Polytope of Type {4,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,40}*1280d
if this polytope has a name.
Group : SmallGroup(1280,90302)
Rank : 3
Schlafli Type : {4,40}
Number of vertices, edges, etc : 16, 320, 160
Order of s0s1s2 : 40
Order of s0s1s2s1 : 8
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
4-fold quotients : {4,20}*320
5-fold quotients : {4,8}*256d
8-fold quotients : {4,20}*160
10-fold quotients : {4,8}*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 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)
( 9,169)( 10,170)( 11,176)( 12,177)( 13,178)( 14,179)( 15,180)( 16,171)
( 17,172)( 18,173)( 19,174)( 20,175)( 21,186)( 22,187)( 23,188)( 24,189)
( 25,190)( 26,181)( 27,182)( 28,183)( 29,184)( 30,185)( 31,191)( 32,192)
( 33,193)( 34,194)( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)( 40,200)
( 41,201)( 42,202)( 43,203)( 44,204)( 45,205)( 46,206)( 47,207)( 48,208)
( 49,209)( 50,210)( 51,216)( 52,217)( 53,218)( 54,219)( 55,220)( 56,211)
( 57,212)( 58,213)( 59,214)( 60,215)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,221)( 67,222)( 68,223)( 69,224)( 70,225)( 71,231)( 72,232)
( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)( 80,240)
( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,276)( 92,277)( 93,278)( 94,279)( 95,280)( 96,271)
( 97,272)( 98,273)( 99,274)(100,275)(101,241)(102,242)(103,243)(104,244)
(105,245)(106,246)(107,247)(108,248)(109,249)(110,250)(111,256)(112,257)
(113,258)(114,259)(115,260)(116,251)(117,252)(118,253)(119,254)(120,255)
(121,306)(122,307)(123,308)(124,309)(125,310)(126,301)(127,302)(128,303)
(129,304)(130,305)(131,311)(132,312)(133,313)(134,314)(135,315)(136,316)
(137,317)(138,318)(139,319)(140,320)(141,286)(142,287)(143,288)(144,289)
(145,290)(146,281)(147,282)(148,283)(149,284)(150,285)(151,291)(152,292)
(153,293)(154,294)(155,295)(156,296)(157,297)(158,298)(159,299)(160,300)
(321,481)(322,482)(323,483)(324,484)(325,485)(326,486)(327,487)(328,488)
(329,489)(330,490)(331,496)(332,497)(333,498)(334,499)(335,500)(336,491)
(337,492)(338,493)(339,494)(340,495)(341,506)(342,507)(343,508)(344,509)
(345,510)(346,501)(347,502)(348,503)(349,504)(350,505)(351,511)(352,512)
(353,513)(354,514)(355,515)(356,516)(357,517)(358,518)(359,519)(360,520)
(361,521)(362,522)(363,523)(364,524)(365,525)(366,526)(367,527)(368,528)
(369,529)(370,530)(371,536)(372,537)(373,538)(374,539)(375,540)(376,531)
(377,532)(378,533)(379,534)(380,535)(381,546)(382,547)(383,548)(384,549)
(385,550)(386,541)(387,542)(388,543)(389,544)(390,545)(391,551)(392,552)
(393,553)(394,554)(395,555)(396,556)(397,557)(398,558)(399,559)(400,560)
(401,581)(402,582)(403,583)(404,584)(405,585)(406,586)(407,587)(408,588)
(409,589)(410,590)(411,596)(412,597)(413,598)(414,599)(415,600)(416,591)
(417,592)(418,593)(419,594)(420,595)(421,561)(422,562)(423,563)(424,564)
(425,565)(426,566)(427,567)(428,568)(429,569)(430,570)(431,576)(432,577)
(433,578)(434,579)(435,580)(436,571)(437,572)(438,573)(439,574)(440,575)
(441,626)(442,627)(443,628)(444,629)(445,630)(446,621)(447,622)(448,623)
(449,624)(450,625)(451,631)(452,632)(453,633)(454,634)(455,635)(456,636)
(457,637)(458,638)(459,639)(460,640)(461,606)(462,607)(463,608)(464,609)
(465,610)(466,601)(467,602)(468,603)(469,604)(470,605)(471,611)(472,612)
(473,613)(474,614)(475,615)(476,616)(477,617)(478,618)(479,619)(480,620);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)( 28, 39)
( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)
( 57, 60)( 58, 59)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 76)
( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81, 86)( 82, 90)( 83, 89)( 84, 88)
( 85, 87)( 91, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)(101,116)(102,120)
(103,119)(104,118)(105,117)(106,111)(107,115)(108,114)(109,113)(110,112)
(121,126)(122,130)(123,129)(124,128)(125,127)(131,136)(132,140)(133,139)
(134,138)(135,137)(141,156)(142,160)(143,159)(144,158)(145,157)(146,151)
(147,155)(148,154)(149,153)(150,152)(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)
(181,231)(182,235)(183,234)(184,233)(185,232)(186,236)(187,240)(188,239)
(189,238)(190,237)(191,221)(192,225)(193,224)(194,223)(195,222)(196,226)
(197,230)(198,229)(199,228)(200,227)(241,291)(242,295)(243,294)(244,293)
(245,292)(246,296)(247,300)(248,299)(249,298)(250,297)(251,281)(252,285)
(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)(260,287)
(261,301)(262,305)(263,304)(264,303)(265,302)(266,306)(267,310)(268,309)
(269,308)(270,307)(271,311)(272,315)(273,314)(274,313)(275,312)(276,316)
(277,320)(278,319)(279,318)(280,317)(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)
(341,431)(342,435)(343,434)(344,433)(345,432)(346,436)(347,440)(348,439)
(349,438)(350,437)(351,421)(352,425)(353,424)(354,423)(355,422)(356,426)
(357,430)(358,429)(359,428)(360,427)(361,441)(362,445)(363,444)(364,443)
(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,451)(372,455)
(373,454)(374,453)(375,452)(376,456)(377,460)(378,459)(379,458)(380,457)
(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)(481,626)(482,630)(483,629)(484,628)
(485,627)(486,621)(487,625)(488,624)(489,623)(490,622)(491,636)(492,640)
(493,639)(494,638)(495,637)(496,631)(497,635)(498,634)(499,633)(500,632)
(501,611)(502,615)(503,614)(504,613)(505,612)(506,616)(507,620)(508,619)
(509,618)(510,617)(511,601)(512,605)(513,604)(514,603)(515,602)(516,606)
(517,610)(518,609)(519,608)(520,607)(521,581)(522,585)(523,584)(524,583)
(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)(532,595)
(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)(540,597)
(541,576)(542,580)(543,579)(544,578)(545,577)(546,571)(547,575)(548,574)
(549,573)(550,572)(551,566)(552,570)(553,569)(554,568)(555,567)(556,561)
(557,565)(558,564)(559,563)(560,562);;
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)( 21,508)( 22,507)( 23,506)( 24,510)
( 25,509)( 26,503)( 27,502)( 28,501)( 29,505)( 30,504)( 31,518)( 32,517)
( 33,516)( 34,520)( 35,519)( 36,513)( 37,512)( 38,511)( 39,515)( 40,514)
( 41,558)( 42,557)( 43,556)( 44,560)( 45,559)( 46,553)( 47,552)( 48,551)
( 49,555)( 50,554)( 51,548)( 52,547)( 53,546)( 54,550)( 55,549)( 56,543)
( 57,542)( 58,541)( 59,545)( 60,544)( 61,538)( 62,537)( 63,536)( 64,540)
( 65,539)( 66,533)( 67,532)( 68,531)( 69,535)( 70,534)( 71,528)( 72,527)
( 73,526)( 74,530)( 75,529)( 76,523)( 77,522)( 78,521)( 79,525)( 80,524)
( 81,588)( 82,587)( 83,586)( 84,590)( 85,589)( 86,583)( 87,582)( 88,581)
( 89,585)( 90,584)( 91,598)( 92,597)( 93,596)( 94,600)( 95,599)( 96,593)
( 97,592)( 98,591)( 99,595)(100,594)(101,568)(102,567)(103,566)(104,570)
(105,569)(106,563)(107,562)(108,561)(109,565)(110,564)(111,578)(112,577)
(113,576)(114,580)(115,579)(116,573)(117,572)(118,571)(119,575)(120,574)
