Polytope of Type {40,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,8}*1280h
if this polytope has a name.
Group : SmallGroup(1280,90329)
Rank : 3
Schlafli Type : {40,8}
Number of vertices, edges, etc : 80, 320, 16
Order of s0s1s2 : 40
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
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 : {20,8}*640b
4-fold quotients : {20,4}*320
5-fold quotients : {8,8}*256g
8-fold quotients : {20,4}*160
10-fold quotients : {4,8}*128b
16-fold quotients : {20,2}*80, {10,4}*80
20-fold quotients : {4,4}*64
32-fold quotients : {10,2}*40
40-fold quotients : {4,4}*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)( 11,336)( 12,340)( 13,339)( 14,338)( 15,337)( 16,331)
( 17,335)( 18,334)( 19,333)( 20,332)( 21,341)( 22,345)( 23,344)( 24,343)
( 25,342)( 26,346)( 27,350)( 28,349)( 29,348)( 30,347)( 31,356)( 32,360)
( 33,359)( 34,358)( 35,357)( 36,351)( 37,355)( 38,354)( 39,353)( 40,352)
( 41,396)( 42,400)( 43,399)( 44,398)( 45,397)( 46,391)( 47,395)( 48,394)
( 49,393)( 50,392)( 51,381)( 52,385)( 53,384)( 54,383)( 55,382)( 56,386)
( 57,390)( 58,389)( 59,388)( 60,387)( 61,371)( 62,375)( 63,374)( 64,373)
( 65,372)( 66,376)( 67,380)( 68,379)( 69,378)( 70,377)( 71,366)( 72,370)
( 73,369)( 74,368)( 75,367)( 76,361)( 77,365)( 78,364)( 79,363)( 80,362)
( 81,406)( 82,410)( 83,409)( 84,408)( 85,407)( 86,401)( 87,405)( 88,404)
( 89,403)( 90,402)( 91,411)( 92,415)( 93,414)( 94,413)( 95,412)( 96,416)
( 97,420)( 98,419)( 99,418)(100,417)(101,426)(102,430)(103,429)(104,428)
(105,427)(106,421)(107,425)(108,424)(109,423)(110,422)(111,431)(112,435)
(113,434)(114,433)(115,432)(116,436)(117,440)(118,439)(119,438)(120,437)
(121,471)(122,475)(123,474)(124,473)(125,472)(126,476)(127,480)(128,479)
(129,478)(130,477)(131,466)(132,470)(133,469)(134,468)(135,467)(136,461)
(137,465)(138,464)(139,463)(140,462)(141,456)(142,460)(143,459)(144,458)
(145,457)(146,451)(147,455)(148,454)(149,453)(150,452)(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)(171,496)(172,500)(173,499)(174,498)(175,497)(176,491)
(177,495)(178,494)(179,493)(180,492)(181,501)(182,505)(183,504)(184,503)
(185,502)(186,506)(187,510)(188,509)(189,508)(190,507)(191,516)(192,520)
(193,519)(194,518)(195,517)(196,511)(197,515)(198,514)(199,513)(200,512)
(201,556)(202,560)(203,559)(204,558)(205,557)(206,551)(207,555)(208,554)
(209,553)(210,552)(211,541)(212,545)(213,544)(214,543)(215,542)(216,546)
(217,550)(218,549)(219,548)(220,547)(221,531)(222,535)(223,534)(224,533)
(225,532)(226,536)(227,540)(228,539)(229,538)(230,537)(231,526)(232,530)
(233,529)(234,528)(235,527)(236,521)(237,525)(238,524)(239,523)(240,522)
(241,566)(242,570)(243,569)(244,568)(245,567)(246,561)(247,565)(248,564)
(249,563)(250,562)(251,571)(252,575)(253,574)(254,573)(255,572)(256,576)
(257,580)(258,579)(259,578)(260,577)(261,586)(262,590)(263,589)(264,588)
(265,587)(266,581)(267,585)(268,584)(269,583)(270,582)(271,591)(272,595)
(273,594)(274,593)(275,592)(276,596)(277,600)(278,599)(279,598)(280,597)
(281,631)(282,635)(283,634)(284,633)(285,632)(286,636)(287,640)(288,639)
(289,638)(290,637)(291,626)(292,630)(293,629)(294,628)(295,627)(296,621)
(297,625)(298,624)(299,623)(300,622)(301,616)(302,620)(303,619)(304,618)
(305,617)(306,611)(307,615)(308,614)(309,613)(310,612)(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, 33)( 22, 32)( 23, 31)( 24, 35)( 25, 34)( 26, 38)( 27, 37)( 28, 36)
( 29, 40)( 30, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 58)
