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