Polytope of Type {20,32}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,32}*1280b
if this polytope has a name.
Group : SmallGroup(1280,90242)
Rank : 3
Schlafli Type : {20,32}
Number of vertices, edges, etc : 20, 320, 32
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 : {20,16}*640a
4-fold quotients : {20,8}*320a, {10,16}*320
5-fold quotients : {4,32}*256b
8-fold quotients : {20,4}*160, {10,8}*160
10-fold quotients : {4,16}*128a
16-fold quotients : {20,2}*80, {10,4}*80
20-fold quotients : {4,8}*64a, {2,16}*64
32-fold quotients : {10,2}*40
40-fold quotients : {4,4}*32, {2,8}*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 := ( 1,161)( 2,165)( 3,164)( 4,163)( 5,162)( 6,166)( 7,170)( 8,169)
( 9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)( 16,176)
( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)( 24,183)
( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)( 32,195)
( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)( 40,197)
( 41,201)( 42,205)( 43,204)( 44,203)( 45,202)( 46,206)( 47,210)( 48,209)
( 49,208)( 50,207)( 51,211)( 52,215)( 53,214)( 54,213)( 55,212)( 56,216)
( 57,220)( 58,219)( 59,218)( 60,217)( 61,221)( 62,225)( 63,224)( 64,223)
( 65,222)( 66,226)( 67,230)( 68,229)( 69,228)( 70,227)( 71,231)( 72,235)
( 73,234)( 74,233)( 75,232)( 76,236)( 77,240)( 78,239)( 79,238)( 80,237)
( 81,246)( 82,250)( 83,249)( 84,248)( 85,247)( 86,241)( 87,245)( 88,244)
( 89,243)( 90,242)( 91,256)( 92,260)( 93,259)( 94,258)( 95,257)( 96,251)
( 97,255)( 98,254)( 99,253)(100,252)(101,266)(102,270)(103,269)(104,268)
(105,267)(106,261)(107,265)(108,264)(109,263)(110,262)(111,276)(112,280)
(113,279)(114,278)(115,277)(116,271)(117,275)(118,274)(119,273)(120,272)
(121,286)(122,290)(123,289)(124,288)(125,287)(126,281)(127,285)(128,284)
(129,283)(130,282)(131,296)(132,300)(133,299)(134,298)(135,297)(136,291)
(137,295)(138,294)(139,293)(140,292)(141,306)(142,310)(143,309)(144,308)
(145,307)(146,301)(147,305)(148,304)(149,303)(150,302)(151,316)(152,320)
(153,319)(154,318)(155,317)(156,311)(157,315)(158,314)(159,313)(160,312)
(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)(328,489)
(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)(336,496)
(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)(344,503)
(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)(352,515)
(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)(360,517)
(361,521)(362,525)(363,524)(364,523)(365,522)(366,526)(367,530)(368,529)
(369,528)(370,527)(371,531)(372,535)(373,534)(374,533)(375,532)(376,536)
(377,540)(378,539)(379,538)(380,537)(381,541)(382,545)(383,544)(384,543)
(385,542)(386,546)(387,550)(388,549)(389,548)(390,547)(391,551)(392,555)
(393,554)(394,553)(395,552)(396,556)(397,560)(398,559)(399,558)(400,557)
(401,566)(402,570)(403,569)(404,568)(405,567)(406,561)(407,565)(408,564)
(409,563)(410,562)(411,576)(412,580)(413,579)(414,578)(415,577)(416,571)
(417,575)(418,574)(419,573)(420,572)(421,586)(422,590)(423,589)(424,588)
(425,587)(426,581)(427,585)(428,584)(429,583)(430,582)(431,596)(432,600)
(433,599)(434,598)(435,597)(436,591)(437,595)(438,594)(439,593)(440,592)
(441,606)(442,610)(443,609)(444,608)(445,607)(446,601)(447,605)(448,604)
(449,603)(450,602)(451,616)(452,620)(453,619)(454,618)(455,617)(456,611)
(457,615)(458,614)(459,613)(460,612)(461,626)(462,630)(463,629)(464,628)
(465,627)(466,621)(467,625)(468,624)(469,623)(470,622)(471,636)(472,640)
(473,639)(474,638)(475,637)(476,631)(477,635)(478,634)(479,633)(480,632);;
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)(481,608)(482,607)
(483,606)(484,610)(485,609)(486,603)(487,602)(488,601)(489,605)(490,604)
(491,613)(492,612)(493,611)(494,615)(495,614)(496,618)(497,617)(498,616)
(499,620)(500,619)(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)
(507,632)(508,631)(509,635)(510,634)(511,628)(512,627)(513,626)(514,630)
(515,629)(516,623)(517,622)(518,621)(519,625)(520,624)(521,568)(522,567)
(523,566)(524,570)(525,569)(526,563)(527,562)(528,561)(529,565)(530,564)
(531,573)(532,572)(533,571)(534,575)(535,574)(536,578)(537,577)(538,576)
(539,580)(540,579)(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)
(547,592)(548,591)(549,595)(550,594)(551,588)(552,587)(553,586)(554,590)
