Polytope of Type {8,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20}*1280d
if this polytope has a name.
Group : SmallGroup(1280,90303)
Rank : 3
Schlafli Type : {8,20}
Number of vertices, edges, etc : 32, 320, 80
Order of s0s1s2 : 40
Order of s0s1s2s1 : 8
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 : {8,20}*640b
4-fold quotients : {4,20}*320
5-fold quotients : {8,4}*256d
8-fold quotients : {4,20}*160
10-fold quotients : {8,4}*128b
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,4}*64
32-fold quotients : {2,10}*40
40-fold quotients : {4,4}*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 := ( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)( 8,488)
( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)( 24,509)
( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,516)( 32,517)
( 33,518)( 34,519)( 35,520)( 36,511)( 37,512)( 38,513)( 39,514)( 40,515)
( 41,556)( 42,557)( 43,558)( 44,559)( 45,560)( 46,551)( 47,552)( 48,553)
( 49,554)( 50,555)( 51,546)( 52,547)( 53,548)( 54,549)( 55,550)( 56,541)
( 57,542)( 58,543)( 59,544)( 60,545)( 61,536)( 62,537)( 63,538)( 64,539)
( 65,540)( 66,531)( 67,532)( 68,533)( 69,534)( 70,535)( 71,526)( 72,527)
( 73,528)( 74,529)( 75,530)( 76,521)( 77,522)( 78,523)( 79,524)( 80,525)
( 81,586)( 82,587)( 83,588)( 84,589)( 85,590)( 86,581)( 87,582)( 88,583)
( 89,584)( 90,585)( 91,596)( 92,597)( 93,598)( 94,599)( 95,600)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,566)(102,567)(103,568)(104,569)
(105,570)(106,561)(107,562)(108,563)(109,564)(110,565)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,571)(117,572)(118,573)(119,574)(120,575)
(121,611)(122,612)(123,613)(124,614)(125,615)(126,616)(127,617)(128,618)
(129,619)(130,620)(131,601)(132,602)(133,603)(134,604)(135,605)(136,606)
(137,607)(138,608)(139,609)(140,610)(141,636)(142,637)(143,638)(144,639)
(145,640)(146,631)(147,632)(148,633)(149,634)(150,635)(151,626)(152,627)
(153,628)(154,629)(155,630)(156,621)(157,622)(158,623)(159,624)(160,625)
(161,321)(162,322)(163,323)(164,324)(165,325)(166,326)(167,327)(168,328)
(169,329)(170,330)(171,331)(172,332)(173,333)(174,334)(175,335)(176,336)
(177,337)(178,338)(179,339)(180,340)(181,346)(182,347)(183,348)(184,349)
(185,350)(186,341)(187,342)(188,343)(189,344)(190,345)(191,356)(192,357)
(193,358)(194,359)(195,360)(196,351)(197,352)(198,353)(199,354)(200,355)
(201,396)(202,397)(203,398)(204,399)(205,400)(206,391)(207,392)(208,393)
(209,394)(210,395)(211,386)(212,387)(213,388)(214,389)(215,390)(216,381)
(217,382)(218,383)(219,384)(220,385)(221,376)(222,377)(223,378)(224,379)
(225,380)(226,371)(227,372)(228,373)(229,374)(230,375)(231,366)(232,367)
(233,368)(234,369)(235,370)(236,361)(237,362)(238,363)(239,364)(240,365)
(241,426)(242,427)(243,428)(244,429)(245,430)(246,421)(247,422)(248,423)
(249,424)(250,425)(251,436)(252,437)(253,438)(254,439)(255,440)(256,431)
(257,432)(258,433)(259,434)(260,435)(261,406)(262,407)(263,408)(264,409)
(265,410)(266,401)(267,402)(268,403)(269,404)(270,405)(271,416)(272,417)
(273,418)(274,419)(275,420)(276,411)(277,412)(278,413)(279,414)(280,415)
(281,451)(282,452)(283,453)(284,454)(285,455)(286,456)(287,457)(288,458)
(289,459)(290,460)(291,441)(292,442)(293,443)(294,444)(295,445)(296,446)
(297,447)(298,448)(299,449)(300,450)(301,476)(302,477)(303,478)(304,479)
(305,480)(306,471)(307,472)(308,473)(309,474)(310,475)(311,466)(312,467)
(313,468)(314,469)(315,470)(316,461)(317,462)(318,463)(319,464)(320,465);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)( 28, 39)
( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)
( 57, 60)( 58, 59)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 76)
( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81, 86)( 82, 90)( 83, 89)( 84, 88)
( 85, 87)( 91, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)(101,116)(102,120)
(103,119)(104,118)(105,117)(106,111)(107,115)(108,114)(109,113)(110,112)
(121,126)(122,130)(123,129)(124,128)(125,127)(131,136)(132,140)(133,139)
(134,138)(135,137)(141,156)(142,160)(143,159)(144,158)(145,157)(146,151)
(147,155)(148,154)(149,153)(150,152)(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)
(181,231)(182,235)(183,234)(184,233)(185,232)(186,236)(187,240)(188,239)
(189,238)(190,237)(191,221)(192,225)(193,224)(194,223)(195,222)(196,226)
(197,230)(198,229)(199,228)(200,227)(241,291)(242,295)(243,294)(244,293)
(245,292)(246,296)(247,300)(248,299)(249,298)(250,297)(251,281)(252,285)
(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)(260,287)
(261,301)(262,305)(263,304)(264,303)(265,302)(266,306)(267,310)(268,309)
(269,308)(270,307)(271,311)(272,315)(273,314)(274,313)(275,312)(276,316)
(277,320)(278,319)(279,318)(280,317)(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)
(341,431)(342,435)(343,434)(344,433)(345,432)(346,436)(347,440)(348,439)
(349,438)(350,437)(351,421)(352,425)(353,424)(354,423)(355,422)(356,426)
(357,430)(358,429)(359,428)(360,427)(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)
(381,471)(382,475)(383,474)(384,473)(385,472)(386,476)(387,480)(388,479)
(389,478)(390,477)(391,461)(392,465)(393,464)(394,463)(395,462)(396,466)
(397,470)(398,469)(399,468)(400,467)(481,626)(482,630)(483,629)(484,628)
(485,627)(486,621)(487,625)(488,624)(489,623)(490,622)(491,636)(492,640)
(493,639)(494,638)(495,637)(496,631)(497,635)(498,634)(499,633)(500,632)
(501,611)(502,615)(503,614)(504,613)(505,612)(506,616)(507,620)(508,619)
(509,618)(510,617)(511,601)(512,605)(513,604)(514,603)(515,602)(516,606)
(517,610)(518,609)(519,608)(520,607)(521,581)(522,585)(523,584)(524,583)
(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)(532,595)
(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)(540,597)
(541,576)(542,580)(543,579)(544,578)(545,577)(546,571)(547,575)(548,574)
(549,573)(550,572)(551,566)(552,570)(553,569)(554,568)(555,567)(556,561)
(557,565)(558,564)(559,563)(560,562);;
s2 := ( 1,163)( 2,162)( 3,161)( 4,165)( 5,164)( 6,168)( 7,167)( 8,166)
( 9,170)( 10,169)( 11,178)( 12,177)( 13,176)( 14,180)( 15,179)( 16,173)
( 17,172)( 18,171)( 19,175)( 20,174)( 21,188)( 22,187)( 23,186)( 24,190)
( 25,189)( 26,183)( 27,182)( 28,181)( 29,185)( 30,184)( 31,193)( 32,192)
( 33,191)( 34,195)( 35,194)( 36,198)( 37,197)( 38,196)( 39,200)( 40,199)
( 41,203)( 42,202)( 43,201)( 44,205)( 45,204)( 46,208)( 47,207)( 48,206)
( 49,210)( 50,209)( 51,218)( 52,217)( 53,216)( 54,220)( 55,219)( 56,213)
( 57,212)( 58,211)( 59,215)( 60,214)( 61,228)( 62,227)( 63,226)( 64,230)
( 65,229)( 66,223)( 67,222)( 68,221)( 69,225)( 70,224)( 71,233)( 72,232)
( 73,231)( 74,235)( 75,234)( 76,238)( 77,237)( 78,236)( 79,240)( 80,239)
( 81,263)( 82,262)( 83,261)( 84,265)( 85,264)( 86,268)( 87,267)( 88,266)
( 89,270)( 90,269)( 91,278)( 92,277)( 93,276)( 94,280)( 95,279)( 96,273)
( 97,272)( 98,271)( 99,275)(100,274)(101,243)(102,242)(103,241)(104,245)
(105,244)(106,248)(107,247)(108,246)(109,250)(110,249)(111,258)(112,257)
