Polytope of Type {40,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,4,4}*1280a
Also Known As : {{40,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1280,200568)
Rank : 4
Schlafli Type : {40,4,4}
Number of vertices, edges, etc : 40, 80, 8, 4
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {20,4,4}*640, {40,4,2}*640a, {40,2,4}*640
4-fold quotients : {20,4,2}*320, {20,2,4}*320, {10,4,4}*320, {40,2,2}*320
5-fold quotients : {8,4,4}*256a
8-fold quotients : {20,2,2}*160, {10,2,4}*160, {10,4,2}*160
10-fold quotients : {4,4,4}*128, {8,4,2}*128a, {8,2,4}*128
16-fold quotients : {5,2,4}*80, {10,2,2}*80
20-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {8,2,2}*64
32-fold quotients : {5,2,2}*40
40-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)( 8, 89)
( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)
( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)( 24,103)
( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)( 32,115)
( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,126)( 42,130)( 43,129)( 44,128)( 45,127)( 46,121)( 47,125)( 48,124)
( 49,123)( 50,122)( 51,136)( 52,140)( 53,139)( 54,138)( 55,137)( 56,131)
( 57,135)( 58,134)( 59,133)( 60,132)( 61,146)( 62,150)( 63,149)( 64,148)
( 65,147)( 66,141)( 67,145)( 68,144)( 69,143)( 70,142)( 71,156)( 72,160)
( 73,159)( 74,158)( 75,157)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)
(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)(168,249)
(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)(176,256)
(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)(184,263)
(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)(192,275)
(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)(200,277)
(201,286)(202,290)(203,289)(204,288)(205,287)(206,281)(207,285)(208,284)
(209,283)(210,282)(211,296)(212,300)(213,299)(214,298)(215,297)(216,291)
(217,295)(218,294)(219,293)(220,292)(221,306)(222,310)(223,309)(224,308)
(225,307)(226,301)(227,305)(228,304)(229,303)(230,302)(231,316)(232,320)
(233,319)(234,318)(235,317)(236,311)(237,315)(238,314)(239,313)(240,312)
(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)(341,421)(342,425)(343,424)(344,423)
(345,422)(346,426)(347,430)(348,429)(349,428)(350,427)(351,431)(352,435)
(353,434)(354,433)(355,432)(356,436)(357,440)(358,439)(359,438)(360,437)
(361,446)(362,450)(363,449)(364,448)(365,447)(366,441)(367,445)(368,444)
(369,443)(370,442)(371,456)(372,460)(373,459)(374,458)(375,457)(376,451)
(377,455)(378,454)(379,453)(380,452)(381,466)(382,470)(383,469)(384,468)
(385,467)(386,461)(387,465)(388,464)(389,463)(390,462)(391,476)(392,480)
(393,479)(394,478)(395,477)(396,471)(397,475)(398,474)(399,473)(400,472)
(481,561)(482,565)(483,564)(484,563)(485,562)(486,566)(487,570)(488,569)
(489,568)(490,567)(491,571)(492,575)(493,574)(494,573)(495,572)(496,576)
(497,580)(498,579)(499,578)(500,577)(501,581)(502,585)(503,584)(504,583)
(505,582)(506,586)(507,590)(508,589)(509,588)(510,587)(511,591)(512,595)
(513,594)(514,593)(515,592)(516,596)(517,600)(518,599)(519,598)(520,597)
(521,606)(522,610)(523,609)(524,608)(525,607)(526,601)(527,605)(528,604)
(529,603)(530,602)(531,616)(532,620)(533,619)(534,618)(535,617)(536,611)
(537,615)(538,614)(539,613)(540,612)(541,626)(542,630)(543,629)(544,628)
(545,627)(546,621)(547,625)(548,624)(549,623)(550,622)(551,636)(552,640)
(553,639)(554,638)(555,637)(556,631)(557,635)(558,634)(559,633)(560,632);;
