Polytope of Type {4,80}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,80}*1280a
if this polytope has a name.
Group : SmallGroup(1280,81667)
Rank : 3
Schlafli Type : {4,80}
Number of vertices, edges, etc : 8, 320, 160
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {4,40}*640a, {4,80}*640a, {4,80}*640b
4-fold quotients : {4,40}*320a, {4,20}*320, {4,40}*320b, {2,80}*320
5-fold quotients : {4,16}*256a
8-fold quotients : {4,20}*160, {2,40}*160
10-fold quotients : {4,8}*128a, {4,16}*128a, {4,16}*128b
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64, {2,16}*64
32-fold quotients : {2,10}*40
40-fold quotients : {4,4}*32, {2,8}*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 := ( 1,161)( 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)
( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,256)( 87,257)( 88,258)
( 89,259)( 90,260)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,246)
( 97,247)( 98,248)( 99,249)(100,250)(101,271)(102,272)(103,273)(104,274)
(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,261)(112,262)
(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)
(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)(128,298)
(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,311)(142,312)(143,313)(144,314)
(145,315)(146,316)(147,317)(148,318)(149,319)(150,320)(151,301)(152,302)
(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)(160,310)
(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)
(401,571)(402,572)(403,573)(404,574)(405,575)(406,576)(407,577)(408,578)
(409,579)(410,580)(411,561)(412,562)(413,563)(414,564)(415,565)(416,566)
(417,567)(418,568)(419,569)(420,570)(421,591)(422,592)(423,593)(424,594)
(425,595)(426,596)(427,597)(428,598)(429,599)(430,600)(431,581)(432,582)
(433,583)(434,584)(435,585)(436,586)(437,587)(438,588)(439,589)(440,590)
(441,611)(442,612)(443,613)(444,614)(445,615)(446,616)(447,617)(448,618)
(449,619)(450,620)(451,601)(452,602)(453,603)(454,604)(455,605)(456,606)
(457,607)(458,608)(459,609)(460,610)(461,631)(462,632)(463,633)(464,634)
(465,635)(466,636)(467,637)(468,638)(469,639)(470,640)(471,621)(472,622)
(473,623)(474,624)(475,625)(476,626)(477,627)(478,628)(479,629)(480,630);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 36)( 32, 40)( 33, 39)
( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)
( 57, 60)( 58, 59)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 71, 76)
( 72, 80)( 73, 79)( 74, 78)( 75, 77)( 81,101)( 82,105)( 83,104)( 84,103)
( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,111)( 92,115)
( 93,114)( 94,113)( 95,112)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)
(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)(128,149)
(129,148)(130,147)(131,151)(132,155)(133,154)(134,153)(135,152)(136,156)
(137,160)(138,159)(139,158)(140,157)(161,201)(162,205)(163,204)(164,203)
(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,211)(172,215)
(173,214)(174,213)(175,212)(176,216)(177,220)(178,219)(179,218)(180,217)
(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)(187,225)(188,224)
(189,223)(190,222)(191,236)(192,240)(193,239)(194,238)(195,237)(196,231)
(197,235)(198,234)(199,233)(200,232)(241,301)(242,305)(243,304)(244,303)
(245,302)(246,306)(247,310)(248,309)(249,308)(250,307)(251,311)(252,315)
(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)(260,317)
(261,281)(262,285)(263,284)(264,283)(265,282)(266,286)(267,290)(268,289)
(269,288)(270,287)(271,291)(272,295)(273,294)(274,293)(275,292)(276,296)
(277,300)(278,299)(279,298)(280,297)(321,401)(322,405)(323,404)(324,403)
(325,402)(326,406)(327,410)(328,409)(329,408)(330,407)(331,411)(332,415)
(333,414)(334,413)(335,412)(336,416)(337,420)(338,419)(339,418)(340,417)
