Polytope of Type {80,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {80,8}*1280c
if this polytope has a name.
Group : SmallGroup(1280,82994)
Rank : 3
Schlafli Type : {80,8}
Number of vertices, edges, etc : 80, 320, 8
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {40,8}*640a, {80,4}*640a
4-fold quotients : {40,4}*320a, {20,8}*320b, {80,2}*320
5-fold quotients : {16,8}*256c
8-fold quotients : {20,4}*160, {40,2}*160
10-fold quotients : {8,8}*128c, {16,4}*128a
16-fold quotients : {20,2}*80, {10,4}*80
20-fold quotients : {8,4}*64a, {4,8}*64b, {16,2}*64
32-fold quotients : {10,2}*40
40-fold quotients : {4,4}*32, {8,2}*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 := ( 1,321)( 2,325)( 3,324)( 4,323)( 5,322)( 6,326)( 7,330)( 8,329)
( 9,328)( 10,327)( 11,331)( 12,335)( 13,334)( 14,333)( 15,332)( 16,336)
( 17,340)( 18,339)( 19,338)( 20,337)( 21,346)( 22,350)( 23,349)( 24,348)
( 25,347)( 26,341)( 27,345)( 28,344)( 29,343)( 30,342)( 31,356)( 32,360)
( 33,359)( 34,358)( 35,357)( 36,351)( 37,355)( 38,354)( 39,353)( 40,352)
( 41,371)( 42,375)( 43,374)( 44,373)( 45,372)( 46,376)( 47,380)( 48,379)
( 49,378)( 50,377)( 51,361)( 52,365)( 53,364)( 54,363)( 55,362)( 56,366)
( 57,370)( 58,369)( 59,368)( 60,367)( 61,396)( 62,400)( 63,399)( 64,398)
( 65,397)( 66,391)( 67,395)( 68,394)( 69,393)( 70,392)( 71,386)( 72,390)
( 73,389)( 74,388)( 75,387)( 76,381)( 77,385)( 78,384)( 79,383)( 80,382)
( 81,421)( 82,425)( 83,424)( 84,423)( 85,422)( 86,426)( 87,430)( 88,429)
( 89,428)( 90,427)( 91,431)( 92,435)( 93,434)( 94,433)( 95,432)( 96,436)
( 97,440)( 98,439)( 99,438)(100,437)(101,401)(102,405)(103,404)(104,403)
(105,402)(106,406)(107,410)(108,409)(109,408)(110,407)(111,411)(112,415)
(113,414)(114,413)(115,412)(116,416)(117,420)(118,419)(119,418)(120,417)
(121,471)(122,475)(123,474)(124,473)(125,472)(126,476)(127,480)(128,479)
(129,478)(130,477)(131,461)(132,465)(133,464)(134,463)(135,462)(136,466)
(137,470)(138,469)(139,468)(140,467)(141,451)(142,455)(143,454)(144,453)
(145,452)(146,456)(147,460)(148,459)(149,458)(150,457)(151,441)(152,445)
(153,444)(154,443)(155,442)(156,446)(157,450)(158,449)(159,448)(160,447)
(161,481)(162,485)(163,484)(164,483)(165,482)(166,486)(167,490)(168,489)
(169,488)(170,487)(171,491)(172,495)(173,494)(174,493)(175,492)(176,496)
(177,500)(178,499)(179,498)(180,497)(181,506)(182,510)(183,509)(184,508)
(185,507)(186,501)(187,505)(188,504)(189,503)(190,502)(191,516)(192,520)
(193,519)(194,518)(195,517)(196,511)(197,515)(198,514)(199,513)(200,512)
(201,531)(202,535)(203,534)(204,533)(205,532)(206,536)(207,540)(208,539)
(209,538)(210,537)(211,521)(212,525)(213,524)(214,523)(215,522)(216,526)
(217,530)(218,529)(219,528)(220,527)(221,556)(222,560)(223,559)(224,558)
(225,557)(226,551)(227,555)(228,554)(229,553)(230,552)(231,546)(232,550)
(233,549)(234,548)(235,547)(236,541)(237,545)(238,544)(239,543)(240,542)
(241,581)(242,585)(243,584)(244,583)(245,582)(246,586)(247,590)(248,589)
(249,588)(250,587)(251,591)(252,595)(253,594)(254,593)(255,592)(256,596)
(257,600)(258,599)(259,598)(260,597)(261,561)(262,565)(263,564)(264,563)
(265,562)(266,566)(267,570)(268,569)(269,568)(270,567)(271,571)(272,575)
(273,574)(274,573)(275,572)(276,576)(277,580)(278,579)(279,578)(280,577)
(281,631)(282,635)(283,634)(284,633)(285,632)(286,636)(287,640)(288,639)
(289,638)(290,637)(291,621)(292,625)(293,624)(294,623)(295,622)(296,626)
(297,630)(298,629)(299,628)(300,627)(301,611)(302,615)(303,614)(304,613)
(305,612)(306,616)(307,620)(308,619)(309,618)(310,617)(311,601)(312,605)
(313,604)(314,603)(315,602)(316,606)(317,610)(318,609)(319,608)(320,607);;
s1 := ( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)
( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 38)( 32, 37)( 33, 36)
( 34, 40)( 35, 39)( 41, 53)( 42, 52)( 43, 51)( 44, 55)( 45, 54)( 46, 58)
( 47, 57)( 48, 56)( 49, 60)( 50, 59)( 61, 78)( 62, 77)( 63, 76)( 64, 80)
