Polytope of Type {8,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,40}*1280b
if this polytope has a name.
Group : SmallGroup(1280,81598)
Rank : 3
Schlafli Type : {8,40}
Number of vertices, edges, etc : 16, 320, 80
Order of s0s1s2 : 20
Order of s0s1s2s1 : 4
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 : {4,40}*640b, {8,20}*640b
4-fold quotients : {4,20}*320
5-fold quotients : {8,8}*256b
8-fold quotients : {4,20}*160
10-fold quotients : {4,8}*128b, {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 := ( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)( 8,328)
( 9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)( 16,336)
( 17,337)( 18,338)( 19,339)( 20,340)( 21,341)( 22,342)( 23,343)( 24,344)
( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)( 32,352)
( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)( 40,360)
( 41,376)( 42,377)( 43,378)( 44,379)( 45,380)( 46,371)( 47,372)( 48,373)
( 49,374)( 50,375)( 51,366)( 52,367)( 53,368)( 54,369)( 55,370)( 56,361)
( 57,362)( 58,363)( 59,364)( 60,365)( 61,396)( 62,397)( 63,398)( 64,399)
( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)( 72,387)
( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)( 80,385)
( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)( 88,428)
( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)( 96,436)
( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)(104,404)
(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)(112,412)
(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)(120,420)
(121,476)(122,477)(123,478)(124,479)(125,480)(126,471)(127,472)(128,473)
(129,474)(130,475)(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)(151,446)(152,447)
(153,448)(154,449)(155,450)(156,441)(157,442)(158,443)(159,444)(160,445)
(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)
(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)(176,496)
(177,497)(178,498)(179,499)(180,500)(181,501)(182,502)(183,503)(184,504)
(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,511)(192,512)
(193,513)(194,514)(195,515)(196,516)(197,517)(198,518)(199,519)(200,520)
(201,536)(202,537)(203,538)(204,539)(205,540)(206,531)(207,532)(208,533)
(209,534)(210,535)(211,526)(212,527)(213,528)(214,529)(215,530)(216,521)
(217,522)(218,523)(219,524)(220,525)(221,556)(222,557)(223,558)(224,559)
(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)(232,547)
(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)(240,545)
(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)(248,588)
(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)(256,596)
(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)(264,564)
(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)(272,572)
(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)(280,580)
(281,636)(282,637)(283,638)(284,639)(285,640)(286,631)(287,632)(288,633)
(289,634)(290,635)(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)(311,606)(312,607)
(313,608)(314,609)(315,610)(316,601)(317,602)(318,603)(319,604)(320,605);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 11, 16)( 12, 20)( 13, 19)( 14, 18)
( 15, 17)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 31, 36)( 32, 40)( 33, 39)
( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 56)( 52, 60)
( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 71, 76)
( 72, 80)( 73, 79)( 74, 78)( 75, 77)( 81,101)( 82,105)( 83,104)( 84,103)
( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,116)( 92,120)
