Polytope of Type {32,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,20}*1280a
Also Known As : {32,20|2}. if this polytope has another name.
Group : SmallGroup(1280,90208)
Rank : 3
Schlafli Type : {32,20}
Number of vertices, edges, etc : 32, 320, 20
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 : {16,20}*640a, {32,10}*640
4-fold quotients : {8,20}*320a, {16,10}*320
5-fold quotients : {32,4}*256a
8-fold quotients : {4,20}*160, {8,10}*160
10-fold quotients : {16,4}*128a, {32,2}*128
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {8,4}*64a, {16,2}*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)( 11,336)( 12,337)( 13,338)( 14,339)( 15,340)( 16,331)
( 17,332)( 18,333)( 19,334)( 20,335)( 21,351)( 22,352)( 23,353)( 24,354)
( 25,355)( 26,356)( 27,357)( 28,358)( 29,359)( 30,360)( 31,341)( 32,342)
( 33,343)( 34,344)( 35,345)( 36,346)( 37,347)( 38,348)( 39,349)( 40,350)
( 41,361)( 42,362)( 43,363)( 44,364)( 45,365)( 46,366)( 47,367)( 48,368)
( 49,369)( 50,370)( 51,376)( 52,377)( 53,378)( 54,379)( 55,380)( 56,371)
( 57,372)( 58,373)( 59,374)( 60,375)( 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)( 91,436)( 92,437)( 93,438)( 94,439)( 95,440)( 96,431)
( 97,432)( 98,433)( 99,434)(100,435)(101,401)(102,402)(103,403)(104,404)
(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,416)(112,417)
(113,418)(114,419)(115,420)(116,411)(117,412)(118,413)(119,414)(120,415)
(121,461)(122,462)(123,463)(124,464)(125,465)(126,466)(127,467)(128,468)
(129,469)(130,470)(131,476)(132,477)(133,478)(134,479)(135,480)(136,471)
(137,472)(138,473)(139,474)(140,475)(141,441)(142,442)(143,443)(144,444)
(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,456)(152,457)
(153,458)(154,459)(155,460)(156,451)(157,452)(158,453)(159,454)(160,455)
(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)
(169,489)(170,490)(171,496)(172,497)(173,498)(174,499)(175,500)(176,491)
(177,492)(178,493)(179,494)(180,495)(181,511)(182,512)(183,513)(184,514)
(185,515)(186,516)(187,517)(188,518)(189,519)(190,520)(191,501)(192,502)
(193,503)(194,504)(195,505)(196,506)(197,507)(198,508)(199,509)(200,510)
(201,521)(202,522)(203,523)(204,524)(205,525)(206,526)(207,527)(208,528)
(209,529)(210,530)(211,536)(212,537)(213,538)(214,539)(215,540)(216,531)
(217,532)(218,533)(219,534)(220,535)(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)(251,596)(252,597)(253,598)(254,599)(255,600)(256,591)
(257,592)(258,593)(259,594)(260,595)(261,561)(262,562)(263,563)(264,564)
(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,576)(272,577)
(273,578)(274,579)(275,580)(276,571)(277,572)(278,573)(279,574)(280,575)
(281,621)(282,622)(283,623)(284,624)(285,625)(286,626)(287,627)(288,628)
(289,629)(290,630)(291,636)(292,637)(293,638)(294,639)(295,640)(296,631)
(297,632)(298,633)(299,634)(300,635)(301,601)(302,602)(303,603)(304,604)
(305,605)(306,606)(307,607)(308,608)(309,609)(310,610)(311,616)(312,617)
(313,618)(314,619)(315,620)(316,611)(317,612)(318,613)(319,614)(320,615);;
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 := ( 1,163)( 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*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 ];;
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)( 11,336)( 12,337)( 13,338)( 14,339)( 15,340)
( 16,331)( 17,332)( 18,333)( 19,334)( 20,335)( 21,351)( 22,352)( 23,353)
( 24,354)( 25,355)( 26,356)( 27,357)( 28,358)( 29,359)( 30,360)( 31,341)
( 32,342)( 33,343)( 34,344)( 35,345)( 36,346)( 37,347)( 38,348)( 39,349)
( 40,350)( 41,361)( 42,362)( 43,363)( 44,364)( 45,365)( 46,366)( 47,367)
( 48,368)( 49,369)( 50,370)( 51,376)( 52,377)( 53,378)( 54,379)( 55,380)
( 56,371)( 57,372)( 58,373)( 59,374)( 60,375)( 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)( 91,436)( 92,437)( 93,438)( 94,439)( 95,440)
( 96,431)( 97,432)( 98,433)( 99,434)(100,435)(101,401)(102,402)(103,403)
(104,404)(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,416)
(112,417)(113,418)(114,419)(115,420)(116,411)(117,412)(118,413)(119,414)
(120,415)(121,461)(122,462)(123,463)(124,464)(125,465)(126,466)(127,467)
(128,468)(129,469)(130,470)(131,476)(132,477)(133,478)(134,479)(135,480)
(136,471)(137,472)(138,473)(139,474)(140,475)(141,441)(142,442)(143,443)
(144,444)(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,456)
(152,457)(153,458)(154,459)(155,460)(156,451)(157,452)(158,453)(159,454)
(160,455)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)
(168,488)(169,489)(170,490)(171,496)(172,497)(173,498)(174,499)(175,500)
(176,491)(177,492)(178,493)(179,494)(180,495)(181,511)(182,512)(183,513)
(184,514)(185,515)(186,516)(187,517)(188,518)(189,519)(190,520)(191,501)
(192,502)(193,503)(194,504)(195,505)(196,506)(197,507)(198,508)(199,509)
(200,510)(201,521)(202,522)(203,523)(204,524)(205,525)(206,526)(207,527)
(208,528)(209,529)(210,530)(211,536)(212,537)(213,538)(214,539)(215,540)
(216,531)(217,532)(218,533)(219,534)(220,535)(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)(251,596)(252,597)(253,598)(254,599)(255,600)
(256,591)(257,592)(258,593)(259,594)(260,595)(261,561)(262,562)(263,563)
(264,564)(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,576)
(272,577)(273,578)(274,579)(275,580)(276,571)(277,572)(278,573)(279,574)
(280,575)(281,621)(282,622)(283,623)(284,624)(285,625)(286,626)(287,627)
(288,628)(289,629)(290,630)(291,636)(292,637)(293,638)(294,639)(295,640)
(296,631)(297,632)(298,633)(299,634)(300,635)(301,601)(302,602)(303,603)
(304,604)(305,605)(306,606)(307,607)(308,608)(309,609)(310,610)(311,616)
(312,617)(313,618)(314,619)(315,620)(316,611)(317,612)(318,613)(319,614)
(320,615);
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)!( 1,163)( 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*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 >;
References : None.
to this polytope