Polytope of Type {16,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,40}*1280f
if this polytope has a name.
Group : SmallGroup(1280,83051)
Rank : 3
Schlafli Type : {16,40}
Number of vertices, edges, etc : 16, 320, 40
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {8,40}*640b, {16,20}*640b
4-fold quotients : {4,40}*320a, {8,20}*320a
5-fold quotients : {16,8}*256f
8-fold quotients : {4,20}*160, {2,40}*160, {8,10}*160
10-fold quotients : {8,8}*128b, {16,4}*128b
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,8}*64a, {8,4}*64a
32-fold quotients : {2,10}*40
40-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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 := ( 1,481)( 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)
( 41,526)( 42,527)( 43,528)( 44,529)( 45,530)( 46,521)( 47,522)( 48,523)
( 49,524)( 50,525)( 51,536)( 52,537)( 53,538)( 54,539)( 55,540)( 56,531)
( 57,532)( 58,533)( 59,534)( 60,535)( 61,541)( 62,542)( 63,543)( 64,544)
( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)( 72,552)
( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)( 80,560)
( 81,591)( 82,592)( 83,593)( 84,594)( 85,595)( 86,596)( 87,597)( 88,598)
( 89,599)( 90,600)( 91,581)( 92,582)( 93,583)( 94,584)( 95,585)( 96,586)
( 97,587)( 98,588)( 99,589)(100,590)(101,571)(102,572)(103,573)(104,574)
(105,575)(106,576)(107,577)(108,578)(109,579)(110,580)(111,561)(112,562)
(113,563)(114,564)(115,565)(116,566)(117,567)(118,568)(119,569)(120,570)
(121,636)(122,637)(123,638)(124,639)(125,640)(126,631)(127,632)(128,633)
(129,634)(130,635)(131,626)(132,627)(133,628)(134,629)(135,630)(136,621)
(137,622)(138,623)(139,624)(140,625)(141,616)(142,617)(143,618)(144,619)
(145,620)(146,611)(147,612)(148,613)(149,614)(150,615)(151,606)(152,607)
(153,608)(154,609)(155,610)(156,601)(157,602)(158,603)(159,604)(160,605)
(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)
(201,366)(202,367)(203,368)(204,369)(205,370)(206,361)(207,362)(208,363)
(209,364)(210,365)(211,376)(212,377)(213,378)(214,379)(215,380)(216,371)
(217,372)(218,373)(219,374)(220,375)(221,381)(222,382)(223,383)(224,384)
(225,385)(226,386)(227,387)(228,388)(229,389)(230,390)(231,391)(232,392)
(233,393)(234,394)(235,395)(236,396)(237,397)(238,398)(239,399)(240,400)
(241,431)(242,432)(243,433)(244,434)(245,435)(246,436)(247,437)(248,438)
(249,439)(250,440)(251,421)(252,422)(253,423)(254,424)(255,425)(256,426)
(257,427)(258,428)(259,429)(260,430)(261,411)(262,412)(263,413)(264,414)
(265,415)(266,416)(267,417)(268,418)(269,419)(270,420)(271,401)(272,402)
(273,403)(274,404)(275,405)(276,406)(277,407)(278,408)(279,409)(280,410)
(281,476)(282,477)(283,478)(284,479)(285,480)(286,471)(287,472)(288,473)
(289,474)(290,475)(291,466)(292,467)(293,468)(294,469)(295,470)(296,461)
(297,462)(298,463)(299,464)(300,465)(301,456)(302,457)(303,458)(304,459)
(305,460)(306,451)(307,452)(308,453)(309,454)(310,455)(311,446)(312,447)
(313,448)(314,449)(315,450)(316,441)(317,442)(318,443)(319,444)(320,445);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 36)( 32, 40)( 33, 39)
( 34, 38)( 35, 37)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 46, 51)
( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 61, 71)( 62, 75)( 63, 74)( 64, 73)
( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81,101)( 82,105)
( 83,104)( 84,103)( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)