(113,256)(114,260)(115,259)(116,253)(117,252)(118,251)(119,255)(120,254)
(121,308)(122,307)(123,306)(124,310)(125,309)(126,303)(127,302)(128,301)
(129,305)(130,304)(131,313)(132,312)(133,311)(134,315)(135,314)(136,318)
(137,317)(138,316)(139,320)(140,319)(141,288)(142,287)(143,286)(144,290)
(145,289)(146,283)(147,282)(148,281)(149,285)(150,284)(151,293)(152,292)
(153,291)(154,295)(155,294)(156,298)(157,297)(158,296)(159,300)(160,299)
(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)(328,486)
(329,490)(330,489)(331,498)(332,497)(333,496)(334,500)(335,499)(336,493)
(337,492)(338,491)(339,495)(340,494)(341,508)(342,507)(343,506)(344,510)
(345,509)(346,503)(347,502)(348,501)(349,505)(350,504)(351,513)(352,512)
(353,511)(354,515)(355,514)(356,518)(357,517)(358,516)(359,520)(360,519)
(361,523)(362,522)(363,521)(364,525)(365,524)(366,528)(367,527)(368,526)
(369,530)(370,529)(371,538)(372,537)(373,536)(374,540)(375,539)(376,533)
(377,532)(378,531)(379,535)(380,534)(381,548)(382,547)(383,546)(384,550)
(385,549)(386,543)(387,542)(388,541)(389,545)(390,544)(391,553)(392,552)
(393,551)(394,555)(395,554)(396,558)(397,557)(398,556)(399,560)(400,559)
(401,583)(402,582)(403,581)(404,585)(405,584)(406,588)(407,587)(408,586)
(409,590)(410,589)(411,598)(412,597)(413,596)(414,600)(415,599)(416,593)
(417,592)(418,591)(419,595)(420,594)(421,563)(422,562)(423,561)(424,565)
(425,564)(426,568)(427,567)(428,566)(429,570)(430,569)(431,578)(432,577)
(433,576)(434,580)(435,579)(436,573)(437,572)(438,571)(439,575)(440,574)
(441,628)(442,627)(443,626)(444,630)(445,629)(446,623)(447,622)(448,621)
(449,625)(450,624)(451,633)(452,632)(453,631)(454,635)(455,634)(456,638)
(457,637)(458,636)(459,640)(460,639)(461,608)(462,607)(463,606)(464,610)
(465,609)(466,603)(467,602)(468,601)(469,605)(470,604)(471,613)(472,612)
(473,611)(474,615)(475,614)(476,618)(477,617)(478,616)(479,620)(480,619);;
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*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(640)!( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)
( 8,488)( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)
( 24,509)( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,516)
( 32,517)( 33,518)( 34,519)( 35,520)( 36,511)( 37,512)( 38,513)( 39,514)
( 40,515)( 41,556)( 42,557)( 43,558)( 44,559)( 45,560)( 46,551)( 47,552)
( 48,553)( 49,554)( 50,555)( 51,546)( 52,547)( 53,548)( 54,549)( 55,550)
( 56,541)( 57,542)( 58,543)( 59,544)( 60,545)( 61,536)( 62,537)( 63,538)
( 64,539)( 65,540)( 66,531)( 67,532)( 68,533)( 69,534)( 70,535)( 71,526)
( 72,527)( 73,528)( 74,529)( 75,530)( 76,521)( 77,522)( 78,523)( 79,524)
( 80,525)( 81,586)( 82,587)( 83,588)( 84,589)( 85,590)( 86,581)( 87,582)
( 88,583)( 89,584)( 90,585)( 91,596)( 92,597)( 93,598)( 94,599)( 95,600)
( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,566)(102,567)(103,568)
(104,569)(105,570)(106,561)(107,562)(108,563)(109,564)(110,565)(111,576)
(112,577)(113,578)(114,579)(115,580)(116,571)(117,572)(118,573)(119,574)
(120,575)(121,611)(122,612)(123,613)(124,614)(125,615)(126,616)(127,617)
(128,618)(129,619)(130,620)(131,601)(132,602)(133,603)(134,604)(135,605)
(136,606)(137,607)(138,608)(139,609)(140,610)(141,636)(142,637)(143,638)
(144,639)(145,640)(146,631)(147,632)(148,633)(149,634)(150,635)(151,626)
(152,627)(153,628)(154,629)(155,630)(156,621)(157,622)(158,623)(159,624)
(160,625)(161,321)(162,322)(163,323)(164,324)(165,325)(166,326)(167,327)
(168,328)(169,329)(170,330)(171,331)(172,332)(173,333)(174,334)(175,335)