( 52, 57)( 53, 56)( 54, 60)( 55, 59)( 61, 78)( 62, 77)( 63, 76)( 64, 80)
( 65, 79)( 66, 73)( 67, 72)( 68, 71)( 69, 75)( 70, 74)( 81, 88)( 82, 87)
( 83, 86)( 84, 90)( 85, 89)( 91, 98)( 92, 97)( 93, 96)( 94,100)( 95, 99)
(101,118)(102,117)(103,116)(104,120)(105,119)(106,113)(107,112)(108,111)
(109,115)(110,114)(121,123)(124,125)(126,128)(129,130)(131,133)(134,135)
(136,138)(139,140)(141,153)(142,152)(143,151)(144,155)(145,154)(146,158)
(147,157)(148,156)(149,160)(150,159)(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)
(181,233)(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)(241,293)(242,292)(243,291)(244,295)
(245,294)(246,298)(247,297)(248,296)(249,300)(250,299)(251,283)(252,282)
(253,281)(254,285)(255,284)(256,288)(257,287)(258,286)(259,290)(260,289)
(261,303)(262,302)(263,301)(264,305)(265,304)(266,308)(267,307)(268,306)
(269,310)(270,309)(271,313)(272,312)(273,311)(274,315)(275,314)(276,318)
(277,317)(278,316)(279,320)(280,319)(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)
(341,433)(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)(361,448)(362,447)(363,446)(364,450)
(365,449)(366,443)(367,442)(368,441)(369,445)(370,444)(371,458)(372,457)
(373,456)(374,460)(375,459)(376,453)(377,452)(378,451)(379,455)(380,454)
(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)(481,628)(482,627)(483,626)(484,630)
(485,629)(486,623)(487,622)(488,621)(489,625)(490,624)(491,638)(492,637)
(493,636)(494,640)(495,639)(496,633)(497,632)(498,631)(499,635)(500,634)
(501,613)(502,612)(503,611)(504,615)(505,614)(506,618)(507,617)(508,616)
(509,620)(510,619)(511,603)(512,602)(513,601)(514,605)(515,604)(516,608)
(517,607)(518,606)(519,610)(520,609)(521,583)(522,582)(523,581)(524,585)
(525,584)(526,588)(527,587)(528,586)(529,590)(530,589)(531,593)(532,592)
(533,591)(534,595)(535,594)(536,598)(537,597)(538,596)(539,600)(540,599)
(541,578)(542,577)(543,576)(544,580)(545,579)(546,573)(547,572)(548,571)
(549,575)(550,574)(551,568)(552,567)(553,566)(554,570)(555,569)(556,563)
(557,562)(558,561)(559,565)(560,564);;
s2 := ( 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)
( 41,551)( 42,552)( 43,553)( 44,554)( 45,555)( 46,556)( 47,557)( 48,558)
( 49,559)( 50,560)( 51,541)( 52,542)( 53,543)( 54,544)( 55,545)( 56,546)
( 57,547)( 58,548)( 59,549)( 60,550)( 61,531)( 62,532)( 63,533)( 64,534)
( 65,535)( 66,536)( 67,537)( 68,538)( 69,539)( 70,540)( 71,521)( 72,522)
( 73,523)( 74,524)( 75,525)( 76,526)( 77,527)( 78,528)( 79,529)( 80,530)
( 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)
(121,616)(122,617)(123,618)(124,619)(125,620)(126,611)(127,612)(128,613)
(129,614)(130,615)(131,606)(132,607)(133,608)(134,609)(135,610)(136,601)
(137,602)(138,603)(139,604)(140,605)(141,631)(142,632)(143,633)(144,634)
(145,635)(146,636)(147,637)(148,638)(149,639)(150,640)(151,621)(152,622)
(153,623)(154,624)(155,625)(156,626)(157,627)(158,628)(159,629)(160,630)
(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)
(201,391)(202,392)(203,393)(204,394)(205,395)(206,396)(207,397)(208,398)
(209,399)(210,400)(211,381)(212,382)(213,383)(214,384)(215,385)(216,386)
(217,387)(218,388)(219,389)(220,390)(221,371)(222,372)(223,373)(224,374)
(225,375)(226,376)(227,377)(228,378)(229,379)(230,380)(231,361)(232,362)
(233,363)(234,364)(235,365)(236,366)(237,367)(238,368)(239,369)(240,370)
(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)
(281,456)(282,457)(283,458)(284,459)(285,460)(286,451)(287,452)(288,453)
(289,454)(290,455)(291,446)(292,447)(293,448)(294,449)(295,450)(296,441)
