Polytope of Type {16,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,40}*1280d
Also Known As : {16,40|2}. if this polytope has another name.
Group : SmallGroup(1280,82995)
Rank : 3
Schlafli Type : {16,40}
Number of vertices, edges, etc : 16, 320, 40
Order of s0s1s2 : 80
Order of s0s1s2s1 : 2
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}*640a
4-fold quotients : {4,40}*320a, {8,20}*320a, {16,10}*320
5-fold quotients : {16,8}*256d
8-fold quotients : {4,20}*160, {2,40}*160, {8,10}*160
10-fold quotients : {8,8}*128b, {16,4}*128a
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,8}*64a, {8,4}*64a, {16,2}*64
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)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 61,546)( 62,547)( 63,548)( 64,549)
( 65,550)( 66,541)( 67,542)( 68,543)( 69,544)( 70,545)( 71,556)( 72,557)
( 73,558)( 74,559)( 75,560)( 76,551)( 77,552)( 78,553)( 79,554)( 80,555)
( 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)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)
(129,639)(130,640)(131,621)(132,622)(133,623)(134,624)(135,625)(136,626)
(137,627)(138,628)(139,629)(140,630)(141,611)(142,612)(143,613)(144,614)
(145,615)(146,616)(147,617)(148,618)(149,619)(150,620)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(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)
(201,361)(202,362)(203,363)(204,364)(205,365)(206,366)(207,367)(208,368)
(209,369)(210,370)(211,371)(212,372)(213,373)(214,374)(215,375)(216,376)
(217,377)(218,378)(219,379)(220,380)(221,386)(222,387)(223,388)(224,389)
(225,390)(226,381)(227,382)(228,383)(229,384)(230,385)(231,396)(232,397)
(233,398)(234,399)(235,400)(236,391)(237,392)(238,393)(239,394)(240,395)
(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)
(281,471)(282,472)(283,473)(284,474)(285,475)(286,476)(287,477)(288,478)
(289,479)(290,480)(291,461)(292,462)(293,463)(294,464)(295,465)(296,466)
(297,467)(298,468)(299,469)(300,470)(301,451)(302,452)(303,453)(304,454)
(305,455)(306,456)(307,457)(308,458)(309,459)(310,460)(311,441)(312,442)
(313,443)(314,444)(315,445)(316,446)(317,447)(318,448)(319,449)(320,450);;
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, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 46, 56)
( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 61, 76)( 62, 80)( 63, 79)( 64, 78)
( 65, 77)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 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)(121,151)(122,155)(123,154)(124,153)(125,152)(126,156)
(127,160)(128,159)(129,158)(130,157)(131,141)(132,145)(133,144)(134,143)
(135,142)(136,146)(137,150)(138,149)(139,148)(140,147)(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)(361,451)(362,455)
(363,454)(364,453)(365,452)(366,456)(367,460)(368,459)(369,458)(370,457)
(371,441)(372,445)(373,444)(374,443)(375,442)(376,446)(377,450)(378,449)
(379,448)(380,447)(381,476)(382,480)(383,479)(384,478)(385,477)(386,471)
(387,475)(388,474)(389,473)(390,472)(391,466)(392,470)(393,469)(394,468)
(395,467)(396,461)(397,465)(398,464)(399,463)(400,462)(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)
( 41,213)( 42,212)( 43,211)( 44,215)( 45,214)( 46,218)( 47,217)( 48,216)
( 49,220)( 50,219)( 51,203)( 52,202)( 53,201)( 54,205)( 55,204)( 56,208)
( 57,207)( 58,206)( 59,210)( 60,209)( 61,233)( 62,232)( 63,231)( 64,235)
( 65,234)( 66,238)( 67,237)( 68,236)( 69,240)( 70,239)( 71,223)( 72,222)
( 73,221)( 74,225)( 75,224)( 76,228)( 77,227)( 78,226)( 79,230)( 80,229)
( 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)
(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)(128,286)
(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)(136,298)
(137,297)(138,296)(139,300)(140,299)(141,303)(142,302)(143,301)(144,305)
(145,304)(146,308)(147,307)(148,306)(149,310)(150,309)(151,313)(152,312)
(153,311)(154,315)(155,314)(156,318)(157,317)(158,316)(159,320)(160,319)
(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)
(361,533)(362,532)(363,531)(364,535)(365,534)(366,538)(367,537)(368,536)
(369,540)(370,539)(371,523)(372,522)(373,521)(374,525)(375,524)(376,528)
(377,527)(378,526)(379,530)(380,529)(381,553)(382,552)(383,551)(384,555)
(385,554)(386,558)(387,557)(388,556)(389,560)(390,559)(391,543)(392,542)
(393,541)(394,545)(395,544)(396,548)(397,547)(398,546)(399,550)(400,549)
(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)
(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)(448,606)
(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)(456,618)
(457,617)(458,616)(459,620)(460,619)(461,623)(462,622)(463,621)(464,625)
(465,624)(466,628)(467,627)(468,626)(469,630)(470,629)(471,633)(472,632)
