Polytope of Type {20,32}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,32}*1280a
Also Known As : {20,32|2}. if this polytope has another name.
Group : SmallGroup(1280,90208)
Rank : 3
Schlafli Type : {20,32}
Number of vertices, edges, etc : 20, 320, 32
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 : {20,16}*640a, {10,32}*640
4-fold quotients : {20,8}*320a, {10,16}*320
5-fold quotients : {4,32}*256a
8-fold quotients : {20,4}*160, {10,8}*160
10-fold quotients : {4,16}*128a, {2,32}*128
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)
( 81,241)( 82,245)( 83,244)( 84,243)( 85,242)( 86,246)( 87,250)( 88,249)
( 89,248)( 90,247)( 91,251)( 92,255)( 93,254)( 94,253)( 95,252)( 96,256)
( 97,260)( 98,259)( 99,258)(100,257)(101,261)(102,265)(103,264)(104,263)
(105,262)(106,266)(107,270)(108,269)(109,268)(110,267)(111,271)(112,275)
(113,274)(114,273)(115,272)(116,276)(117,280)(118,279)(119,278)(120,277)
(121,281)(122,285)(123,284)(124,283)(125,282)(126,286)(127,290)(128,289)
(129,288)(130,287)(131,291)(132,295)(133,294)(134,293)(135,292)(136,296)
(137,300)(138,299)(139,298)(140,297)(141,301)(142,305)(143,304)(144,303)
(145,302)(146,306)(147,310)(148,309)(149,308)(150,307)(151,311)(152,315)
(153,314)(154,313)(155,312)(156,316)(157,320)(158,319)(159,318)(160,317)
(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)
(401,561)(402,565)(403,564)(404,563)(405,562)(406,566)(407,570)(408,569)
(409,568)(410,567)(411,571)(412,575)(413,574)(414,573)(415,572)(416,576)
(417,580)(418,579)(419,578)(420,577)(421,581)(422,585)(423,584)(424,583)
(425,582)(426,586)(427,590)(428,589)(429,588)(430,587)(431,591)(432,595)
(433,594)(434,593)(435,592)(436,596)(437,600)(438,599)(439,598)(440,597)
(441,601)(442,605)(443,604)(444,603)(445,602)(446,606)(447,610)(448,609)
(449,608)(450,607)(451,611)(452,615)(453,614)(454,613)(455,612)(456,616)
(457,620)(458,619)(459,618)(460,617)(461,621)(462,625)(463,624)(464,623)
(465,622)(466,626)(467,630)(468,629)(469,628)(470,627)(471,631)(472,635)
(473,634)(474,633)(475,632)(476,636)(477,640)(478,639)(479,638)(480,637);;
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 := ( 1,321)( 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);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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)( 2,165)( 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)( 81,241)( 82,245)( 83,244)( 84,243)( 85,242)( 86,246)( 87,250)
( 88,249)( 89,248)( 90,247)( 91,251)( 92,255)( 93,254)( 94,253)( 95,252)
( 96,256)( 97,260)( 98,259)( 99,258)(100,257)(101,261)(102,265)(103,264)
(104,263)(105,262)(106,266)(107,270)(108,269)(109,268)(110,267)(111,271)
(112,275)(113,274)(114,273)(115,272)(116,276)(117,280)(118,279)(119,278)
(120,277)(121,281)(122,285)(123,284)(124,283)(125,282)(126,286)(127,290)
(128,289)(129,288)(130,287)(131,291)(132,295)(133,294)(134,293)(135,292)
(136,296)(137,300)(138,299)(139,298)(140,297)(141,301)(142,305)(143,304)
(144,303)(145,302)(146,306)(147,310)(148,309)(149,308)(150,307)(151,311)
(152,315)(153,314)(154,313)(155,312)(156,316)(157,320)(158,319)(159,318)
(160,317)(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)(401,561)(402,565)(403,564)(404,563)(405,562)(406,566)(407,570)
(408,569)(409,568)(410,567)(411,571)(412,575)(413,574)(414,573)(415,572)
(416,576)(417,580)(418,579)(419,578)(420,577)(421,581)(422,585)(423,584)
(424,583)(425,582)(426,586)(427,590)(428,589)(429,588)(430,587)(431,591)
(432,595)(433,594)(434,593)(435,592)(436,596)(437,600)(438,599)(439,598)
(440,597)(441,601)(442,605)(443,604)(444,603)(445,602)(446,606)(447,610)
(448,609)(449,608)(450,607)(451,611)(452,615)(453,614)(454,613)(455,612)
(456,616)(457,620)(458,619)(459,618)(460,617)(461,621)(462,625)(463,624)
(464,623)(465,622)(466,626)(467,630)(468,629)(469,628)(470,627)(471,631)
(472,635)(473,634)(474,633)(475,632)(476,636)(477,640)(478,639)(479,638)
(480,637);
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)!( 1,321)( 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);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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