( 91,111)( 92,115)( 93,114)( 94,113)( 95,112)( 96,116)( 97,120)( 98,119)
( 99,118)(100,117)(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)
(127,155)(128,154)(129,153)(130,152)(131,146)(132,150)(133,149)(134,148)
(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(161,201)(162,205)
(163,204)(164,203)(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)
(171,211)(172,215)(173,214)(174,213)(175,212)(176,216)(177,220)(178,219)
(179,218)(180,217)(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)
(187,225)(188,224)(189,223)(190,222)(191,236)(192,240)(193,239)(194,238)
(195,237)(196,231)(197,235)(198,234)(199,233)(200,232)(241,301)(242,305)
(243,304)(244,303)(245,302)(246,306)(247,310)(248,309)(249,308)(250,307)
(251,311)(252,315)(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)
(259,318)(260,317)(261,281)(262,285)(263,284)(264,283)(265,282)(266,286)
(267,290)(268,289)(269,288)(270,287)(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)
(331,411)(332,415)(333,414)(334,413)(335,412)(336,416)(337,420)(338,419)
(339,418)(340,417)(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)
(347,425)(348,424)(349,423)(350,422)(351,436)(352,440)(353,439)(354,438)
(355,437)(356,431)(357,435)(358,434)(359,433)(360,432)(361,456)(362,460)
(363,459)(364,458)(365,457)(366,451)(367,455)(368,454)(369,453)(370,452)
(371,446)(372,450)(373,449)(374,448)(375,447)(376,441)(377,445)(378,444)
(379,443)(380,442)(381,471)(382,475)(383,474)(384,473)(385,472)(386,476)
(387,480)(388,479)(389,478)(390,477)(391,461)(392,465)(393,464)(394,463)
(395,462)(396,466)(397,470)(398,469)(399,468)(400,467)(481,611)(482,615)
(483,614)(484,613)(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)
(491,601)(492,605)(493,604)(494,603)(495,602)(496,606)(497,610)(498,609)
(499,608)(500,607)(501,636)(502,640)(503,639)(504,638)(505,637)(506,631)
(507,635)(508,634)(509,633)(510,632)(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)
(531,561)(532,565)(533,564)(534,563)(535,562)(536,566)(537,570)(538,569)
(539,568)(540,567)(541,596)(542,600)(543,599)(544,598)(545,597)(546,591)
(547,595)(548,594)(549,593)(550,592)(551,586)(552,590)(553,589)(554,588)
(555,587)(556,581)(557,585)(558,584)(559,583)(560,582);;
s2 := ( 1,163)( 2,162)( 3,161)( 4,165)( 5,164)( 6,168)( 7,167)( 8,166)
( 9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)( 16,178)
( 17,177)( 18,176)( 19,180)( 20,179)( 21,183)( 22,182)( 23,181)( 24,185)
( 25,184)( 26,188)( 27,187)( 28,186)( 29,190)( 30,189)( 31,193)( 32,192)
( 33,191)( 34,195)( 35,194)( 36,198)( 37,197)( 38,196)( 39,200)( 40,199)
( 41,218)( 42,217)( 43,216)( 44,220)( 45,219)( 46,213)( 47,212)( 48,211)
( 49,215)( 50,214)( 51,208)( 52,207)( 53,206)( 54,210)( 55,209)( 56,203)
( 57,202)( 58,201)( 59,205)( 60,204)( 61,238)( 62,237)( 63,236)( 64,240)
( 65,239)( 66,233)( 67,232)( 68,231)( 69,235)( 70,234)( 71,228)( 72,227)
( 73,226)( 74,230)( 75,229)( 76,223)( 77,222)( 78,221)( 79,225)( 80,224)
( 81,253)( 82,252)( 83,251)( 84,255)( 85,254)( 86,258)( 87,257)( 88,256)
( 89,260)( 90,259)( 91,243)( 92,242)( 93,241)( 94,245)( 95,244)( 96,248)
( 97,247)( 98,246)( 99,250)(100,249)(101,273)(102,272)(103,271)(104,275)
(105,274)(106,278)(107,277)(108,276)(109,280)(110,279)(111,263)(112,262)
(113,261)(114,265)(115,264)(116,268)(117,267)(118,266)(119,270)(120,269)
