Polytope of Type {40,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,8}*1280f
if this polytope has a name.
Group : SmallGroup(1280,90303)
Rank : 3
Schlafli Type : {40,8}
Number of vertices, edges, etc : 80, 320, 16
Order of s0s1s2 : 20
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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}*256e
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, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 53)( 54, 55)
( 56, 58)( 59, 60)( 61, 73)( 62, 72)( 63, 71)( 64, 75)( 65, 74)( 66, 78)
( 67, 77)( 68, 76)( 69, 80)( 70, 79)( 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)
(121,128)(122,127)(123,126)(124,130)(125,129)(131,138)(132,137)(133,136)
(134,140)(135,139)(141,158)(142,157)(143,156)(144,160)(145,159)(146,153)
(147,152)(148,151)(149,155)(150,154)(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)(361,443)(362,442)(363,441)(364,445)
(365,444)(366,448)(367,447)(368,446)(369,450)(370,449)(371,453)(372,452)
(373,451)(374,455)(375,454)(376,458)(377,457)(378,456)(379,460)(380,459)
(381,473)(382,472)(383,471)(384,475)(385,474)(386,478)(387,477)(388,476)
(389,480)(390,479)(391,463)(392,462)(393,461)(394,465)(395,464)(396,468)
(397,467)(398,466)(399,470)(400,469)(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)
( 41,556)( 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);;
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*s0*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*s0*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0 ];;
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, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 53)
( 54, 55)( 56, 58)( 59, 60)( 61, 73)( 62, 72)( 63, 71)( 64, 75)( 65, 74)
( 66, 78)( 67, 77)( 68, 76)( 69, 80)( 70, 79)( 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)(121,128)(122,127)(123,126)(124,130)(125,129)(131,138)(132,137)
(133,136)(134,140)(135,139)(141,158)(142,157)(143,156)(144,160)(145,159)
(146,153)(147,152)(148,151)(149,155)(150,154)(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)(361,443)(362,442)(363,441)
(364,445)(365,444)(366,448)(367,447)(368,446)(369,450)(370,449)(371,453)
(372,452)(373,451)(374,455)(375,454)(376,458)(377,457)(378,456)(379,460)
(380,459)(381,473)(382,472)(383,471)(384,475)(385,474)(386,478)(387,477)
(388,476)(389,480)(390,479)(391,463)(392,462)(393,461)(394,465)(395,464)
(396,468)(397,467)(398,466)(399,470)(400,469)(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)( 41,556)( 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);
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*s0*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*s0*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0 >;
References : None.
to this polytope