(176,336)(177,337)(178,338)(179,339)(180,340)(181,346)(182,347)(183,348)
(184,349)(185,350)(186,341)(187,342)(188,343)(189,344)(190,345)(191,356)
(192,357)(193,358)(194,359)(195,360)(196,351)(197,352)(198,353)(199,354)
(200,355)(201,396)(202,397)(203,398)(204,399)(205,400)(206,391)(207,392)
(208,393)(209,394)(210,395)(211,386)(212,387)(213,388)(214,389)(215,390)
(216,381)(217,382)(218,383)(219,384)(220,385)(221,376)(222,377)(223,378)
(224,379)(225,380)(226,371)(227,372)(228,373)(229,374)(230,375)(231,366)
(232,367)(233,368)(234,369)(235,370)(236,361)(237,362)(238,363)(239,364)
(240,365)(241,426)(242,427)(243,428)(244,429)(245,430)(246,421)(247,422)
(248,423)(249,424)(250,425)(251,436)(252,437)(253,438)(254,439)(255,440)
(256,431)(257,432)(258,433)(259,434)(260,435)(261,406)(262,407)(263,408)
(264,409)(265,410)(266,401)(267,402)(268,403)(269,404)(270,405)(271,416)
(272,417)(273,418)(274,419)(275,420)(276,411)(277,412)(278,413)(279,414)
(280,415)(281,451)(282,452)(283,453)(284,454)(285,455)(286,456)(287,457)
(288,458)(289,459)(290,460)(291,441)(292,442)(293,443)(294,444)(295,445)
(296,446)(297,447)(298,448)(299,449)(300,450)(301,476)(302,477)(303,478)
(304,479)(305,480)(306,471)(307,472)(308,473)(309,474)(310,475)(311,466)
(312,467)(313,468)(314,469)(315,470)(316,461)(317,462)(318,463)(319,464)
(320,465);
s1 := Sym(640)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)
( 28, 39)( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)
( 53, 54)( 57, 60)( 58, 59)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)
( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81, 86)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)( 91, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)(101,116)
(102,120)(103,119)(104,118)(105,117)(106,111)(107,115)(108,114)(109,113)
(110,112)(121,126)(122,130)(123,129)(124,128)(125,127)(131,136)(132,140)
(133,139)(134,138)(135,137)(141,156)(142,160)(143,159)(144,158)(145,157)
(146,151)(147,155)(148,154)(149,153)(150,152)(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)(181,231)(182,235)(183,234)(184,233)(185,232)(186,236)(187,240)
(188,239)(189,238)(190,237)(191,221)(192,225)(193,224)(194,223)(195,222)
(196,226)(197,230)(198,229)(199,228)(200,227)(241,291)(242,295)(243,294)
(244,293)(245,292)(246,296)(247,300)(248,299)(249,298)(250,297)(251,281)
(252,285)(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)
(260,287)(261,301)(262,305)(263,304)(264,303)(265,302)(266,306)(267,310)
(268,309)(269,308)(270,307)(271,311)(272,315)(273,314)(274,313)(275,312)
(276,316)(277,320)(278,319)(279,318)(280,317)(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)(341,431)(342,435)(343,434)(344,433)(345,432)(346,436)(347,440)
(348,439)(349,438)(350,437)(351,421)(352,425)(353,424)(354,423)(355,422)
(356,426)(357,430)(358,429)(359,428)(360,427)(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)(381,471)(382,475)(383,474)(384,473)(385,472)(386,476)(387,480)
(388,479)(389,478)(390,477)(391,461)(392,465)(393,464)(394,463)(395,462)
(396,466)(397,470)(398,469)(399,468)(400,467)(481,626)(482,630)(483,629)
(484,628)(485,627)(486,621)(487,625)(488,624)(489,623)(490,622)(491,636)
(492,640)(493,639)(494,638)(495,637)(496,631)(497,635)(498,634)(499,633)
(500,632)(501,611)(502,615)(503,614)(504,613)(505,612)(506,616)(507,620)
(508,619)(509,618)(510,617)(511,601)(512,605)(513,604)(514,603)(515,602)
(516,606)(517,610)(518,609)(519,608)(520,607)(521,581)(522,585)(523,584)