s1 := ( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)
( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 33)( 34, 35)( 36, 38)( 39, 40)
( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 58)( 52, 57)( 53, 56)
( 54, 60)( 55, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 70)( 65, 69)( 71, 78)
( 72, 77)( 73, 76)( 74, 80)( 75, 79)( 81,123)( 82,122)( 83,121)( 84,125)
( 85,124)( 86,128)( 87,127)( 88,126)( 89,130)( 90,129)( 91,133)( 92,132)
( 93,131)( 94,135)( 95,134)( 96,138)( 97,137)( 98,136)( 99,140)(100,139)
(101,143)(102,142)(103,141)(104,145)(105,144)(106,148)(107,147)(108,146)
(109,150)(110,149)(111,153)(112,152)(113,151)(114,155)(115,154)(116,158)
(117,157)(118,156)(119,160)(120,159)(161,183)(162,182)(163,181)(164,185)
(165,184)(166,188)(167,187)(168,186)(169,190)(170,189)(171,193)(172,192)
(173,191)(174,195)(175,194)(176,198)(177,197)(178,196)(179,200)(180,199)
(201,228)(202,227)(203,226)(204,230)(205,229)(206,223)(207,222)(208,221)
(209,225)(210,224)(211,238)(212,237)(213,236)(214,240)(215,239)(216,233)
(217,232)(218,231)(219,235)(220,234)(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)(321,363)(322,362)(323,361)(324,365)
(325,364)(326,368)(327,367)(328,366)(329,370)(330,369)(331,373)(332,372)
(333,371)(334,375)(335,374)(336,378)(337,377)(338,376)(339,380)(340,379)
(341,383)(342,382)(343,381)(344,385)(345,384)(346,388)(347,387)(348,386)
(349,390)(350,389)(351,393)(352,392)(353,391)(354,395)(355,394)(356,398)
(357,397)(358,396)(359,400)(360,399)(401,403)(404,405)(406,408)(409,410)
(411,413)(414,415)(416,418)(419,420)(421,423)(424,425)(426,428)(429,430)
(431,433)(434,435)(436,438)(439,440)(441,448)(442,447)(443,446)(444,450)
(445,449)(451,458)(452,457)(453,456)(454,460)(455,459)(461,468)(462,467)
(463,466)(464,470)(465,469)(471,478)(472,477)(473,476)(474,480)(475,479)
(481,543)(482,542)(483,541)(484,545)(485,544)(486,548)(487,547)(488,546)
(489,550)(490,549)(491,553)(492,552)(493,551)(494,555)(495,554)(496,558)
(497,557)(498,556)(499,560)(500,559)(501,523)(502,522)(503,521)(504,525)
(505,524)(506,528)(507,527)(508,526)(509,530)(510,529)(511,533)(512,532)
(513,531)(514,535)(515,534)(516,538)(517,537)(518,536)(519,540)(520,539)
(561,583)(562,582)(563,581)(564,585)(565,584)(566,588)(567,587)(568,586)
(569,590)(570,589)(571,593)(572,592)(573,591)(574,595)(575,594)(576,598)
(577,597)(578,596)(579,600)(580,599)(601,628)(602,627)(603,626)(604,630)
(605,629)(606,623)(607,622)(608,621)(609,625)(610,624)(611,638)(612,637)
(613,636)(614,640)(615,639)(616,633)(617,632)(618,631)(619,635)(620,634);;
s2 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)
( 9,169)( 10,170)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)( 16,176)
( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)( 24,184)
( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 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)( 51,211)( 52,212)( 53,213)( 54,214)( 55,215)( 56,216)
( 57,217)( 58,218)( 59,219)( 60,220)( 61,221)( 62,222)( 63,223)( 64,224)
( 65,225)( 66,226)( 67,227)( 68,228)( 69,229)( 70,230)( 71,231)( 72,232)
( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)( 80,240)
( 81,241)( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)( 88,248)
( 89,249)( 90,250)( 91,251)( 92,252)( 93,253)( 94,254)( 95,255)( 96,256)
( 97,257)( 98,258)( 99,259)(100,260)(101,261)(102,262)(103,263)(104,264)
(105,265)(106,266)(107,267)(108,268)(109,269)(110,270)(111,271)(112,272)
