Polytope of Type {32,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,20}*1280b
if this polytope has a name.
Group : SmallGroup(1280,90242)
Rank : 3
Schlafli Type : {32,20}
Number of vertices, edges, etc : 32, 320, 20
Order of s0s1s2 : 160
Order of s0s1s2s1 : 4
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
4-fold quotients : {8,20}*320a, {16,10}*320
5-fold quotients : {32,4}*256b
8-fold quotients : {4,20}*160, {8,10}*160
10-fold quotients : {16,4}*128a
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)
( 41,366)( 42,367)( 43,368)( 44,369)( 45,370)( 46,361)( 47,362)( 48,363)
( 49,364)( 50,365)( 51,371)( 52,372)( 53,373)( 54,374)( 55,375)( 56,376)
( 57,377)( 58,378)( 59,379)( 60,380)( 61,396)( 62,397)( 63,398)( 64,399)
( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)( 72,387)
( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)( 80,385)
( 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)
(121,466)(122,467)(123,468)(124,469)(125,470)(126,461)(127,462)(128,463)
(129,464)(130,465)(131,471)(132,472)(133,473)(134,474)(135,475)(136,476)
(137,477)(138,478)(139,479)(140,480)(141,446)(142,447)(143,448)(144,449)
(145,450)(146,441)(147,442)(148,443)(149,444)(150,445)(151,451)(152,452)
(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)(160,460)
(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)
(201,526)(202,527)(203,528)(204,529)(205,530)(206,521)(207,522)(208,523)
(209,524)(210,525)(211,531)(212,532)(213,533)(214,534)(215,535)(216,536)
(217,537)(218,538)(219,539)(220,540)(221,556)(222,557)(223,558)(224,559)
(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)(232,547)
(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)(240,545)
(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)
(281,626)(282,627)(283,628)(284,629)(285,630)(286,621)(287,622)(288,623)
(289,624)(290,625)(291,631)(292,632)(293,633)(294,634)(295,635)(296,636)
(297,637)(298,638)(299,639)(300,640)(301,606)(302,607)(303,608)(304,609)
(305,610)(306,601)(307,602)(308,603)(309,604)(310,605)(311,611)(312,612)
(313,613)(314,614)(315,615)(316,616)(317,617)(318,618)(319,619)(320,620);;
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)(481,606)(482,610)
(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)(490,602)
(491,611)(492,615)(493,614)(494,613)(495,612)(496,616)(497,620)(498,619)
(499,618)(500,617)(501,636)(502,640)(503,639)(504,638)(505,637)(506,631)
(507,635)(508,634)(509,633)(510,632)(511,626)(512,630)(513,629)(514,628)
(515,627)(516,621)(517,625)(518,624)(519,623)(520,622)(521,566)(522,570)
(523,569)(524,568)(525,567)(526,561)(527,565)(528,564)(529,563)(530,562)
(531,571)(532,575)(533,574)(534,573)(535,572)(536,576)(537,580)(538,579)
(539,578)(540,577)(541,596)(542,600)(543,599)(544,598)(545,597)(546,591)
(547,595)(548,594)(549,593)(550,592)(551,586)(552,590)(553,589)(554,588)
(555,587)(556,581)(557,585)(558,584)(559,583)(560,582);;
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)
( 81,248)( 82,247)( 83,246)( 84,250)( 85,249)( 86,243)( 87,242)( 88,241)
( 89,245)( 90,244)( 91,258)( 92,257)( 93,256)( 94,260)( 95,259)( 96,253)
( 97,252)( 98,251)( 99,255)(100,254)(101,268)(102,267)(103,266)(104,270)
(105,269)(106,263)(107,262)(108,261)(109,265)(110,264)(111,278)(112,277)
(113,276)(114,280)(115,279)(116,273)(117,272)(118,271)(119,275)(120,274)
(121,288)(122,287)(123,286)(124,290)(125,289)(126,283)(127,282)(128,281)
(129,285)(130,284)(131,298)(132,297)(133,296)(134,300)(135,299)(136,293)
(137,292)(138,291)(139,295)(140,294)(141,308)(142,307)(143,306)(144,310)
(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)(152,317)
(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)(160,314)
(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)
(401,568)(402,567)(403,566)(404,570)(405,569)(406,563)(407,562)(408,561)
(409,565)(410,564)(411,578)(412,577)(413,576)(414,580)(415,579)(416,573)
(417,572)(418,571)(419,575)(420,574)(421,588)(422,587)(423,586)(424,590)
(425,589)(426,583)(427,582)(428,581)(429,585)(430,584)(431,598)(432,597)
(433,596)(434,600)(435,599)(436,593)(437,592)(438,591)(439,595)(440,594)
(441,608)(442,607)(443,606)(444,610)(445,609)(446,603)(447,602)(448,601)
(449,605)(450,604)(451,618)(452,617)(453,616)(454,620)(455,619)(456,613)
(457,612)(458,611)(459,615)(460,614)(461,628)(462,627)(463,626)(464,630)