(121,288)(122,287)(123,286)(124,290)(125,289)(126,283)(127,282)(128,281)
(129,285)(130,284)(131,298)(132,297)(133,296)(134,300)(135,299)(136,293)
(137,292)(138,291)(139,295)(140,294)(141,308)(142,307)(143,306)(144,310)
(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)(152,317)
(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)(160,314)
(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)(328,486)
(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)(336,498)
(337,497)(338,496)(339,500)(340,499)(341,503)(342,502)(343,501)(344,505)
(345,504)(346,508)(347,507)(348,506)(349,510)(350,509)(351,513)(352,512)
(353,511)(354,515)(355,514)(356,518)(357,517)(358,516)(359,520)(360,519)
(361,538)(362,537)(363,536)(364,540)(365,539)(366,533)(367,532)(368,531)
(369,535)(370,534)(371,528)(372,527)(373,526)(374,530)(375,529)(376,523)
(377,522)(378,521)(379,525)(380,524)(381,558)(382,557)(383,556)(384,560)
(385,559)(386,553)(387,552)(388,551)(389,555)(390,554)(391,548)(392,547)
(393,546)(394,550)(395,549)(396,543)(397,542)(398,541)(399,545)(400,544)
(401,573)(402,572)(403,571)(404,575)(405,574)(406,578)(407,577)(408,576)
(409,580)(410,579)(411,563)(412,562)(413,561)(414,565)(415,564)(416,568)
(417,567)(418,566)(419,570)(420,569)(421,593)(422,592)(423,591)(424,595)
(425,594)(426,598)(427,597)(428,596)(429,600)(430,599)(431,583)(432,582)
(433,581)(434,585)(435,584)(436,588)(437,587)(438,586)(439,590)(440,589)
(441,608)(442,607)(443,606)(444,610)(445,609)(446,603)(447,602)(448,601)
(449,605)(450,604)(451,618)(452,617)(453,616)(454,620)(455,619)(456,613)
(457,612)(458,611)(459,615)(460,614)(461,628)(462,627)(463,626)(464,630)
(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)(472,637)
(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)(480,634);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*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*s0*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*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*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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 41,526)( 42,527)( 43,528)( 44,529)( 45,530)( 46,521)( 47,522)
( 48,523)( 49,524)( 50,525)( 51,536)( 52,537)( 53,538)( 54,539)( 55,540)
( 56,531)( 57,532)( 58,533)( 59,534)( 60,535)( 61,541)( 62,542)( 63,543)
( 64,544)( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)
( 72,552)( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)
( 80,560)( 81,591)( 82,592)( 83,593)( 84,594)( 85,595)( 86,596)( 87,597)
( 88,598)( 89,599)( 90,600)( 91,581)( 92,582)( 93,583)( 94,584)( 95,585)
( 96,586)( 97,587)( 98,588)( 99,589)(100,590)(101,571)(102,572)(103,573)
(104,574)(105,575)(106,576)(107,577)(108,578)(109,579)(110,580)(111,561)
(112,562)(113,563)(114,564)(115,565)(116,566)(117,567)(118,568)(119,569)
(120,570)(121,636)(122,637)(123,638)(124,639)(125,640)(126,631)(127,632)
(128,633)(129,634)(130,635)(131,626)(132,627)(133,628)(134,629)(135,630)
(136,621)(137,622)(138,623)(139,624)(140,625)(141,616)(142,617)(143,618)
(144,619)(145,620)(146,611)(147,612)(148,613)(149,614)(150,615)(151,606)
(152,607)(153,608)(154,609)(155,610)(156,601)(157,602)(158,603)(159,604)
(160,605)(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)(201,366)(202,367)(203,368)(204,369)(205,370)(206,361)(207,362)
(208,363)(209,364)(210,365)(211,376)(212,377)(213,378)(214,379)(215,380)