(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)(347,425)(348,424)
(349,423)(350,422)(351,436)(352,440)(353,439)(354,438)(355,437)(356,431)
(357,435)(358,434)(359,433)(360,432)(361,441)(362,445)(363,444)(364,443)
(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,451)(372,455)
(373,454)(374,453)(375,452)(376,456)(377,460)(378,459)(379,458)(380,457)
(381,466)(382,470)(383,469)(384,468)(385,467)(386,461)(387,465)(388,464)
(389,463)(390,462)(391,476)(392,480)(393,479)(394,478)(395,477)(396,471)
(397,475)(398,474)(399,473)(400,472)(481,611)(482,615)(483,614)(484,613)
(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,601)(492,605)
(493,604)(494,603)(495,602)(496,606)(497,610)(498,609)(499,608)(500,607)
(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)(521,571)(522,575)(523,574)(524,573)
(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,561)(532,565)
(533,564)(534,563)(535,562)(536,566)(537,570)(538,569)(539,568)(540,567)
(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 := ( 1,323)( 2,322)( 3,321)( 4,325)( 5,324)( 6,328)( 7,327)( 8,326)
( 9,330)( 10,329)( 11,333)( 12,332)( 13,331)( 14,335)( 15,334)( 16,338)
( 17,337)( 18,336)( 19,340)( 20,339)( 21,348)( 22,347)( 23,346)( 24,350)
( 25,349)( 26,343)( 27,342)( 28,341)( 29,345)( 30,344)( 31,358)( 32,357)
( 33,356)( 34,360)( 35,359)( 36,353)( 37,352)( 38,351)( 39,355)( 40,354)
( 41,373)( 42,372)( 43,371)( 44,375)( 45,374)( 46,378)( 47,377)( 48,376)
( 49,380)( 50,379)( 51,363)( 52,362)( 53,361)( 54,365)( 55,364)( 56,368)
( 57,367)( 58,366)( 59,370)( 60,369)( 61,398)( 62,397)( 63,396)( 64,400)
( 65,399)( 66,393)( 67,392)( 68,391)( 69,395)( 70,394)( 71,388)( 72,387)
( 73,386)( 74,390)( 75,389)( 76,383)( 77,382)( 78,381)( 79,385)( 80,384)
( 81,423)( 82,422)( 83,421)( 84,425)( 85,424)( 86,428)( 87,427)( 88,426)
( 89,430)( 90,429)( 91,433)( 92,432)( 93,431)( 94,435)( 95,434)( 96,438)
( 97,437)( 98,436)( 99,440)(100,439)(101,403)(102,402)(103,401)(104,405)
(105,404)(106,408)(107,407)(108,406)(109,410)(110,409)(111,413)(112,412)
(113,411)(114,415)(115,414)(116,418)(117,417)(118,416)(119,420)(120,419)
(121,473)(122,472)(123,471)(124,475)(125,474)(126,478)(127,477)(128,476)
(129,480)(130,479)(131,463)(132,462)(133,461)(134,465)(135,464)(136,468)
(137,467)(138,466)(139,470)(140,469)(141,453)(142,452)(143,451)(144,455)
(145,454)(146,458)(147,457)(148,456)(149,460)(150,459)(151,443)(152,442)
(153,441)(154,445)(155,444)(156,448)(157,447)(158,446)(159,450)(160,449)
(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)(168,486)
(169,490)(170,489)(171,493)(172,492)(173,491)(174,495)(175,494)(176,498)
(177,497)(178,496)(179,500)(180,499)(181,508)(182,507)(183,506)(184,510)
(185,509)(186,503)(187,502)(188,501)(189,505)(190,504)(191,518)(192,517)
(193,516)(194,520)(195,519)(196,513)(197,512)(198,511)(199,515)(200,514)
(201,533)(202,532)(203,531)(204,535)(205,534)(206,538)(207,537)(208,536)
(209,540)(210,539)(211,523)(212,522)(213,521)(214,525)(215,524)(216,528)
(217,527)(218,526)(219,530)(220,529)(221,558)(222,557)(223,556)(224,560)
(225,559)(226,553)(227,552)(228,551)(229,555)(230,554)(231,548)(232,547)
(233,546)(234,550)(235,549)(236,543)(237,542)(238,541)(239,545)(240,544)
(241,583)(242,582)(243,581)(244,585)(245,584)(246,588)(247,587)(248,586)
(249,590)(250,589)(251,593)(252,592)(253,591)(254,595)(255,594)(256,598)
(257,597)(258,596)(259,600)(260,599)(261,563)(262,562)(263,561)(264,565)
(265,564)(266,568)(267,567)(268,566)(269,570)(270,569)(271,573)(272,572)
(273,571)(274,575)(275,574)(276,578)(277,577)(278,576)(279,580)(280,579)
(281,633)(282,632)(283,631)(284,635)(285,634)(286,638)(287,637)(288,636)
(289,640)(290,639)(291,623)(292,622)(293,621)(294,625)(295,624)(296,628)