( 93,119)( 94,118)( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)
(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)(128,149)
(129,148)(130,147)(131,156)(132,160)(133,159)(134,158)(135,157)(136,151)
(137,155)(138,154)(139,153)(140,152)(161,201)(162,205)(163,204)(164,203)
(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,216)(172,220)
(173,219)(174,218)(175,217)(176,211)(177,215)(178,214)(179,213)(180,212)
(181,221)(182,225)(183,224)(184,223)(185,222)(186,226)(187,230)(188,229)
(189,228)(190,227)(191,236)(192,240)(193,239)(194,238)(195,237)(196,231)
(197,235)(198,234)(199,233)(200,232)(241,306)(242,310)(243,309)(244,308)
(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)(251,311)(252,315)
(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)(260,317)
(261,286)(262,290)(263,289)(264,288)(265,287)(266,281)(267,285)(268,284)
(269,283)(270,282)(271,291)(272,295)(273,294)(274,293)(275,292)(276,296)
(277,300)(278,299)(279,298)(280,297)(321,401)(322,405)(323,404)(324,403)
(325,402)(326,406)(327,410)(328,409)(329,408)(330,407)(331,416)(332,420)
(333,419)(334,418)(335,417)(336,411)(337,415)(338,414)(339,413)(340,412)
(341,421)(342,425)(343,424)(344,423)(345,422)(346,426)(347,430)(348,429)
(349,428)(350,427)(351,436)(352,440)(353,439)(354,438)(355,437)(356,431)
(357,435)(358,434)(359,433)(360,432)(361,441)(362,445)(363,444)(364,443)
(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,456)(372,460)
(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)(380,452)
(381,461)(382,465)(383,464)(384,463)(385,462)(386,466)(387,470)(388,469)
(389,468)(390,467)(391,476)(392,480)(393,479)(394,478)(395,477)(396,471)
(397,475)(398,474)(399,473)(400,472)(481,611)(482,615)(483,614)(484,613)
(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,606)(492,610)
(493,609)(494,608)(495,607)(496,601)(497,605)(498,604)(499,603)(500,602)
(501,631)(502,635)(503,634)(504,633)(505,632)(506,636)(507,640)(508,639)
(509,638)(510,637)(511,626)(512,630)(513,629)(514,628)(515,627)(516,621)
(517,625)(518,624)(519,623)(520,622)(521,571)(522,575)(523,574)(524,573)
(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,566)(532,570)
(533,569)(534,568)(535,567)(536,561)(537,565)(538,564)(539,563)(540,562)
(541,591)(542,595)(543,594)(544,593)(545,592)(546,596)(547,600)(548,599)
(549,598)(550,597)(551,586)(552,590)(553,589)(554,588)(555,587)(556,581)
(557,585)(558,584)(559,583)(560,582);;
s2 := ( 1,483)( 2,482)( 3,481)( 4,485)( 5,484)( 6,488)( 7,487)( 8,486)
( 9,490)( 10,489)( 11,493)( 12,492)( 13,491)( 14,495)( 15,494)( 16,498)
( 17,497)( 18,496)( 19,500)( 20,499)( 21,503)( 22,502)( 23,501)( 24,505)
( 25,504)( 26,508)( 27,507)( 28,506)( 29,510)( 30,509)( 31,513)( 32,512)
( 33,511)( 34,515)( 35,514)( 36,518)( 37,517)( 38,516)( 39,520)( 40,519)
( 41,538)( 42,537)( 43,536)( 44,540)( 45,539)( 46,533)( 47,532)( 48,531)
( 49,535)( 50,534)( 51,528)( 52,527)( 53,526)( 54,530)( 55,529)( 56,523)
( 57,522)( 58,521)( 59,525)( 60,524)( 61,558)( 62,557)( 63,556)( 64,560)
( 65,559)( 66,553)( 67,552)( 68,551)( 69,555)( 70,554)( 71,548)( 72,547)
( 73,546)( 74,550)( 75,549)( 76,543)( 77,542)( 78,541)( 79,545)( 80,544)
( 81,593)( 82,592)( 83,591)( 84,595)( 85,594)( 86,598)( 87,597)( 88,596)
( 89,600)( 90,599)( 91,583)( 92,582)( 93,581)( 94,585)( 95,584)( 96,588)
( 97,587)( 98,586)( 99,590)(100,589)(101,573)(102,572)(103,571)(104,575)
(105,574)(106,578)(107,577)(108,576)(109,580)(110,579)(111,563)(112,562)
(113,561)(114,565)(115,564)(116,568)(117,567)(118,566)(119,570)(120,569)
