(134,160)(135,159)(136,153)(137,152)(138,151)(139,155)(140,154)(161,203)
(162,202)(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)
(170,209)(171,218)(172,217)(173,216)(174,220)(175,219)(176,213)(177,212)
(178,211)(179,215)(180,214)(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)(241,303)
(242,302)(243,301)(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)
(250,309)(251,318)(252,317)(253,316)(254,320)(255,319)(256,313)(257,312)
(258,311)(259,315)(260,314)(261,283)(262,282)(263,281)(264,285)(265,284)
(266,288)(267,287)(268,286)(269,290)(270,289)(271,298)(272,297)(273,296)
(274,300)(275,299)(276,293)(277,292)(278,291)(279,295)(280,294)(321,403)
(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)
(330,409)(331,418)(332,417)(333,416)(334,420)(335,419)(336,413)(337,412)
(338,411)(339,415)(340,414)(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)(371,458)(372,457)(373,456)(374,460)(375,459)(376,453)(377,452)
(378,451)(379,455)(380,454)(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)(481,603)
(482,602)(483,601)(484,605)(485,604)(486,608)(487,607)(488,606)(489,610)
(490,609)(491,618)(492,617)(493,616)(494,620)(495,619)(496,613)(497,612)
(498,611)(499,615)(500,614)(501,633)(502,632)(503,631)(504,635)(505,634)
(506,638)(507,637)(508,636)(509,640)(510,639)(511,623)(512,622)(513,621)
(514,625)(515,624)(516,628)(517,627)(518,626)(519,630)(520,629)(521,563)
(522,562)(523,561)(524,565)(525,564)(526,568)(527,567)(528,566)(529,570)
(530,569)(531,578)(532,577)(533,576)(534,580)(535,579)(536,573)(537,572)
(538,571)(539,575)(540,574)(541,593)(542,592)(543,591)(544,595)(545,594)
(546,598)(547,597)(548,596)(549,600)(550,599)(551,583)(552,582)(553,581)
(554,585)(555,584)(556,588)(557,587)(558,586)(559,590)(560,589);
s2 := 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);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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