(297,627)(298,626)(299,630)(300,629)(301,613)(302,612)(303,611)(304,615)
(305,614)(306,618)(307,617)(308,616)(309,620)(310,619)(311,603)(312,602)
(313,601)(314,605)(315,604)(316,608)(317,607)(318,606)(319,610)(320,609);;
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*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*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)( 2,162)( 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)( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,256)( 87,257)
( 88,258)( 89,259)( 90,260)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,246)( 97,247)( 98,248)( 99,249)(100,250)(101,271)(102,272)(103,273)
(104,274)(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,261)
(112,262)(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)
(120,270)(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)
(128,298)(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,311)(142,312)(143,313)
(144,314)(145,315)(146,316)(147,317)(148,318)(149,319)(150,320)(151,301)
(152,302)(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)
(160,310)(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)(401,571)(402,572)(403,573)(404,574)(405,575)(406,576)(407,577)
(408,578)(409,579)(410,580)(411,561)(412,562)(413,563)(414,564)(415,565)
(416,566)(417,567)(418,568)(419,569)(420,570)(421,591)(422,592)(423,593)
(424,594)(425,595)(426,596)(427,597)(428,598)(429,599)(430,600)(431,581)
(432,582)(433,583)(434,584)(435,585)(436,586)(437,587)(438,588)(439,589)
(440,590)(441,611)(442,612)(443,613)(444,614)(445,615)(446,616)(447,617)
(448,618)(449,619)(450,620)(451,601)(452,602)(453,603)(454,604)(455,605)
(456,606)(457,607)(458,608)(459,609)(460,610)(461,631)(462,632)(463,633)
(464,634)(465,635)(466,636)(467,637)(468,638)(469,639)(470,640)(471,621)
(472,622)(473,623)(474,624)(475,625)(476,626)(477,627)(478,628)(479,629)
(480,630);
s1 := Sym(640)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 36)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)
( 53, 54)( 57, 60)( 58, 59)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)
( 71, 76)( 72, 80)( 73, 79)( 74, 78)( 75, 77)( 81,101)( 82,105)( 83,104)
( 84,103)( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,111)
( 92,115)( 93,114)( 94,113)( 95,112)( 96,116)( 97,120)( 98,119)( 99,118)
(100,117)(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)
(128,149)(129,148)(130,147)(131,151)(132,155)(133,154)(134,153)(135,152)
(136,156)(137,160)(138,159)(139,158)(140,157)(161,201)(162,205)(163,204)
(164,203)(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,211)
(172,215)(173,214)(174,213)(175,212)(176,216)(177,220)(178,219)(179,218)
(180,217)(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)(187,225)
(188,224)(189,223)(190,222)(191,236)(192,240)(193,239)(194,238)(195,237)
(196,231)(197,235)(198,234)(199,233)(200,232)(241,301)(242,305)(243,304)
(244,303)(245,302)(246,306)(247,310)(248,309)(249,308)(250,307)(251,311)
(252,315)(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)
(260,317)(261,281)(262,285)(263,284)(264,283)(265,282)(266,286)(267,290)
(268,289)(269,288)(270,287)(271,291)(272,295)(273,294)(274,293)(275,292)
(276,296)(277,300)(278,299)(279,298)(280,297)(321,401)(322,405)(323,404)
(324,403)(325,402)(326,406)(327,410)(328,409)(329,408)(330,407)(331,411)
(332,415)(333,414)(334,413)(335,412)(336,416)(337,420)(338,419)(339,418)
(340,417)(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)(347,425)
(348,424)(349,423)(350,422)(351,436)(352,440)(353,439)(354,438)(355,437)
(356,431)(357,435)(358,434)(359,433)(360,432)(361,441)(362,445)(363,444)
(364,443)(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,451)
(372,455)(373,454)(374,453)(375,452)(376,456)(377,460)(378,459)(379,458)