(121,628)(122,627)(123,626)(124,630)(125,629)(126,623)(127,622)(128,621)
(129,625)(130,624)(131,638)(132,637)(133,636)(134,640)(135,639)(136,633)
(137,632)(138,631)(139,635)(140,634)(141,608)(142,607)(143,606)(144,610)
(145,609)(146,603)(147,602)(148,601)(149,605)(150,604)(151,618)(152,617)
(153,616)(154,620)(155,619)(156,613)(157,612)(158,611)(159,615)(160,614)
(161,323)(162,322)(163,321)(164,325)(165,324)(166,328)(167,327)(168,326)
(169,330)(170,329)(171,333)(172,332)(173,331)(174,335)(175,334)(176,338)
(177,337)(178,336)(179,340)(180,339)(181,343)(182,342)(183,341)(184,345)
(185,344)(186,348)(187,347)(188,346)(189,350)(190,349)(191,353)(192,352)
(193,351)(194,355)(195,354)(196,358)(197,357)(198,356)(199,360)(200,359)
(201,378)(202,377)(203,376)(204,380)(205,379)(206,373)(207,372)(208,371)
(209,375)(210,374)(211,368)(212,367)(213,366)(214,370)(215,369)(216,363)
(217,362)(218,361)(219,365)(220,364)(221,398)(222,397)(223,396)(224,400)
(225,399)(226,393)(227,392)(228,391)(229,395)(230,394)(231,388)(232,387)
(233,386)(234,390)(235,389)(236,383)(237,382)(238,381)(239,385)(240,384)
(241,433)(242,432)(243,431)(244,435)(245,434)(246,438)(247,437)(248,436)
(249,440)(250,439)(251,423)(252,422)(253,421)(254,425)(255,424)(256,428)
(257,427)(258,426)(259,430)(260,429)(261,413)(262,412)(263,411)(264,415)
(265,414)(266,418)(267,417)(268,416)(269,420)(270,419)(271,403)(272,402)
(273,401)(274,405)(275,404)(276,408)(277,407)(278,406)(279,410)(280,409)
(281,468)(282,467)(283,466)(284,470)(285,469)(286,463)(287,462)(288,461)
(289,465)(290,464)(291,478)(292,477)(293,476)(294,480)(295,479)(296,473)
(297,472)(298,471)(299,475)(300,474)(301,448)(302,447)(303,446)(304,450)
(305,449)(306,443)(307,442)(308,441)(309,445)(310,444)(311,458)(312,457)
(313,456)(314,460)(315,459)(316,453)(317,452)(318,451)(319,455)(320,454);;
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*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s0*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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(640)!( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)
( 8,328)( 9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)
( 16,336)( 17,337)( 18,338)( 19,339)( 20,340)( 21,341)( 22,342)( 23,343)
( 24,344)( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)
( 32,352)( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)
( 40,360)( 41,376)( 42,377)( 43,378)( 44,379)( 45,380)( 46,371)( 47,372)
( 48,373)( 49,374)( 50,375)( 51,366)( 52,367)( 53,368)( 54,369)( 55,370)
( 56,361)( 57,362)( 58,363)( 59,364)( 60,365)( 61,396)( 62,397)( 63,398)
( 64,399)( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)
( 72,387)( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)
( 80,385)( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)
( 88,428)( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)
( 96,436)( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)
(104,404)(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)
(112,412)(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)
(120,420)(121,476)(122,477)(123,478)(124,479)(125,480)(126,471)(127,472)
(128,473)(129,474)(130,475)(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)(151,446)
(152,447)(153,448)(154,449)(155,450)(156,441)(157,442)(158,443)(159,444)
(160,445)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)
(168,488)(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)
(176,496)(177,497)(178,498)(179,499)(180,500)(181,501)(182,502)(183,503)
(184,504)(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,511)