( 65, 79)( 66, 73)( 67, 72)( 68, 71)( 69, 75)( 70, 74)( 81,103)( 82,102)
( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)
( 91,113)( 92,112)( 93,111)( 94,115)( 95,114)( 96,118)( 97,117)( 98,116)
( 99,120)(100,119)(121,153)(122,152)(123,151)(124,155)(125,154)(126,158)
(127,157)(128,156)(129,160)(130,159)(131,143)(132,142)(133,141)(134,145)
(135,144)(136,148)(137,147)(138,146)(139,150)(140,149)(161,203)(162,202)
(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)
(171,213)(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)
(179,220)(180,219)(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)
(187,222)(188,221)(189,225)(190,224)(191,238)(192,237)(193,236)(194,240)
(195,239)(196,233)(197,232)(198,231)(199,235)(200,234)(241,303)(242,302)
(243,301)(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)
(251,313)(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)
(259,320)(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)
(267,287)(268,286)(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)
(275,294)(276,298)(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)
(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)
(331,413)(332,412)(333,411)(334,415)(335,414)(336,418)(337,417)(338,416)
(339,420)(340,419)(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)
(347,422)(348,421)(349,425)(350,424)(351,438)(352,437)(353,436)(354,440)
(355,439)(356,433)(357,432)(358,431)(359,435)(360,434)(361,453)(362,452)
(363,451)(364,455)(365,454)(366,458)(367,457)(368,456)(369,460)(370,459)
(371,443)(372,442)(373,441)(374,445)(375,444)(376,448)(377,447)(378,446)
(379,450)(380,449)(381,478)(382,477)(383,476)(384,480)(385,479)(386,473)
(387,472)(388,471)(389,475)(390,474)(391,468)(392,467)(393,466)(394,470)
(395,469)(396,463)(397,462)(398,461)(399,465)(400,464)(481,613)(482,612)
(483,611)(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)
(491,603)(492,602)(493,601)(494,605)(495,604)(496,608)(497,607)(498,606)
(499,610)(500,609)(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)(521,573)(522,572)
(523,571)(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)
(531,563)(532,562)(533,561)(534,565)(535,564)(536,568)(537,567)(538,566)
(539,570)(540,569)(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 := ( 1,161)( 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)
( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,216)( 47,217)( 48,218)
( 49,219)( 50,220)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)( 56,206)
( 57,207)( 58,208)( 59,209)( 60,210)( 61,231)( 62,232)( 63,233)( 64,234)
( 65,235)( 66,236)( 67,237)( 68,238)( 69,239)( 70,240)( 71,221)( 72,222)
( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)
( 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)
(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)(128,288)
(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)(136,296)
(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)(144,304)
(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)(152,312)
(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)(160,320)
(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)
(361,531)(362,532)(363,533)(364,534)(365,535)(366,536)(367,537)(368,538)
(369,539)(370,540)(371,521)(372,522)(373,523)(374,524)(375,525)(376,526)
(377,527)(378,528)(379,529)(380,530)(381,551)(382,552)(383,553)(384,554)
(385,555)(386,556)(387,557)(388,558)(389,559)(390,560)(391,541)(392,542)
(393,543)(394,544)(395,545)(396,546)(397,547)(398,548)(399,549)(400,550)
(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)
(441,601)(442,602)(443,603)(444,604)(445,605)(446,606)(447,607)(448,608)
(449,609)(450,610)(451,611)(452,612)(453,613)(454,614)(455,615)(456,616)
(457,617)(458,618)(459,619)(460,620)(461,621)(462,622)(463,623)(464,624)
(465,625)(466,626)(467,627)(468,628)(469,629)(470,630)(471,631)(472,632)
(473,633)(474,634)(475,635)(476,636)(477,637)(478,638)(479,639)(480,640);;
