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