(121,613)(122,612)(123,611)(124,615)(125,614)(126,618)(127,617)(128,616)
(129,620)(130,619)(131,603)(132,602)(133,601)(134,605)(135,604)(136,608)
(137,607)(138,606)(139,610)(140,609)(141,638)(142,637)(143,636)(144,640)
(145,639)(146,633)(147,632)(148,631)(149,635)(150,634)(151,628)(152,627)
(153,626)(154,630)(155,629)(156,623)(157,622)(158,621)(159,625)(160,624)
(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)(181,348)(182,347)(183,346)(184,350)
(185,349)(186,343)(187,342)(188,341)(189,345)(190,344)(191,358)(192,357)
(193,356)(194,360)(195,359)(196,353)(197,352)(198,351)(199,355)(200,354)
(201,398)(202,397)(203,396)(204,400)(205,399)(206,393)(207,392)(208,391)
(209,395)(210,394)(211,388)(212,387)(213,386)(214,390)(215,389)(216,383)
(217,382)(218,381)(219,385)(220,384)(221,378)(222,377)(223,376)(224,380)
(225,379)(226,373)(227,372)(228,371)(229,375)(230,374)(231,368)(232,367)
(233,366)(234,370)(235,369)(236,363)(237,362)(238,361)(239,365)(240,364)
(241,428)(242,427)(243,426)(244,430)(245,429)(246,423)(247,422)(248,421)
(249,425)(250,424)(251,438)(252,437)(253,436)(254,440)(255,439)(256,433)
(257,432)(258,431)(259,435)(260,434)(261,408)(262,407)(263,406)(264,410)
(265,409)(266,403)(267,402)(268,401)(269,405)(270,404)(271,418)(272,417)
(273,416)(274,420)(275,419)(276,413)(277,412)(278,411)(279,415)(280,414)
(281,453)(282,452)(283,451)(284,455)(285,454)(286,458)(287,457)(288,456)
(289,460)(290,459)(291,443)(292,442)(293,441)(294,445)(295,444)(296,448)
(297,447)(298,446)(299,450)(300,449)(301,478)(302,477)(303,476)(304,480)
(305,479)(306,473)(307,472)(308,471)(309,475)(310,474)(311,468)(312,467)
(313,466)(314,470)(315,469)(316,463)(317,462)(318,461)(319,465)(320,464);;
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,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*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*s0*s2*s1*s2*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(640)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)
( 8,168)( 9,169)( 10,170)( 11,176)( 12,177)( 13,178)( 14,179)( 15,180)
( 16,171)( 17,172)( 18,173)( 19,174)( 20,175)( 21,186)( 22,187)( 23,188)
( 24,189)( 25,190)( 26,181)( 27,182)( 28,183)( 29,184)( 30,185)( 31,191)
( 32,192)( 33,193)( 34,194)( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)
( 40,200)( 41,201)( 42,202)( 43,203)( 44,204)( 45,205)( 46,206)( 47,207)
( 48,208)( 49,209)( 50,210)( 51,216)( 52,217)( 53,218)( 54,219)( 55,220)
( 56,211)( 57,212)( 58,213)( 59,214)( 60,215)( 61,226)( 62,227)( 63,228)
( 64,229)( 65,230)( 66,221)( 67,222)( 68,223)( 69,224)( 70,225)( 71,231)
( 72,232)( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)
( 80,240)( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,276)( 92,277)( 93,278)( 94,279)( 95,280)
( 96,271)( 97,272)( 98,273)( 99,274)(100,275)(101,241)(102,242)(103,243)
(104,244)(105,245)(106,246)(107,247)(108,248)(109,249)(110,250)(111,256)
(112,257)(113,258)(114,259)(115,260)(116,251)(117,252)(118,253)(119,254)
(120,255)(121,306)(122,307)(123,308)(124,309)(125,310)(126,301)(127,302)
(128,303)(129,304)(130,305)(131,311)(132,312)(133,313)(134,314)(135,315)
(136,316)(137,317)(138,318)(139,319)(140,320)(141,286)(142,287)(143,288)
(144,289)(145,290)(146,281)(147,282)(148,283)(149,284)(150,285)(151,291)
(152,292)(153,293)(154,294)(155,295)(156,296)(157,297)(158,298)(159,299)
(160,300)(321,481)(322,482)(323,483)(324,484)(325,485)(326,486)(327,487)