(473,631)(474,635)(475,634)(476,638)(477,637)(478,636)(479,640)(480,639);;
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*s2*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*s0*s1*s0*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*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)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,546)( 62,547)( 63,548)
( 64,549)( 65,550)( 66,541)( 67,542)( 68,543)( 69,544)( 70,545)( 71,556)
( 72,557)( 73,558)( 74,559)( 75,560)( 76,551)( 77,552)( 78,553)( 79,554)
( 80,555)( 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)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)
(128,638)(129,639)(130,640)(131,621)(132,622)(133,623)(134,624)(135,625)
(136,626)(137,627)(138,628)(139,629)(140,630)(141,611)(142,612)(143,613)
(144,614)(145,615)(146,616)(147,617)(148,618)(149,619)(150,620)(151,601)
(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)
(160,610)(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)(201,361)(202,362)(203,363)(204,364)(205,365)(206,366)(207,367)
(208,368)(209,369)(210,370)(211,371)(212,372)(213,373)(214,374)(215,375)
(216,376)(217,377)(218,378)(219,379)(220,380)(221,386)(222,387)(223,388)
(224,389)(225,390)(226,381)(227,382)(228,383)(229,384)(230,385)(231,396)
(232,397)(233,398)(234,399)(235,400)(236,391)(237,392)(238,393)(239,394)
(240,395)(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)(281,471)(282,472)(283,473)(284,474)(285,475)(286,476)(287,477)
(288,478)(289,479)(290,480)(291,461)(292,462)(293,463)(294,464)(295,465)
(296,466)(297,467)(298,468)(299,469)(300,470)(301,451)(302,452)(303,453)
(304,454)(305,455)(306,456)(307,457)(308,458)(309,459)(310,460)(311,441)
(312,442)(313,443)(314,444)(315,445)(316,446)(317,447)(318,448)(319,449)
(320,450);
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, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 56)( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 61, 76)( 62, 80)( 63, 79)
( 64, 78)( 65, 77)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 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)(121,151)(122,155)(123,154)(124,153)(125,152)
(126,156)(127,160)(128,159)(129,158)(130,157)(131,141)(132,145)(133,144)
(134,143)(135,142)(136,146)(137,150)(138,149)(139,148)(140,147)(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)(361,451)
(362,455)(363,454)(364,453)(365,452)(366,456)(367,460)(368,459)(369,458)
(370,457)(371,441)(372,445)(373,444)(374,443)(375,442)(376,446)(377,450)
(378,449)(379,448)(380,447)(381,476)(382,480)(383,479)(384,478)(385,477)
(386,471)(387,475)(388,474)(389,473)(390,472)(391,466)(392,470)(393,469)
(394,468)(395,467)(396,461)(397,465)(398,464)(399,463)(400,462)(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)( 41,213)( 42,212)( 43,211)( 44,215)( 45,214)( 46,218)( 47,217)
( 48,216)( 49,220)( 50,219)( 51,203)( 52,202)( 53,201)( 54,205)( 55,204)
( 56,208)( 57,207)( 58,206)( 59,210)( 60,209)( 61,233)( 62,232)( 63,231)
( 64,235)( 65,234)( 66,238)( 67,237)( 68,236)( 69,240)( 70,239)( 71,223)
( 72,222)( 73,221)( 74,225)( 75,224)( 76,228)( 77,227)( 78,226)( 79,230)
( 80,229)( 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)(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)
(128,286)(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)
(136,298)(137,297)(138,296)(139,300)(140,299)(141,303)(142,302)(143,301)
(144,305)(145,304)(146,308)(147,307)(148,306)(149,310)(150,309)(151,313)
(152,312)(153,311)(154,315)(155,314)(156,318)(157,317)(158,316)(159,320)
(160,319)(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)(361,533)(362,532)(363,531)(364,535)(365,534)(366,538)(367,537)
(368,536)(369,540)(370,539)(371,523)(372,522)(373,521)(374,525)(375,524)
(376,528)(377,527)(378,526)(379,530)(380,529)(381,553)(382,552)(383,551)
(384,555)(385,554)(386,558)(387,557)(388,556)(389,560)(390,559)(391,543)
(392,542)(393,541)(394,545)(395,544)(396,548)(397,547)(398,546)(399,550)
(400,549)(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)(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)
(448,606)(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)
(456,618)(457,617)(458,616)(459,620)(460,619)(461,623)(462,622)(463,621)
(464,625)(465,624)(466,628)(467,627)(468,626)(469,630)(470,629)(471,633)
(472,632)(473,631)(474,635)(475,634)(476,638)(477,637)(478,636)(479,640)
(480,639);
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*s2*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*s0*s1*s0*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*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