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