(328,488)(329,489)(330,490)(331,496)(332,497)(333,498)(334,499)(335,500)
(336,491)(337,492)(338,493)(339,494)(340,495)(341,506)(342,507)(343,508)
(344,509)(345,510)(346,501)(347,502)(348,503)(349,504)(350,505)(351,511)
(352,512)(353,513)(354,514)(355,515)(356,516)(357,517)(358,518)(359,519)
(360,520)(361,521)(362,522)(363,523)(364,524)(365,525)(366,526)(367,527)
(368,528)(369,529)(370,530)(371,536)(372,537)(373,538)(374,539)(375,540)
(376,531)(377,532)(378,533)(379,534)(380,535)(381,546)(382,547)(383,548)
(384,549)(385,550)(386,541)(387,542)(388,543)(389,544)(390,545)(391,551)
(392,552)(393,553)(394,554)(395,555)(396,556)(397,557)(398,558)(399,559)
(400,560)(401,581)(402,582)(403,583)(404,584)(405,585)(406,586)(407,587)
(408,588)(409,589)(410,590)(411,596)(412,597)(413,598)(414,599)(415,600)
(416,591)(417,592)(418,593)(419,594)(420,595)(421,561)(422,562)(423,563)
(424,564)(425,565)(426,566)(427,567)(428,568)(429,569)(430,570)(431,576)
(432,577)(433,578)(434,579)(435,580)(436,571)(437,572)(438,573)(439,574)
(440,575)(441,626)(442,627)(443,628)(444,629)(445,630)(446,621)(447,622)
(448,623)(449,624)(450,625)(451,631)(452,632)(453,633)(454,634)(455,635)
(456,636)(457,637)(458,638)(459,639)(460,640)(461,606)(462,607)(463,608)
(464,609)(465,610)(466,601)(467,602)(468,603)(469,604)(470,605)(471,611)
(472,612)(473,613)(474,614)(475,615)(476,616)(477,617)(478,618)(479,619)
(480,620);
s1 := Sym(640)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)
( 28, 39)( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)
( 53, 54)( 57, 60)( 58, 59)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)
( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81, 86)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)( 91, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)(101,116)
(102,120)(103,119)(104,118)(105,117)(106,111)(107,115)(108,114)(109,113)
(110,112)(121,126)(122,130)(123,129)(124,128)(125,127)(131,136)(132,140)
(133,139)(134,138)(135,137)(141,156)(142,160)(143,159)(144,158)(145,157)
(146,151)(147,155)(148,154)(149,153)(150,152)(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)(181,231)(182,235)(183,234)(184,233)(185,232)(186,236)(187,240)
(188,239)(189,238)(190,237)(191,221)(192,225)(193,224)(194,223)(195,222)
(196,226)(197,230)(198,229)(199,228)(200,227)(241,291)(242,295)(243,294)
(244,293)(245,292)(246,296)(247,300)(248,299)(249,298)(250,297)(251,281)
(252,285)(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)
(260,287)(261,301)(262,305)(263,304)(264,303)(265,302)(266,306)(267,310)
(268,309)(269,308)(270,307)(271,311)(272,315)(273,314)(274,313)(275,312)
(276,316)(277,320)(278,319)(279,318)(280,317)(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)(341,431)(342,435)(343,434)(344,433)(345,432)(346,436)(347,440)
(348,439)(349,438)(350,437)(351,421)(352,425)(353,424)(354,423)(355,422)
(356,426)(357,430)(358,429)(359,428)(360,427)(361,441)(362,445)(363,444)
(364,443)(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,451)
(372,455)(373,454)(374,453)(375,452)(376,456)(377,460)(378,459)(379,458)
(380,457)(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)(481,626)(482,630)(483,629)
(484,628)(485,627)(486,621)(487,625)(488,624)(489,623)(490,622)(491,636)
(492,640)(493,639)(494,638)(495,637)(496,631)(497,635)(498,634)(499,633)
(500,632)(501,611)(502,615)(503,614)(504,613)(505,612)(506,616)(507,620)