(524,583)(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)
(532,595)(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)
(540,597)(541,576)(542,580)(543,579)(544,578)(545,577)(546,571)(547,575)
(548,574)(549,573)(550,572)(551,566)(552,570)(553,569)(554,568)(555,567)
(556,561)(557,565)(558,564)(559,563)(560,562);
s2 := Sym(640)!( 1,163)( 2,162)( 3,161)( 4,165)( 5,164)( 6,168)( 7,167)
( 8,166)( 9,170)( 10,169)( 11,178)( 12,177)( 13,176)( 14,180)( 15,179)
( 16,173)( 17,172)( 18,171)( 19,175)( 20,174)( 21,188)( 22,187)( 23,186)
( 24,190)( 25,189)( 26,183)( 27,182)( 28,181)( 29,185)( 30,184)( 31,193)
( 32,192)( 33,191)( 34,195)( 35,194)( 36,198)( 37,197)( 38,196)( 39,200)
( 40,199)( 41,203)( 42,202)( 43,201)( 44,205)( 45,204)( 46,208)( 47,207)
( 48,206)( 49,210)( 50,209)( 51,218)( 52,217)( 53,216)( 54,220)( 55,219)
( 56,213)( 57,212)( 58,211)( 59,215)( 60,214)( 61,228)( 62,227)( 63,226)
( 64,230)( 65,229)( 66,223)( 67,222)( 68,221)( 69,225)( 70,224)( 71,233)
( 72,232)( 73,231)( 74,235)( 75,234)( 76,238)( 77,237)( 78,236)( 79,240)
( 80,239)( 81,263)( 82,262)( 83,261)( 84,265)( 85,264)( 86,268)( 87,267)
( 88,266)( 89,270)( 90,269)( 91,278)( 92,277)( 93,276)( 94,280)( 95,279)
( 96,273)( 97,272)( 98,271)( 99,275)(100,274)(101,243)(102,242)(103,241)
(104,245)(105,244)(106,248)(107,247)(108,246)(109,250)(110,249)(111,258)
(112,257)(113,256)(114,260)(115,259)(116,253)(117,252)(118,251)(119,255)
(120,254)(121,308)(122,307)(123,306)(124,310)(125,309)(126,303)(127,302)
(128,301)(129,305)(130,304)(131,313)(132,312)(133,311)(134,315)(135,314)
(136,318)(137,317)(138,316)(139,320)(140,319)(141,288)(142,287)(143,286)
(144,290)(145,289)(146,283)(147,282)(148,281)(149,285)(150,284)(151,293)
(152,292)(153,291)(154,295)(155,294)(156,298)(157,297)(158,296)(159,300)
(160,299)(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)
(328,486)(329,490)(330,489)(331,498)(332,497)(333,496)(334,500)(335,499)
(336,493)(337,492)(338,491)(339,495)(340,494)(341,508)(342,507)(343,506)
(344,510)(345,509)(346,503)(347,502)(348,501)(349,505)(350,504)(351,513)
(352,512)(353,511)(354,515)(355,514)(356,518)(357,517)(358,516)(359,520)
(360,519)(361,523)(362,522)(363,521)(364,525)(365,524)(366,528)(367,527)
(368,526)(369,530)(370,529)(371,538)(372,537)(373,536)(374,540)(375,539)
(376,533)(377,532)(378,531)(379,535)(380,534)(381,548)(382,547)(383,546)
(384,550)(385,549)(386,543)(387,542)(388,541)(389,545)(390,544)(391,553)
(392,552)(393,551)(394,555)(395,554)(396,558)(397,557)(398,556)(399,560)
(400,559)(401,583)(402,582)(403,581)(404,585)(405,584)(406,588)(407,587)
(408,586)(409,590)(410,589)(411,598)(412,597)(413,596)(414,600)(415,599)
(416,593)(417,592)(418,591)(419,595)(420,594)(421,563)(422,562)(423,561)
(424,565)(425,564)(426,568)(427,567)(428,566)(429,570)(430,569)(431,578)
(432,577)(433,576)(434,580)(435,579)(436,573)(437,572)(438,571)(439,575)
(440,574)(441,628)(442,627)(443,626)(444,630)(445,629)(446,623)(447,622)
(448,621)(449,625)(450,624)(451,633)(452,632)(453,631)(454,635)(455,634)
(456,638)(457,637)(458,636)(459,640)(460,639)(461,608)(462,607)(463,606)
(464,610)(465,609)(466,603)(467,602)(468,601)(469,605)(470,604)(471,613)
(472,612)(473,611)(474,615)(475,614)(476,618)(477,617)(478,616)(479,620)
(480,619);
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*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*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 >;
References : None.
to this polytope