(192,512)(193,513)(194,514)(195,515)(196,516)(197,517)(198,518)(199,519)
(200,520)(201,536)(202,537)(203,538)(204,539)(205,540)(206,531)(207,532)
(208,533)(209,534)(210,535)(211,526)(212,527)(213,528)(214,529)(215,530)
(216,521)(217,522)(218,523)(219,524)(220,525)(221,556)(222,557)(223,558)
(224,559)(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)
(232,547)(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)
(240,545)(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)
(248,588)(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)
(256,596)(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)
(264,564)(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)
(272,572)(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)
(280,580)(281,636)(282,637)(283,638)(284,639)(285,640)(286,631)(287,632)
(288,633)(289,634)(290,635)(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)(311,606)
(312,607)(313,608)(314,609)(315,610)(316,601)(317,602)(318,603)(319,604)
(320,605);
s1 := Sym(640)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 11, 16)( 12, 20)( 13, 19)
( 14, 18)( 15, 17)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 31, 36)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 67, 70)( 68, 69)
( 71, 76)( 72, 80)( 73, 79)( 74, 78)( 75, 77)( 81,101)( 82,105)( 83,104)
( 84,103)( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,116)
( 92,120)( 93,119)( 94,118)( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)
(100,112)(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)
(128,149)(129,148)(130,147)(131,156)(132,160)(133,159)(134,158)(135,157)
(136,151)(137,155)(138,154)(139,153)(140,152)(161,201)(162,205)(163,204)
(164,203)(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,216)
(172,220)(173,219)(174,218)(175,217)(176,211)(177,215)(178,214)(179,213)
(180,212)(181,221)(182,225)(183,224)(184,223)(185,222)(186,226)(187,230)
(188,229)(189,228)(190,227)(191,236)(192,240)(193,239)(194,238)(195,237)
(196,231)(197,235)(198,234)(199,233)(200,232)(241,306)(242,310)(243,309)
(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)(251,311)
(252,315)(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)
(260,317)(261,286)(262,290)(263,289)(264,288)(265,287)(266,281)(267,285)
(268,284)(269,283)(270,282)(271,291)(272,295)(273,294)(274,293)(275,292)
(276,296)(277,300)(278,299)(279,298)(280,297)(321,401)(322,405)(323,404)
(324,403)(325,402)(326,406)(327,410)(328,409)(329,408)(330,407)(331,416)
(332,420)(333,419)(334,418)(335,417)(336,411)(337,415)(338,414)(339,413)
(340,412)(341,421)(342,425)(343,424)(344,423)(345,422)(346,426)(347,430)
(348,429)(349,428)(350,427)(351,436)(352,440)(353,439)(354,438)(355,437)
(356,431)(357,435)(358,434)(359,433)(360,432)(361,441)(362,445)(363,444)
(364,443)(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,456)
(372,460)(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)
(380,452)(381,461)(382,465)(383,464)(384,463)(385,462)(386,466)(387,470)
(388,469)(389,468)(390,467)(391,476)(392,480)(393,479)(394,478)(395,477)
(396,471)(397,475)(398,474)(399,473)(400,472)(481,611)(482,615)(483,614)
(484,613)(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,606)
(492,610)(493,609)(494,608)(495,607)(496,601)(497,605)(498,604)(499,603)
(500,602)(501,631)(502,635)(503,634)(504,633)(505,632)(506,636)(507,640)
(508,639)(509,638)(510,637)(511,626)(512,630)(513,629)(514,628)(515,627)
(516,621)(517,625)(518,624)(519,623)(520,622)(521,571)(522,575)(523,574)