(380,457)(381,466)(382,470)(383,469)(384,468)(385,467)(386,461)(387,465)
(388,464)(389,463)(390,462)(391,476)(392,480)(393,479)(394,478)(395,477)
(396,471)(397,475)(398,474)(399,473)(400,472)(481,611)(482,615)(483,614)
(484,613)(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,601)
(492,605)(493,604)(494,603)(495,602)(496,606)(497,610)(498,609)(499,608)
(500,607)(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)(521,571)(522,575)(523,574)
(524,573)(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,561)
(532,565)(533,564)(534,563)(535,562)(536,566)(537,570)(538,569)(539,568)
(540,567)(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)!( 1,323)( 2,322)( 3,321)( 4,325)( 5,324)( 6,328)( 7,327)
( 8,326)( 9,330)( 10,329)( 11,333)( 12,332)( 13,331)( 14,335)( 15,334)
( 16,338)( 17,337)( 18,336)( 19,340)( 20,339)( 21,348)( 22,347)( 23,346)
( 24,350)( 25,349)( 26,343)( 27,342)( 28,341)( 29,345)( 30,344)( 31,358)
( 32,357)( 33,356)( 34,360)( 35,359)( 36,353)( 37,352)( 38,351)( 39,355)
( 40,354)( 41,373)( 42,372)( 43,371)( 44,375)( 45,374)( 46,378)( 47,377)
( 48,376)( 49,380)( 50,379)( 51,363)( 52,362)( 53,361)( 54,365)( 55,364)
( 56,368)( 57,367)( 58,366)( 59,370)( 60,369)( 61,398)( 62,397)( 63,396)
( 64,400)( 65,399)( 66,393)( 67,392)( 68,391)( 69,395)( 70,394)( 71,388)
( 72,387)( 73,386)( 74,390)( 75,389)( 76,383)( 77,382)( 78,381)( 79,385)
( 80,384)( 81,423)( 82,422)( 83,421)( 84,425)( 85,424)( 86,428)( 87,427)
( 88,426)( 89,430)( 90,429)( 91,433)( 92,432)( 93,431)( 94,435)( 95,434)
( 96,438)( 97,437)( 98,436)( 99,440)(100,439)(101,403)(102,402)(103,401)
(104,405)(105,404)(106,408)(107,407)(108,406)(109,410)(110,409)(111,413)
(112,412)(113,411)(114,415)(115,414)(116,418)(117,417)(118,416)(119,420)
(120,419)(121,473)(122,472)(123,471)(124,475)(125,474)(126,478)(127,477)
(128,476)(129,480)(130,479)(131,463)(132,462)(133,461)(134,465)(135,464)
(136,468)(137,467)(138,466)(139,470)(140,469)(141,453)(142,452)(143,451)
(144,455)(145,454)(146,458)(147,457)(148,456)(149,460)(150,459)(151,443)
(152,442)(153,441)(154,445)(155,444)(156,448)(157,447)(158,446)(159,450)
(160,449)(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)
(168,486)(169,490)(170,489)(171,493)(172,492)(173,491)(174,495)(175,494)
(176,498)(177,497)(178,496)(179,500)(180,499)(181,508)(182,507)(183,506)
(184,510)(185,509)(186,503)(187,502)(188,501)(189,505)(190,504)(191,518)
(192,517)(193,516)(194,520)(195,519)(196,513)(197,512)(198,511)(199,515)
(200,514)(201,533)(202,532)(203,531)(204,535)(205,534)(206,538)(207,537)
(208,536)(209,540)(210,539)(211,523)(212,522)(213,521)(214,525)(215,524)
(216,528)(217,527)(218,526)(219,530)(220,529)(221,558)(222,557)(223,556)
(224,560)(225,559)(226,553)(227,552)(228,551)(229,555)(230,554)(231,548)
(232,547)(233,546)(234,550)(235,549)(236,543)(237,542)(238,541)(239,545)
(240,544)(241,583)(242,582)(243,581)(244,585)(245,584)(246,588)(247,587)
(248,586)(249,590)(250,589)(251,593)(252,592)(253,591)(254,595)(255,594)
(256,598)(257,597)(258,596)(259,600)(260,599)(261,563)(262,562)(263,561)
(264,565)(265,564)(266,568)(267,567)(268,566)(269,570)(270,569)(271,573)
(272,572)(273,571)(274,575)(275,574)(276,578)(277,577)(278,576)(279,580)
(280,579)(281,633)(282,632)(283,631)(284,635)(285,634)(286,638)(287,637)
(288,636)(289,640)(290,639)(291,623)(292,622)(293,621)(294,625)(295,624)
(296,628)(297,627)(298,626)(299,630)(300,629)(301,613)(302,612)(303,611)
(304,615)(305,614)(306,618)(307,617)(308,616)(309,620)(310,619)(311,603)
(312,602)(313,601)(314,605)(315,604)(316,608)(317,607)(318,606)(319,610)
(320,609);
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*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*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