(508,619)(509,618)(510,617)(511,601)(512,605)(513,604)(514,603)(515,602)
(516,606)(517,610)(518,609)(519,608)(520,607)(521,581)(522,585)(523,584)
(524,583)(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)
(532,595)(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)
(540,597)(541,576)(542,580)(543,579)(544,578)(545,577)(546,571)(547,575)
(548,574)(549,573)(550,572)(551,566)(552,570)(553,569)(554,568)(555,567)
(556,561)(557,565)(558,564)(559,563)(560,562);
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)( 21,508)( 22,507)( 23,506)
( 24,510)( 25,509)( 26,503)( 27,502)( 28,501)( 29,505)( 30,504)( 31,518)
( 32,517)( 33,516)( 34,520)( 35,519)( 36,513)( 37,512)( 38,511)( 39,515)
( 40,514)( 41,558)( 42,557)( 43,556)( 44,560)( 45,559)( 46,553)( 47,552)
( 48,551)( 49,555)( 50,554)( 51,548)( 52,547)( 53,546)( 54,550)( 55,549)
( 56,543)( 57,542)( 58,541)( 59,545)( 60,544)( 61,538)( 62,537)( 63,536)
( 64,540)( 65,539)( 66,533)( 67,532)( 68,531)( 69,535)( 70,534)( 71,528)
( 72,527)( 73,526)( 74,530)( 75,529)( 76,523)( 77,522)( 78,521)( 79,525)
( 80,524)( 81,588)( 82,587)( 83,586)( 84,590)( 85,589)( 86,583)( 87,582)
( 88,581)( 89,585)( 90,584)( 91,598)( 92,597)( 93,596)( 94,600)( 95,599)
( 96,593)( 97,592)( 98,591)( 99,595)(100,594)(101,568)(102,567)(103,566)
(104,570)(105,569)(106,563)(107,562)(108,561)(109,565)(110,564)(111,578)
(112,577)(113,576)(114,580)(115,579)(116,573)(117,572)(118,571)(119,575)
(120,574)(121,613)(122,612)(123,611)(124,615)(125,614)(126,618)(127,617)
(128,616)(129,620)(130,619)(131,603)(132,602)(133,601)(134,605)(135,604)
(136,608)(137,607)(138,606)(139,610)(140,609)(141,638)(142,637)(143,636)
(144,640)(145,639)(146,633)(147,632)(148,631)(149,635)(150,634)(151,628)
(152,627)(153,626)(154,630)(155,629)(156,623)(157,622)(158,621)(159,625)
(160,624)(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)(181,348)(182,347)(183,346)
(184,350)(185,349)(186,343)(187,342)(188,341)(189,345)(190,344)(191,358)
(192,357)(193,356)(194,360)(195,359)(196,353)(197,352)(198,351)(199,355)
(200,354)(201,398)(202,397)(203,396)(204,400)(205,399)(206,393)(207,392)
(208,391)(209,395)(210,394)(211,388)(212,387)(213,386)(214,390)(215,389)
(216,383)(217,382)(218,381)(219,385)(220,384)(221,378)(222,377)(223,376)
(224,380)(225,379)(226,373)(227,372)(228,371)(229,375)(230,374)(231,368)
(232,367)(233,366)(234,370)(235,369)(236,363)(237,362)(238,361)(239,365)
(240,364)(241,428)(242,427)(243,426)(244,430)(245,429)(246,423)(247,422)
(248,421)(249,425)(250,424)(251,438)(252,437)(253,436)(254,440)(255,439)
(256,433)(257,432)(258,431)(259,435)(260,434)(261,408)(262,407)(263,406)
(264,410)(265,409)(266,403)(267,402)(268,401)(269,405)(270,404)(271,418)
(272,417)(273,416)(274,420)(275,419)(276,413)(277,412)(278,411)(279,415)
(280,414)(281,453)(282,452)(283,451)(284,455)(285,454)(286,458)(287,457)
(288,456)(289,460)(290,459)(291,443)(292,442)(293,441)(294,445)(295,444)
(296,448)(297,447)(298,446)(299,450)(300,449)(301,478)(302,477)(303,476)
(304,480)(305,479)(306,473)(307,472)(308,471)(309,475)(310,474)(311,468)
(312,467)(313,466)(314,470)(315,469)(316,463)(317,462)(318,461)(319,465)
(320,464);
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,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*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*s0*s2*s1*s2*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;
References : None.
to this polytope