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*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*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*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*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)( 2,325)( 3,324)( 4,323)( 5,322)( 6,326)( 7,330)
( 8,329)( 9,328)( 10,327)( 11,331)( 12,335)( 13,334)( 14,333)( 15,332)
( 16,336)( 17,340)( 18,339)( 19,338)( 20,337)( 21,346)( 22,350)( 23,349)
( 24,348)( 25,347)( 26,341)( 27,345)( 28,344)( 29,343)( 30,342)( 31,356)
( 32,360)( 33,359)( 34,358)( 35,357)( 36,351)( 37,355)( 38,354)( 39,353)
( 40,352)( 41,371)( 42,375)( 43,374)( 44,373)( 45,372)( 46,376)( 47,380)
( 48,379)( 49,378)( 50,377)( 51,361)( 52,365)( 53,364)( 54,363)( 55,362)
( 56,366)( 57,370)( 58,369)( 59,368)( 60,367)( 61,396)( 62,400)( 63,399)
( 64,398)( 65,397)( 66,391)( 67,395)( 68,394)( 69,393)( 70,392)( 71,386)
( 72,390)( 73,389)( 74,388)( 75,387)( 76,381)( 77,385)( 78,384)( 79,383)
( 80,382)( 81,421)( 82,425)( 83,424)( 84,423)( 85,422)( 86,426)( 87,430)
( 88,429)( 89,428)( 90,427)( 91,431)( 92,435)( 93,434)( 94,433)( 95,432)
( 96,436)( 97,440)( 98,439)( 99,438)(100,437)(101,401)(102,405)(103,404)
(104,403)(105,402)(106,406)(107,410)(108,409)(109,408)(110,407)(111,411)
(112,415)(113,414)(114,413)(115,412)(116,416)(117,420)(118,419)(119,418)
(120,417)(121,471)(122,475)(123,474)(124,473)(125,472)(126,476)(127,480)
(128,479)(129,478)(130,477)(131,461)(132,465)(133,464)(134,463)(135,462)
(136,466)(137,470)(138,469)(139,468)(140,467)(141,451)(142,455)(143,454)
(144,453)(145,452)(146,456)(147,460)(148,459)(149,458)(150,457)(151,441)
(152,445)(153,444)(154,443)(155,442)(156,446)(157,450)(158,449)(159,448)
(160,447)(161,481)(162,485)(163,484)(164,483)(165,482)(166,486)(167,490)
(168,489)(169,488)(170,487)(171,491)(172,495)(173,494)(174,493)(175,492)
(176,496)(177,500)(178,499)(179,498)(180,497)(181,506)(182,510)(183,509)
(184,508)(185,507)(186,501)(187,505)(188,504)(189,503)(190,502)(191,516)
(192,520)(193,519)(194,518)(195,517)(196,511)(197,515)(198,514)(199,513)
(200,512)(201,531)(202,535)(203,534)(204,533)(205,532)(206,536)(207,540)
(208,539)(209,538)(210,537)(211,521)(212,525)(213,524)(214,523)(215,522)
(216,526)(217,530)(218,529)(219,528)(220,527)(221,556)(222,560)(223,559)
(224,558)(225,557)(226,551)(227,555)(228,554)(229,553)(230,552)(231,546)
(232,550)(233,549)(234,548)(235,547)(236,541)(237,545)(238,544)(239,543)
(240,542)(241,581)(242,585)(243,584)(244,583)(245,582)(246,586)(247,590)
(248,589)(249,588)(250,587)(251,591)(252,595)(253,594)(254,593)(255,592)
(256,596)(257,600)(258,599)(259,598)(260,597)(261,561)(262,565)(263,564)
(264,563)(265,562)(266,566)(267,570)(268,569)(269,568)(270,567)(271,571)
(272,575)(273,574)(274,573)(275,572)(276,576)(277,580)(278,579)(279,578)
(280,577)(281,631)(282,635)(283,634)(284,633)(285,632)(286,636)(287,640)
(288,639)(289,638)(290,637)(291,621)(292,625)(293,624)(294,623)(295,622)
(296,626)(297,630)(298,629)(299,628)(300,627)(301,611)(302,615)(303,614)
(304,613)(305,612)(306,616)(307,620)(308,619)(309,618)(310,617)(311,601)
(312,605)(313,604)(314,603)(315,602)(316,606)(317,610)(318,609)(319,608)
(320,607);
s1 := Sym(640)!( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 13)( 14, 15)( 16, 18)
( 19, 20)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 38)( 32, 37)
( 33, 36)( 34, 40)( 35, 39)( 41, 53)( 42, 52)( 43, 51)( 44, 55)( 45, 54)
( 46, 58)( 47, 57)( 48, 56)( 49, 60)( 50, 59)( 61, 78)( 62, 77)( 63, 76)
( 64, 80)( 65, 79)( 66, 73)( 67, 72)( 68, 71)( 69, 75)( 70, 74)( 81,103)
( 82,102)( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)
( 90,109)( 91,113)( 92,112)( 93,111)( 94,115)( 95,114)( 96,118)( 97,117)
( 98,116)( 99,120)(100,119)(121,153)(122,152)(123,151)(124,155)(125,154)
(126,158)(127,157)(128,156)(129,160)(130,159)(131,143)(132,142)(133,141)