(524,573)(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,566)
(532,570)(533,569)(534,568)(535,567)(536,561)(537,565)(538,564)(539,563)
(540,562)(541,591)(542,595)(543,594)(544,593)(545,592)(546,596)(547,600)
(548,599)(549,598)(550,597)(551,586)(552,590)(553,589)(554,588)(555,587)
(556,581)(557,585)(558,584)(559,583)(560,582);
s2 := Sym(640)!( 1,483)( 2,482)( 3,481)( 4,485)( 5,484)( 6,488)( 7,487)
( 8,486)( 9,490)( 10,489)( 11,493)( 12,492)( 13,491)( 14,495)( 15,494)
( 16,498)( 17,497)( 18,496)( 19,500)( 20,499)( 21,503)( 22,502)( 23,501)
( 24,505)( 25,504)( 26,508)( 27,507)( 28,506)( 29,510)( 30,509)( 31,513)
( 32,512)( 33,511)( 34,515)( 35,514)( 36,518)( 37,517)( 38,516)( 39,520)
( 40,519)( 41,538)( 42,537)( 43,536)( 44,540)( 45,539)( 46,533)( 47,532)
( 48,531)( 49,535)( 50,534)( 51,528)( 52,527)( 53,526)( 54,530)( 55,529)
( 56,523)( 57,522)( 58,521)( 59,525)( 60,524)( 61,558)( 62,557)( 63,556)
( 64,560)( 65,559)( 66,553)( 67,552)( 68,551)( 69,555)( 70,554)( 71,548)
( 72,547)( 73,546)( 74,550)( 75,549)( 76,543)( 77,542)( 78,541)( 79,545)
( 80,544)( 81,593)( 82,592)( 83,591)( 84,595)( 85,594)( 86,598)( 87,597)
( 88,596)( 89,600)( 90,599)( 91,583)( 92,582)( 93,581)( 94,585)( 95,584)
( 96,588)( 97,587)( 98,586)( 99,590)(100,589)(101,573)(102,572)(103,571)
(104,575)(105,574)(106,578)(107,577)(108,576)(109,580)(110,579)(111,563)
(112,562)(113,561)(114,565)(115,564)(116,568)(117,567)(118,566)(119,570)
(120,569)(121,628)(122,627)(123,626)(124,630)(125,629)(126,623)(127,622)
(128,621)(129,625)(130,624)(131,638)(132,637)(133,636)(134,640)(135,639)
(136,633)(137,632)(138,631)(139,635)(140,634)(141,608)(142,607)(143,606)
(144,610)(145,609)(146,603)(147,602)(148,601)(149,605)(150,604)(151,618)
(152,617)(153,616)(154,620)(155,619)(156,613)(157,612)(158,611)(159,615)
(160,614)(161,323)(162,322)(163,321)(164,325)(165,324)(166,328)(167,327)
(168,326)(169,330)(170,329)(171,333)(172,332)(173,331)(174,335)(175,334)
(176,338)(177,337)(178,336)(179,340)(180,339)(181,343)(182,342)(183,341)
(184,345)(185,344)(186,348)(187,347)(188,346)(189,350)(190,349)(191,353)
(192,352)(193,351)(194,355)(195,354)(196,358)(197,357)(198,356)(199,360)
(200,359)(201,378)(202,377)(203,376)(204,380)(205,379)(206,373)(207,372)
(208,371)(209,375)(210,374)(211,368)(212,367)(213,366)(214,370)(215,369)
(216,363)(217,362)(218,361)(219,365)(220,364)(221,398)(222,397)(223,396)
(224,400)(225,399)(226,393)(227,392)(228,391)(229,395)(230,394)(231,388)
(232,387)(233,386)(234,390)(235,389)(236,383)(237,382)(238,381)(239,385)
(240,384)(241,433)(242,432)(243,431)(244,435)(245,434)(246,438)(247,437)
(248,436)(249,440)(250,439)(251,423)(252,422)(253,421)(254,425)(255,424)
(256,428)(257,427)(258,426)(259,430)(260,429)(261,413)(262,412)(263,411)
(264,415)(265,414)(266,418)(267,417)(268,416)(269,420)(270,419)(271,403)
(272,402)(273,401)(274,405)(275,404)(276,408)(277,407)(278,406)(279,410)
(280,409)(281,468)(282,467)(283,466)(284,470)(285,469)(286,463)(287,462)
(288,461)(289,465)(290,464)(291,478)(292,477)(293,476)(294,480)(295,479)
(296,473)(297,472)(298,471)(299,475)(300,474)(301,448)(302,447)(303,446)
(304,450)(305,449)(306,443)(307,442)(308,441)(309,445)(310,444)(311,458)
(312,457)(313,456)(314,460)(315,459)(316,453)(317,452)(318,451)(319,455)
(320,454);
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*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s0*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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;
References : None.
to this polytope