(555,589)(556,583)(557,582)(558,581)(559,585)(560,584);;
s2 := ( 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);;
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,
s2*s0*s1*s2*s1*s2*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*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*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)!( 1,161)( 2,165)( 3,164)( 4,163)( 5,162)( 6,166)( 7,170)
( 8,169)( 9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)
( 16,176)( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)
( 24,183)( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)
( 32,195)( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)
( 40,197)( 41,201)( 42,205)( 43,204)( 44,203)( 45,202)( 46,206)( 47,210)
( 48,209)( 49,208)( 50,207)( 51,211)( 52,215)( 53,214)( 54,213)( 55,212)
( 56,216)( 57,220)( 58,219)( 59,218)( 60,217)( 61,221)( 62,225)( 63,224)
( 64,223)( 65,222)( 66,226)( 67,230)( 68,229)( 69,228)( 70,227)( 71,231)
( 72,235)( 73,234)( 74,233)( 75,232)( 76,236)( 77,240)( 78,239)( 79,238)
( 80,237)( 81,246)( 82,250)( 83,249)( 84,248)( 85,247)( 86,241)( 87,245)
( 88,244)( 89,243)( 90,242)( 91,256)( 92,260)( 93,259)( 94,258)( 95,257)
( 96,251)( 97,255)( 98,254)( 99,253)(100,252)(101,266)(102,270)(103,269)
(104,268)(105,267)(106,261)(107,265)(108,264)(109,263)(110,262)(111,276)
(112,280)(113,279)(114,278)(115,277)(116,271)(117,275)(118,274)(119,273)
(120,272)(121,286)(122,290)(123,289)(124,288)(125,287)(126,281)(127,285)
(128,284)(129,283)(130,282)(131,296)(132,300)(133,299)(134,298)(135,297)
(136,291)(137,295)(138,294)(139,293)(140,292)(141,306)(142,310)(143,309)
(144,308)(145,307)(146,301)(147,305)(148,304)(149,303)(150,302)(151,316)
(152,320)(153,319)(154,318)(155,317)(156,311)(157,315)(158,314)(159,313)
(160,312)(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)
(328,489)(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)
(336,496)(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)
(344,503)(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)
(352,515)(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)
(360,517)(361,521)(362,525)(363,524)(364,523)(365,522)(366,526)(367,530)
(368,529)(369,528)(370,527)(371,531)(372,535)(373,534)(374,533)(375,532)
(376,536)(377,540)(378,539)(379,538)(380,537)(381,541)(382,545)(383,544)
(384,543)(385,542)(386,546)(387,550)(388,549)(389,548)(390,547)(391,551)
(392,555)(393,554)(394,553)(395,552)(396,556)(397,560)(398,559)(399,558)
(400,557)(401,566)(402,570)(403,569)(404,568)(405,567)(406,561)(407,565)
(408,564)(409,563)(410,562)(411,576)(412,580)(413,579)(414,578)(415,577)
(416,571)(417,575)(418,574)(419,573)(420,572)(421,586)(422,590)(423,589)
(424,588)(425,587)(426,581)(427,585)(428,584)(429,583)(430,582)(431,596)
(432,600)(433,599)(434,598)(435,597)(436,591)(437,595)(438,594)(439,593)
(440,592)(441,606)(442,610)(443,609)(444,608)(445,607)(446,601)(447,605)
(448,604)(449,603)(450,602)(451,616)(452,620)(453,619)(454,618)(455,617)
(456,611)(457,615)(458,614)(459,613)(460,612)(461,626)(462,630)(463,629)
(464,628)(465,627)(466,621)(467,625)(468,624)(469,623)(470,622)(471,636)
(472,640)(473,639)(474,638)(475,637)(476,631)(477,635)(478,634)(479,633)
(480,632);
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)(481,608)
(482,607)(483,606)(484,610)(485,609)(486,603)(487,602)(488,601)(489,605)
(490,604)(491,613)(492,612)(493,611)(494,615)(495,614)(496,618)(497,617)
(498,616)(499,620)(500,619)(501,638)(502,637)(503,636)(504,640)(505,639)
(506,633)(507,632)(508,631)(509,635)(510,634)(511,628)(512,627)(513,626)
(514,630)(515,629)(516,623)(517,622)(518,621)(519,625)(520,624)(521,568)
(522,567)(523,566)(524,570)(525,569)(526,563)(527,562)(528,561)(529,565)
(530,564)(531,573)(532,572)(533,571)(534,575)(535,574)(536,578)(537,577)
(538,576)(539,580)(540,579)(541,598)(542,597)(543,596)(544,600)(545,599)
(546,593)(547,592)(548,591)(549,595)(550,594)(551,588)(552,587)(553,586)
(554,590)(555,589)(556,583)(557,582)(558,581)(559,585)(560,584);
s2 := 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);
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,
s2*s0*s1*s2*s1*s2*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope