Polytope of Type {40,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,8}*1280g
if this polytope has a name.
Group : SmallGroup(1280,90328)
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
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 : {40,4}*640b
4-fold quotients : {20,4}*320
5-fold quotients : {8,8}*256h
8-fold quotients : {20,4}*160
10-fold quotients : {8,4}*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 := ( 1,481)( 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)
( 41,551)( 42,555)( 43,554)( 44,553)( 45,552)( 46,556)( 47,560)( 48,559)
( 49,558)( 50,557)( 51,541)( 52,545)( 53,544)( 54,543)( 55,542)( 56,546)
( 57,550)( 58,549)( 59,548)( 60,547)( 61,531)( 62,535)( 63,534)( 64,533)
( 65,532)( 66,536)( 67,540)( 68,539)( 69,538)( 70,537)( 71,521)( 72,525)
( 73,524)( 74,523)( 75,522)( 76,526)( 77,530)( 78,529)( 79,528)( 80,527)
( 81,586)( 82,590)( 83,589)( 84,588)( 85,587)( 86,581)( 87,585)( 88,584)
( 89,583)( 90,582)( 91,596)( 92,600)( 93,599)( 94,598)( 95,597)( 96,591)
( 97,595)( 98,594)( 99,593)(100,592)(101,566)(102,570)(103,569)(104,568)
(105,567)(106,561)(107,565)(108,564)(109,563)(110,562)(111,576)(112,580)
(113,579)(114,578)(115,577)(116,571)(117,575)(118,574)(119,573)(120,572)
(121,616)(122,620)(123,619)(124,618)(125,617)(126,611)(127,615)(128,614)
(129,613)(130,612)(131,606)(132,610)(133,609)(134,608)(135,607)(136,601)
(137,605)(138,604)(139,603)(140,602)(141,631)(142,635)(143,634)(144,633)
(145,632)(146,636)(147,640)(148,639)(149,638)(150,637)(151,621)(152,625)
(153,624)(154,623)(155,622)(156,626)(157,630)(158,629)(159,628)(160,627)
(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)
(201,391)(202,395)(203,394)(204,393)(205,392)(206,396)(207,400)(208,399)
(209,398)(210,397)(211,381)(212,385)(213,384)(214,383)(215,382)(216,386)
(217,390)(218,389)(219,388)(220,387)(221,371)(222,375)(223,374)(224,373)
(225,372)(226,376)(227,380)(228,379)(229,378)(230,377)(231,361)(232,365)
(233,364)(234,363)(235,362)(236,366)(237,370)(238,369)(239,368)(240,367)
(241,426)(242,430)(243,429)(244,428)(245,427)(246,421)(247,425)(248,424)
(249,423)(250,422)(251,436)(252,440)(253,439)(254,438)(255,437)(256,431)
(257,435)(258,434)(259,433)(260,432)(261,406)(262,410)(263,409)(264,408)
(265,407)(266,401)(267,405)(268,404)(269,403)(270,402)(271,416)(272,420)
(273,419)(274,418)(275,417)(276,411)(277,415)(278,414)(279,413)(280,412)
(281,456)(282,460)(283,459)(284,458)(285,457)(286,451)(287,455)(288,454)
(289,453)(290,452)(291,446)(292,450)(293,449)(294,448)(295,447)(296,441)
(297,445)(298,444)(299,443)(300,442)(301,471)(302,475)(303,474)(304,473)
(305,472)(306,476)(307,480)(308,479)(309,478)(310,477)(311,461)(312,465)
(313,464)(314,463)(315,462)(316,466)(317,470)(318,469)(319,468)(320,467);;
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 := ( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)( 8,328)
( 9,329)( 10,330)( 11,336)( 12,337)( 13,338)( 14,339)( 15,340)( 16,331)
( 17,332)( 18,333)( 19,334)( 20,335)( 21,341)( 22,342)( 23,343)( 24,344)
( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,356)( 32,357)
( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)( 40,355)
( 41,396)( 42,397)( 43,398)( 44,399)( 45,400)( 46,391)( 47,392)( 48,393)
( 49,394)( 50,395)( 51,381)( 52,382)( 53,383)( 54,384)( 55,385)( 56,386)
( 57,387)( 58,388)( 59,389)( 60,390)( 61,371)( 62,372)( 63,373)( 64,374)
( 65,375)( 66,376)( 67,377)( 68,378)( 69,379)( 70,380)( 71,366)( 72,367)
( 73,368)( 74,369)( 75,370)( 76,361)( 77,362)( 78,363)( 79,364)( 80,365)
( 81,406)( 82,407)( 83,408)( 84,409)( 85,410)( 86,401)( 87,402)( 88,403)
( 89,404)( 90,405)( 91,411)( 92,412)( 93,413)( 94,414)( 95,415)( 96,416)
( 97,417)( 98,418)( 99,419)(100,420)(101,426)(102,427)(103,428)(104,429)
(105,430)(106,421)(107,422)(108,423)(109,424)(110,425)(111,431)(112,432)
(113,433)(114,434)(115,435)(116,436)(117,437)(118,438)(119,439)(120,440)
(121,471)(122,472)(123,473)(124,474)(125,475)(126,476)(127,477)(128,478)
(129,479)(130,480)(131,466)(132,467)(133,468)(134,469)(135,470)(136,461)
(137,462)(138,463)(139,464)(140,465)(141,456)(142,457)(143,458)(144,459)
(145,460)(146,451)(147,452)(148,453)(149,454)(150,455)(151,441)(152,442)
(153,443)(154,444)(155,445)(156,446)(157,447)(158,448)(159,449)(160,450)
(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)
(169,489)(170,490)(171,496)(172,497)(173,498)(174,499)(175,500)(176,491)
(177,492)(178,493)(179,494)(180,495)(181,501)(182,502)(183,503)(184,504)
(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,516)(192,517)
(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)(200,515)
(201,556)(202,557)(203,558)(204,559)(205,560)(206,551)(207,552)(208,553)
(209,554)(210,555)(211,541)(212,542)(213,543)(214,544)(215,545)(216,546)
(217,547)(218,548)(219,549)(220,550)(221,531)(222,532)(223,533)(224,534)
(225,535)(226,536)(227,537)(228,538)(229,539)(230,540)(231,526)(232,527)
(233,528)(234,529)(235,530)(236,521)(237,522)(238,523)(239,524)(240,525)
(241,566)(242,567)(243,568)(244,569)(245,570)(246,561)(247,562)(248,563)
(249,564)(250,565)(251,571)(252,572)(253,573)(254,574)(255,575)(256,576)
(257,577)(258,578)(259,579)(260,580)(261,586)(262,587)(263,588)(264,589)
(265,590)(266,581)(267,582)(268,583)(269,584)(270,585)(271,591)(272,592)
(273,593)(274,594)(275,595)(276,596)(277,597)(278,598)(279,599)(280,600)
(281,631)(282,632)(283,633)(284,634)(285,635)(286,636)(287,637)(288,638)
(289,639)(290,640)(291,626)(292,627)(293,628)(294,629)(295,630)(296,621)
(297,622)(298,623)(299,624)(300,625)(301,616)(302,617)(303,618)(304,619)
(305,620)(306,611)(307,612)(308,613)(309,614)(310,615)(311,601)(312,602)
(313,603)(314,604)(315,605)(316,606)(317,607)(318,608)(319,609)(320,610);;
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*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*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*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)( 41,551)( 42,555)( 43,554)( 44,553)( 45,552)( 46,556)( 47,560)
( 48,559)( 49,558)( 50,557)( 51,541)( 52,545)( 53,544)( 54,543)( 55,542)
( 56,546)( 57,550)( 58,549)( 59,548)( 60,547)( 61,531)( 62,535)( 63,534)
( 64,533)( 65,532)( 66,536)( 67,540)( 68,539)( 69,538)( 70,537)( 71,521)
( 72,525)( 73,524)( 74,523)( 75,522)( 76,526)( 77,530)( 78,529)( 79,528)
( 80,527)( 81,586)( 82,590)( 83,589)( 84,588)( 85,587)( 86,581)( 87,585)
( 88,584)( 89,583)( 90,582)( 91,596)( 92,600)( 93,599)( 94,598)( 95,597)
( 96,591)( 97,595)( 98,594)( 99,593)(100,592)(101,566)(102,570)(103,569)
(104,568)(105,567)(106,561)(107,565)(108,564)(109,563)(110,562)(111,576)
(112,580)(113,579)(114,578)(115,577)(116,571)(117,575)(118,574)(119,573)
(120,572)(121,616)(122,620)(123,619)(124,618)(125,617)(126,611)(127,615)
(128,614)(129,613)(130,612)(131,606)(132,610)(133,609)(134,608)(135,607)
(136,601)(137,605)(138,604)(139,603)(140,602)(141,631)(142,635)(143,634)
(144,633)(145,632)(146,636)(147,640)(148,639)(149,638)(150,637)(151,621)
(152,625)(153,624)(154,623)(155,622)(156,626)(157,630)(158,629)(159,628)
(160,627)(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)(201,391)(202,395)(203,394)(204,393)(205,392)(206,396)(207,400)
(208,399)(209,398)(210,397)(211,381)(212,385)(213,384)(214,383)(215,382)
(216,386)(217,390)(218,389)(219,388)(220,387)(221,371)(222,375)(223,374)
(224,373)(225,372)(226,376)(227,380)(228,379)(229,378)(230,377)(231,361)
(232,365)(233,364)(234,363)(235,362)(236,366)(237,370)(238,369)(239,368)
(240,367)(241,426)(242,430)(243,429)(244,428)(245,427)(246,421)(247,425)
(248,424)(249,423)(250,422)(251,436)(252,440)(253,439)(254,438)(255,437)
(256,431)(257,435)(258,434)(259,433)(260,432)(261,406)(262,410)(263,409)
(264,408)(265,407)(266,401)(267,405)(268,404)(269,403)(270,402)(271,416)
(272,420)(273,419)(274,418)(275,417)(276,411)(277,415)(278,414)(279,413)
(280,412)(281,456)(282,460)(283,459)(284,458)(285,457)(286,451)(287,455)
(288,454)(289,453)(290,452)(291,446)(292,450)(293,449)(294,448)(295,447)
(296,441)(297,445)(298,444)(299,443)(300,442)(301,471)(302,475)(303,474)
(304,473)(305,472)(306,476)(307,480)(308,479)(309,478)(310,477)(311,461)
(312,465)(313,464)(314,463)(315,462)(316,466)(317,470)(318,469)(319,468)
(320,467);
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)!( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)
( 8,328)( 9,329)( 10,330)( 11,336)( 12,337)( 13,338)( 14,339)( 15,340)
( 16,331)( 17,332)( 18,333)( 19,334)( 20,335)( 21,341)( 22,342)( 23,343)
( 24,344)( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,356)
( 32,357)( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)
( 40,355)( 41,396)( 42,397)( 43,398)( 44,399)( 45,400)( 46,391)( 47,392)
( 48,393)( 49,394)( 50,395)( 51,381)( 52,382)( 53,383)( 54,384)( 55,385)
( 56,386)( 57,387)( 58,388)( 59,389)( 60,390)( 61,371)( 62,372)( 63,373)
( 64,374)( 65,375)( 66,376)( 67,377)( 68,378)( 69,379)( 70,380)( 71,366)
( 72,367)( 73,368)( 74,369)( 75,370)( 76,361)( 77,362)( 78,363)( 79,364)
( 80,365)( 81,406)( 82,407)( 83,408)( 84,409)( 85,410)( 86,401)( 87,402)
( 88,403)( 89,404)( 90,405)( 91,411)( 92,412)( 93,413)( 94,414)( 95,415)
( 96,416)( 97,417)( 98,418)( 99,419)(100,420)(101,426)(102,427)(103,428)
(104,429)(105,430)(106,421)(107,422)(108,423)(109,424)(110,425)(111,431)
(112,432)(113,433)(114,434)(115,435)(116,436)(117,437)(118,438)(119,439)
(120,440)(121,471)(122,472)(123,473)(124,474)(125,475)(126,476)(127,477)
(128,478)(129,479)(130,480)(131,466)(132,467)(133,468)(134,469)(135,470)
(136,461)(137,462)(138,463)(139,464)(140,465)(141,456)(142,457)(143,458)
(144,459)(145,460)(146,451)(147,452)(148,453)(149,454)(150,455)(151,441)
(152,442)(153,443)(154,444)(155,445)(156,446)(157,447)(158,448)(159,449)
(160,450)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)
(168,488)(169,489)(170,490)(171,496)(172,497)(173,498)(174,499)(175,500)
(176,491)(177,492)(178,493)(179,494)(180,495)(181,501)(182,502)(183,503)
(184,504)(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,516)
(192,517)(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)
(200,515)(201,556)(202,557)(203,558)(204,559)(205,560)(206,551)(207,552)
(208,553)(209,554)(210,555)(211,541)(212,542)(213,543)(214,544)(215,545)
(216,546)(217,547)(218,548)(219,549)(220,550)(221,531)(222,532)(223,533)
(224,534)(225,535)(226,536)(227,537)(228,538)(229,539)(230,540)(231,526)
(232,527)(233,528)(234,529)(235,530)(236,521)(237,522)(238,523)(239,524)
(240,525)(241,566)(242,567)(243,568)(244,569)(245,570)(246,561)(247,562)
(248,563)(249,564)(250,565)(251,571)(252,572)(253,573)(254,574)(255,575)
(256,576)(257,577)(258,578)(259,579)(260,580)(261,586)(262,587)(263,588)
(264,589)(265,590)(266,581)(267,582)(268,583)(269,584)(270,585)(271,591)
(272,592)(273,593)(274,594)(275,595)(276,596)(277,597)(278,598)(279,599)
(280,600)(281,631)(282,632)(283,633)(284,634)(285,635)(286,636)(287,637)
(288,638)(289,639)(290,640)(291,626)(292,627)(293,628)(294,629)(295,630)
(296,621)(297,622)(298,623)(299,624)(300,625)(301,616)(302,617)(303,618)
(304,619)(305,620)(306,611)(307,612)(308,613)(309,614)(310,615)(311,601)
(312,602)(313,603)(314,604)(315,605)(316,606)(317,607)(318,608)(319,609)
(320,610);
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*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*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*s0*s1*s0*s1 >;
References : None.
to this polytope