(297,442)(298,443)(299,444)(300,445)(301,471)(302,472)(303,473)(304,474)
(305,475)(306,476)(307,477)(308,478)(309,479)(310,480)(311,461)(312,462)
(313,463)(314,464)(315,465)(316,466)(317,467)(318,468)(319,469)(320,470);;
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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)( 11,336)( 12,340)( 13,339)( 14,338)( 15,337)
( 16,331)( 17,335)( 18,334)( 19,333)( 20,332)( 21,341)( 22,345)( 23,344)
( 24,343)( 25,342)( 26,346)( 27,350)( 28,349)( 29,348)( 30,347)( 31,356)
( 32,360)( 33,359)( 34,358)( 35,357)( 36,351)( 37,355)( 38,354)( 39,353)
( 40,352)( 41,396)( 42,400)( 43,399)( 44,398)( 45,397)( 46,391)( 47,395)
( 48,394)( 49,393)( 50,392)( 51,381)( 52,385)( 53,384)( 54,383)( 55,382)
( 56,386)( 57,390)( 58,389)( 59,388)( 60,387)( 61,371)( 62,375)( 63,374)
( 64,373)( 65,372)( 66,376)( 67,380)( 68,379)( 69,378)( 70,377)( 71,366)
( 72,370)( 73,369)( 74,368)( 75,367)( 76,361)( 77,365)( 78,364)( 79,363)
( 80,362)( 81,406)( 82,410)( 83,409)( 84,408)( 85,407)( 86,401)( 87,405)
( 88,404)( 89,403)( 90,402)( 91,411)( 92,415)( 93,414)( 94,413)( 95,412)
( 96,416)( 97,420)( 98,419)( 99,418)(100,417)(101,426)(102,430)(103,429)
(104,428)(105,427)(106,421)(107,425)(108,424)(109,423)(110,422)(111,431)
(112,435)(113,434)(114,433)(115,432)(116,436)(117,440)(118,439)(119,438)
(120,437)(121,471)(122,475)(123,474)(124,473)(125,472)(126,476)(127,480)
(128,479)(129,478)(130,477)(131,466)(132,470)(133,469)(134,468)(135,467)
(136,461)(137,465)(138,464)(139,463)(140,462)(141,456)(142,460)(143,459)
(144,458)(145,457)(146,451)(147,455)(148,454)(149,453)(150,452)(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)(171,496)(172,500)(173,499)(174,498)(175,497)
(176,491)(177,495)(178,494)(179,493)(180,492)(181,501)(182,505)(183,504)
(184,503)(185,502)(186,506)(187,510)(188,509)(189,508)(190,507)(191,516)
(192,520)(193,519)(194,518)(195,517)(196,511)(197,515)(198,514)(199,513)
(200,512)(201,556)(202,560)(203,559)(204,558)(205,557)(206,551)(207,555)
(208,554)(209,553)(210,552)(211,541)(212,545)(213,544)(214,543)(215,542)
(216,546)(217,550)(218,549)(219,548)(220,547)(221,531)(222,535)(223,534)
(224,533)(225,532)(226,536)(227,540)(228,539)(229,538)(230,537)(231,526)
(232,530)(233,529)(234,528)(235,527)(236,521)(237,525)(238,524)(239,523)
(240,522)(241,566)(242,570)(243,569)(244,568)(245,567)(246,561)(247,565)
(248,564)(249,563)(250,562)(251,571)(252,575)(253,574)(254,573)(255,572)
(256,576)(257,580)(258,579)(259,578)(260,577)(261,586)(262,590)(263,589)
(264,588)(265,587)(266,581)(267,585)(268,584)(269,583)(270,582)(271,591)
(272,595)(273,594)(274,593)(275,592)(276,596)(277,600)(278,599)(279,598)
(280,597)(281,631)(282,635)(283,634)(284,633)(285,632)(286,636)(287,640)
(288,639)(289,638)(290,637)(291,626)(292,630)(293,629)(294,628)(295,627)
(296,621)(297,625)(298,624)(299,623)(300,622)(301,616)(302,620)(303,619)
(304,618)(305,617)(306,611)(307,615)(308,614)(309,613)(310,612)(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, 33)( 22, 32)( 23, 31)( 24, 35)( 25, 34)( 26, 38)( 27, 37)
( 28, 36)( 29, 40)( 30, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)
( 51, 58)( 52, 57)( 53, 56)( 54, 60)( 55, 59)( 61, 78)( 62, 77)( 63, 76)
( 64, 80)( 65, 79)( 66, 73)( 67, 72)( 68, 71)( 69, 75)( 70, 74)( 81, 88)
( 82, 87)( 83, 86)( 84, 90)( 85, 89)( 91, 98)( 92, 97)( 93, 96)( 94,100)
( 95, 99)(101,118)(102,117)(103,116)(104,120)(105,119)(106,113)(107,112)
(108,111)(109,115)(110,114)(121,123)(124,125)(126,128)(129,130)(131,133)
(134,135)(136,138)(139,140)(141,153)(142,152)(143,151)(144,155)(145,154)
(146,158)(147,157)(148,156)(149,160)(150,159)(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)(181,233)(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)(241,293)(242,292)(243,291)
(244,295)(245,294)(246,298)(247,297)(248,296)(249,300)(250,299)(251,283)
(252,282)(253,281)(254,285)(255,284)(256,288)(257,287)(258,286)(259,290)
(260,289)(261,303)(262,302)(263,301)(264,305)(265,304)(266,308)(267,307)
(268,306)(269,310)(270,309)(271,313)(272,312)(273,311)(274,315)(275,314)
(276,318)(277,317)(278,316)(279,320)(280,319)(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)(341,433)(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)(361,448)(362,447)(363,446)
(364,450)(365,449)(366,443)(367,442)(368,441)(369,445)(370,444)(371,458)
(372,457)(373,456)(374,460)(375,459)(376,453)(377,452)(378,451)(379,455)
(380,454)(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)(481,628)(482,627)(483,626)
(484,630)(485,629)(486,623)(487,622)(488,621)(489,625)(490,624)(491,638)
(492,637)(493,636)(494,640)(495,639)(496,633)(497,632)(498,631)(499,635)
(500,634)(501,613)(502,612)(503,611)(504,615)(505,614)(506,618)(507,617)
(508,616)(509,620)(510,619)(511,603)(512,602)(513,601)(514,605)(515,604)
(516,608)(517,607)(518,606)(519,610)(520,609)(521,583)(522,582)(523,581)
(524,585)(525,584)(526,588)(527,587)(528,586)(529,590)(530,589)(531,593)
(532,592)(533,591)(534,595)(535,594)(536,598)(537,597)(538,596)(539,600)
(540,599)(541,578)(542,577)(543,576)(544,580)(545,579)(546,573)(547,572)
(548,571)(549,575)(550,574)(551,568)(552,567)(553,566)(554,570)(555,569)
(556,563)(557,562)(558,561)(559,565)(560,564);
s2 := 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)( 41,551)( 42,552)( 43,553)( 44,554)( 45,555)( 46,556)( 47,557)
( 48,558)( 49,559)( 50,560)( 51,541)( 52,542)( 53,543)( 54,544)( 55,545)
( 56,546)( 57,547)( 58,548)( 59,549)( 60,550)( 61,531)( 62,532)( 63,533)
( 64,534)( 65,535)( 66,536)( 67,537)( 68,538)( 69,539)( 70,540)( 71,521)
( 72,522)( 73,523)( 74,524)( 75,525)( 76,526)( 77,527)( 78,528)( 79,529)
( 80,530)( 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)(121,616)(122,617)(123,618)(124,619)(125,620)(126,611)(127,612)
(128,613)(129,614)(130,615)(131,606)(132,607)(133,608)(134,609)(135,610)
(136,601)(137,602)(138,603)(139,604)(140,605)(141,631)(142,632)(143,633)
(144,634)(145,635)(146,636)(147,637)(148,638)(149,639)(150,640)(151,621)
(152,622)(153,623)(154,624)(155,625)(156,626)(157,627)(158,628)(159,629)
(160,630)(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)(201,391)(202,392)(203,393)(204,394)(205,395)(206,396)(207,397)
(208,398)(209,399)(210,400)(211,381)(212,382)(213,383)(214,384)(215,385)
(216,386)(217,387)(218,388)(219,389)(220,390)(221,371)(222,372)(223,373)
(224,374)(225,375)(226,376)(227,377)(228,378)(229,379)(230,380)(231,361)
(232,362)(233,363)(234,364)(235,365)(236,366)(237,367)(238,368)(239,369)
(240,370)(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)(281,456)(282,457)(283,458)(284,459)(285,460)(286,451)(287,452)
(288,453)(289,454)(290,455)(291,446)(292,447)(293,448)(294,449)(295,450)
(296,441)(297,442)(298,443)(299,444)(300,445)(301,471)(302,472)(303,473)
(304,474)(305,475)(306,476)(307,477)(308,478)(309,479)(310,480)(311,461)
(312,462)(313,463)(314,464)(315,465)(316,466)(317,467)(318,468)(319,469)
(320,470);
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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