(216,371)(217,372)(218,373)(219,374)(220,375)(221,381)(222,382)(223,383)
(224,384)(225,385)(226,386)(227,387)(228,388)(229,389)(230,390)(231,391)
(232,392)(233,393)(234,394)(235,395)(236,396)(237,397)(238,398)(239,399)
(240,400)(241,431)(242,432)(243,433)(244,434)(245,435)(246,436)(247,437)
(248,438)(249,439)(250,440)(251,421)(252,422)(253,423)(254,424)(255,425)
(256,426)(257,427)(258,428)(259,429)(260,430)(261,411)(262,412)(263,413)
(264,414)(265,415)(266,416)(267,417)(268,418)(269,419)(270,420)(271,401)
(272,402)(273,403)(274,404)(275,405)(276,406)(277,407)(278,408)(279,409)
(280,410)(281,476)(282,477)(283,478)(284,479)(285,480)(286,471)(287,472)
(288,473)(289,474)(290,475)(291,466)(292,467)(293,468)(294,469)(295,470)
(296,461)(297,462)(298,463)(299,464)(300,465)(301,456)(302,457)(303,458)
(304,459)(305,460)(306,451)(307,452)(308,453)(309,454)(310,455)(311,446)
(312,447)(313,448)(314,449)(315,450)(316,441)(317,442)(318,443)(319,444)
(320,445);
s1 := Sym(640)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 36)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)
( 46, 51)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 61, 71)( 62, 75)( 63, 74)
( 64, 73)( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81,101)
( 82,105)( 83,104)( 84,103)( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)
( 90,107)( 91,111)( 92,115)( 93,114)( 94,113)( 95,112)( 96,116)( 97,120)
( 98,119)( 99,118)(100,117)(121,156)(122,160)(123,159)(124,158)(125,157)
(126,151)(127,155)(128,154)(129,153)(130,152)(131,146)(132,150)(133,149)
(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(161,201)
(162,205)(163,204)(164,203)(165,202)(166,206)(167,210)(168,209)(169,208)
(170,207)(171,211)(172,215)(173,214)(174,213)(175,212)(176,216)(177,220)
(178,219)(179,218)(180,217)(181,226)(182,230)(183,229)(184,228)(185,227)
(186,221)(187,225)(188,224)(189,223)(190,222)(191,236)(192,240)(193,239)
(194,238)(195,237)(196,231)(197,235)(198,234)(199,233)(200,232)(241,301)
(242,305)(243,304)(244,303)(245,302)(246,306)(247,310)(248,309)(249,308)
(250,307)(251,311)(252,315)(253,314)(254,313)(255,312)(256,316)(257,320)
(258,319)(259,318)(260,317)(261,281)(262,285)(263,284)(264,283)(265,282)
(266,286)(267,290)(268,289)(269,288)(270,287)(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)(331,411)(332,415)(333,414)(334,413)(335,412)(336,416)(337,420)
(338,419)(339,418)(340,417)(341,426)(342,430)(343,429)(344,428)(345,427)
(346,421)(347,425)(348,424)(349,423)(350,422)(351,436)(352,440)(353,439)
(354,438)(355,437)(356,431)(357,435)(358,434)(359,433)(360,432)(361,456)
(362,460)(363,459)(364,458)(365,457)(366,451)(367,455)(368,454)(369,453)
(370,452)(371,446)(372,450)(373,449)(374,448)(375,447)(376,441)(377,445)
(378,444)(379,443)(380,442)(381,471)(382,475)(383,474)(384,473)(385,472)
(386,476)(387,480)(388,479)(389,478)(390,477)(391,461)(392,465)(393,464)
(394,463)(395,462)(396,466)(397,470)(398,469)(399,468)(400,467)(481,611)
(482,615)(483,614)(484,613)(485,612)(486,616)(487,620)(488,619)(489,618)
(490,617)(491,601)(492,605)(493,604)(494,603)(495,602)(496,606)(497,610)
(498,609)(499,608)(500,607)(501,636)(502,640)(503,639)(504,638)(505,637)
(506,631)(507,635)(508,634)(509,633)(510,632)(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)(531,561)(532,565)(533,564)(534,563)(535,562)(536,566)(537,570)
(538,569)(539,568)(540,567)(541,596)(542,600)(543,599)(544,598)(545,597)