(134,145)(135,144)(136,148)(137,147)(138,146)(139,150)(140,149)(161,203)
(162,202)(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)
(170,209)(171,213)(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)
(178,216)(179,220)(180,219)(181,228)(182,227)(183,226)(184,230)(185,229)
(186,223)(187,222)(188,221)(189,225)(190,224)(191,238)(192,237)(193,236)
(194,240)(195,239)(196,233)(197,232)(198,231)(199,235)(200,234)(241,303)
(242,302)(243,301)(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)
(250,309)(251,313)(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)
(258,316)(259,320)(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)
(266,288)(267,287)(268,286)(269,290)(270,289)(271,293)(272,292)(273,291)
(274,295)(275,294)(276,298)(277,297)(278,296)(279,300)(280,299)(321,403)
(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)
(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)(336,418)(337,417)
(338,416)(339,420)(340,419)(341,428)(342,427)(343,426)(344,430)(345,429)
(346,423)(347,422)(348,421)(349,425)(350,424)(351,438)(352,437)(353,436)
(354,440)(355,439)(356,433)(357,432)(358,431)(359,435)(360,434)(361,453)
(362,452)(363,451)(364,455)(365,454)(366,458)(367,457)(368,456)(369,460)
(370,459)(371,443)(372,442)(373,441)(374,445)(375,444)(376,448)(377,447)
(378,446)(379,450)(380,449)(381,478)(382,477)(383,476)(384,480)(385,479)
(386,473)(387,472)(388,471)(389,475)(390,474)(391,468)(392,467)(393,466)
(394,470)(395,469)(396,463)(397,462)(398,461)(399,465)(400,464)(481,613)
(482,612)(483,611)(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)
(490,619)(491,603)(492,602)(493,601)(494,605)(495,604)(496,608)(497,607)
(498,606)(499,610)(500,609)(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)(521,573)
(522,572)(523,571)(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)
(530,579)(531,563)(532,562)(533,561)(534,565)(535,564)(536,568)(537,567)
(538,566)(539,570)(540,569)(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)!( 1,161)( 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)( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,216)( 47,217)
( 48,218)( 49,219)( 50,220)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)
( 56,206)( 57,207)( 58,208)( 59,209)( 60,210)( 61,231)( 62,232)( 63,233)
( 64,234)( 65,235)( 66,236)( 67,237)( 68,238)( 69,239)( 70,240)( 71,221)
( 72,222)( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)
( 80,230)( 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)(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)
(128,288)(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)
(136,296)(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)
(144,304)(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)
(152,312)(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)
(160,320)(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)(361,531)(362,532)(363,533)(364,534)(365,535)(366,536)(367,537)
(368,538)(369,539)(370,540)(371,521)(372,522)(373,523)(374,524)(375,525)
(376,526)(377,527)(378,528)(379,529)(380,530)(381,551)(382,552)(383,553)
(384,554)(385,555)(386,556)(387,557)(388,558)(389,559)(390,560)(391,541)
(392,542)(393,543)(394,544)(395,545)(396,546)(397,547)(398,548)(399,549)
(400,550)(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)(441,601)(442,602)(443,603)(444,604)(445,605)(446,606)(447,607)
(448,608)(449,609)(450,610)(451,611)(452,612)(453,613)(454,614)(455,615)
(456,616)(457,617)(458,618)(459,619)(460,620)(461,621)(462,622)(463,623)
(464,624)(465,625)(466,626)(467,627)(468,628)(469,629)(470,630)(471,631)
(472,632)(473,633)(474,634)(475,635)(476,636)(477,637)(478,638)(479,639)
(480,640);
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*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*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*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*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