(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)(472,637)
(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)(480,634);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 11,336)( 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)( 41,366)( 42,367)( 43,368)( 44,369)( 45,370)( 46,361)( 47,362)
( 48,363)( 49,364)( 50,365)( 51,371)( 52,372)( 53,373)( 54,374)( 55,375)
( 56,376)( 57,377)( 58,378)( 59,379)( 60,380)( 61,396)( 62,397)( 63,398)
( 64,399)( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)
( 72,387)( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)
( 80,385)( 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)(121,466)(122,467)(123,468)(124,469)(125,470)(126,461)(127,462)
(128,463)(129,464)(130,465)(131,471)(132,472)(133,473)(134,474)(135,475)
(136,476)(137,477)(138,478)(139,479)(140,480)(141,446)(142,447)(143,448)
(144,449)(145,450)(146,441)(147,442)(148,443)(149,444)(150,445)(151,451)
(152,452)(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)
(160,460)(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)(201,526)(202,527)(203,528)(204,529)(205,530)(206,521)(207,522)
(208,523)(209,524)(210,525)(211,531)(212,532)(213,533)(214,534)(215,535)
(216,536)(217,537)(218,538)(219,539)(220,540)(221,556)(222,557)(223,558)
(224,559)(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)
(232,547)(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)
(240,545)(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)(281,626)(282,627)(283,628)(284,629)(285,630)(286,621)(287,622)
(288,623)(289,624)(290,625)(291,631)(292,632)(293,633)(294,634)(295,635)
(296,636)(297,637)(298,638)(299,639)(300,640)(301,606)(302,607)(303,608)
(304,609)(305,610)(306,601)(307,602)(308,603)(309,604)(310,605)(311,611)
(312,612)(313,613)(314,614)(315,615)(316,616)(317,617)(318,618)(319,619)
(320,620);
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)(481,606)
(482,610)(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)
(490,602)(491,611)(492,615)(493,614)(494,613)(495,612)(496,616)(497,620)
(498,619)(499,618)(500,617)(501,636)(502,640)(503,639)(504,638)(505,637)
(506,631)(507,635)(508,634)(509,633)(510,632)(511,626)(512,630)(513,629)
(514,628)(515,627)(516,621)(517,625)(518,624)(519,623)(520,622)(521,566)
(522,570)(523,569)(524,568)(525,567)(526,561)(527,565)(528,564)(529,563)
(530,562)(531,571)(532,575)(533,574)(534,573)(535,572)(536,576)(537,580)
(538,579)(539,578)(540,577)(541,596)(542,600)(543,599)(544,598)(545,597)
(546,591)(547,595)(548,594)(549,593)(550,592)(551,586)(552,590)(553,589)
(554,588)(555,587)(556,581)(557,585)(558,584)(559,583)(560,582);
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)( 81,248)( 82,247)( 83,246)( 84,250)( 85,249)( 86,243)( 87,242)
( 88,241)( 89,245)( 90,244)( 91,258)( 92,257)( 93,256)( 94,260)( 95,259)
( 96,253)( 97,252)( 98,251)( 99,255)(100,254)(101,268)(102,267)(103,266)
(104,270)(105,269)(106,263)(107,262)(108,261)(109,265)(110,264)(111,278)
(112,277)(113,276)(114,280)(115,279)(116,273)(117,272)(118,271)(119,275)
(120,274)(121,288)(122,287)(123,286)(124,290)(125,289)(126,283)(127,282)
(128,281)(129,285)(130,284)(131,298)(132,297)(133,296)(134,300)(135,299)
(136,293)(137,292)(138,291)(139,295)(140,294)(141,308)(142,307)(143,306)
(144,310)(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)
(152,317)(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)
(160,314)(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)(401,568)(402,567)(403,566)(404,570)(405,569)(406,563)(407,562)
(408,561)(409,565)(410,564)(411,578)(412,577)(413,576)(414,580)(415,579)
(416,573)(417,572)(418,571)(419,575)(420,574)(421,588)(422,587)(423,586)
(424,590)(425,589)(426,583)(427,582)(428,581)(429,585)(430,584)(431,598)
(432,597)(433,596)(434,600)(435,599)(436,593)(437,592)(438,591)(439,595)
(440,594)(441,608)(442,607)(443,606)(444,610)(445,609)(446,603)(447,602)
(448,601)(449,605)(450,604)(451,618)(452,617)(453,616)(454,620)(455,619)
(456,613)(457,612)(458,611)(459,615)(460,614)(461,628)(462,627)(463,626)
(464,630)(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)
(472,637)(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)
(480,634);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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