(546,591)(547,595)(548,594)(549,593)(550,592)(551,586)(552,590)(553,589)
(554,588)(555,587)(556,581)(557,585)(558,584)(559,583)(560,582);
s2 := Sym(640)!( 1,163)( 2,162)( 3,161)( 4,165)( 5,164)( 6,168)( 7,167)
( 8,166)( 9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)
( 16,178)( 17,177)( 18,176)( 19,180)( 20,179)( 21,183)( 22,182)( 23,181)
( 24,185)( 25,184)( 26,188)( 27,187)( 28,186)( 29,190)( 30,189)( 31,193)
( 32,192)( 33,191)( 34,195)( 35,194)( 36,198)( 37,197)( 38,196)( 39,200)
( 40,199)( 41,218)( 42,217)( 43,216)( 44,220)( 45,219)( 46,213)( 47,212)
( 48,211)( 49,215)( 50,214)( 51,208)( 52,207)( 53,206)( 54,210)( 55,209)
( 56,203)( 57,202)( 58,201)( 59,205)( 60,204)( 61,238)( 62,237)( 63,236)
( 64,240)( 65,239)( 66,233)( 67,232)( 68,231)( 69,235)( 70,234)( 71,228)
( 72,227)( 73,226)( 74,230)( 75,229)( 76,223)( 77,222)( 78,221)( 79,225)
( 80,224)( 81,253)( 82,252)( 83,251)( 84,255)( 85,254)( 86,258)( 87,257)
( 88,256)( 89,260)( 90,259)( 91,243)( 92,242)( 93,241)( 94,245)( 95,244)
( 96,248)( 97,247)( 98,246)( 99,250)(100,249)(101,273)(102,272)(103,271)
(104,275)(105,274)(106,278)(107,277)(108,276)(109,280)(110,279)(111,263)
(112,262)(113,261)(114,265)(115,264)(116,268)(117,267)(118,266)(119,270)
(120,269)(121,288)(122,287)(123,286)(124,290)(125,289)(126,283)(127,282)
(128,281)(129,285)(130,284)(131,298)(132,297)(133,296)(134,300)(135,299)
(136,293)(137,292)(138,291)(139,295)(140,294)(141,308)(142,307)(143,306)
(144,310)(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)
(152,317)(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)
(160,314)(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)
(328,486)(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)
(336,498)(337,497)(338,496)(339,500)(340,499)(341,503)(342,502)(343,501)
(344,505)(345,504)(346,508)(347,507)(348,506)(349,510)(350,509)(351,513)
(352,512)(353,511)(354,515)(355,514)(356,518)(357,517)(358,516)(359,520)
(360,519)(361,538)(362,537)(363,536)(364,540)(365,539)(366,533)(367,532)
(368,531)(369,535)(370,534)(371,528)(372,527)(373,526)(374,530)(375,529)
(376,523)(377,522)(378,521)(379,525)(380,524)(381,558)(382,557)(383,556)
(384,560)(385,559)(386,553)(387,552)(388,551)(389,555)(390,554)(391,548)
(392,547)(393,546)(394,550)(395,549)(396,543)(397,542)(398,541)(399,545)
(400,544)(401,573)(402,572)(403,571)(404,575)(405,574)(406,578)(407,577)
(408,576)(409,580)(410,579)(411,563)(412,562)(413,561)(414,565)(415,564)
(416,568)(417,567)(418,566)(419,570)(420,569)(421,593)(422,592)(423,591)
(424,595)(425,594)(426,598)(427,597)(428,596)(429,600)(430,599)(431,583)
(432,582)(433,581)(434,585)(435,584)(436,588)(437,587)(438,586)(439,590)
(440,589)(441,608)(442,607)(443,606)(444,610)(445,609)(446,603)(447,602)
(448,601)(449,605)(450,604)(451,618)(452,617)(453,616)(454,620)(455,619)
(456,613)(457,612)(458,611)(459,615)(460,614)(461,628)(462,627)(463,626)
(464,630)(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)
(472,637)(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)
(480,634);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*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*s0*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*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*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*s1*s2*s1*s2 >;
References : None.
to this polytope