(113,273)(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)
(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)(128,288)
(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)(136,296)
(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)(144,304)
(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)(152,312)
(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)(160,320)
(321,481)(322,482)(323,483)(324,484)(325,485)(326,486)(327,487)(328,488)
(329,489)(330,490)(331,491)(332,492)(333,493)(334,494)(335,495)(336,496)
(337,497)(338,498)(339,499)(340,500)(341,501)(342,502)(343,503)(344,504)
(345,505)(346,506)(347,507)(348,508)(349,509)(350,510)(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)(371,531)(372,532)(373,533)(374,534)(375,535)(376,536)
(377,537)(378,538)(379,539)(380,540)(381,541)(382,542)(383,543)(384,544)
(385,545)(386,546)(387,547)(388,548)(389,549)(390,550)(391,551)(392,552)
(393,553)(394,554)(395,555)(396,556)(397,557)(398,558)(399,559)(400,560)
(401,561)(402,562)(403,563)(404,564)(405,565)(406,566)(407,567)(408,568)
(409,569)(410,570)(411,571)(412,572)(413,573)(414,574)(415,575)(416,576)
(417,577)(418,578)(419,579)(420,580)(421,581)(422,582)(423,583)(424,584)
(425,585)(426,586)(427,587)(428,588)(429,589)(430,590)(431,591)(432,592)
(433,593)(434,594)(435,595)(436,596)(437,597)(438,598)(439,599)(440,600)
(441,601)(442,602)(443,603)(444,604)(445,605)(446,606)(447,607)(448,608)
(449,609)(450,610)(451,611)(452,612)(453,613)(454,614)(455,615)(456,616)
(457,617)(458,618)(459,619)(460,620)(461,621)(462,622)(463,623)(464,624)
(465,625)(466,626)(467,627)(468,628)(469,629)(470,630)(471,631)(472,632)
(473,633)(474,634)(475,635)(476,636)(477,637)(478,638)(479,639)(480,640);;
s3 := ( 1,401)( 2,402)( 3,403)( 4,404)( 5,405)( 6,406)( 7,407)( 8,408)
( 9,409)( 10,410)( 11,411)( 12,412)( 13,413)( 14,414)( 15,415)( 16,416)
( 17,417)( 18,418)( 19,419)( 20,420)( 21,421)( 22,422)( 23,423)( 24,424)
( 25,425)( 26,426)( 27,427)( 28,428)( 29,429)( 30,430)( 31,431)( 32,432)
( 33,433)( 34,434)( 35,435)( 36,436)( 37,437)( 38,438)( 39,439)( 40,440)
( 41,441)( 42,442)( 43,443)( 44,444)( 45,445)( 46,446)( 47,447)( 48,448)
( 49,449)( 50,450)( 51,451)( 52,452)( 53,453)( 54,454)( 55,455)( 56,456)
( 57,457)( 58,458)( 59,459)( 60,460)( 61,461)( 62,462)( 63,463)( 64,464)
( 65,465)( 66,466)( 67,467)( 68,468)( 69,469)( 70,470)( 71,471)( 72,472)
( 73,473)( 74,474)( 75,475)( 76,476)( 77,477)( 78,478)( 79,479)( 80,480)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,571)(162,572)(163,573)(164,574)(165,575)(166,576)(167,577)(168,578)
(169,579)(170,580)(171,561)(172,562)(173,563)(174,564)(175,565)(176,566)
(177,567)(178,568)(179,569)(180,570)(181,591)(182,592)(183,593)(184,594)
(185,595)(186,596)(187,597)(188,598)(189,599)(190,600)(191,581)(192,582)
(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)(200,590)
(201,611)(202,612)(203,613)(204,614)(205,615)(206,616)(207,617)(208,618)
(209,619)(210,620)(211,601)(212,602)(213,603)(214,604)(215,605)(216,606)
(217,607)(218,608)(219,609)(220,610)(221,631)(222,632)(223,633)(224,634)
(225,635)(226,636)(227,637)(228,638)(229,639)(230,640)(231,621)(232,622)
(233,623)(234,624)(235,625)(236,626)(237,627)(238,628)(239,629)(240,630)
(241,491)(242,492)(243,493)(244,494)(245,495)(246,496)(247,497)(248,498)
(249,499)(250,500)(251,481)(252,482)(253,483)(254,484)(255,485)(256,486)
(257,487)(258,488)(259,489)(260,490)(261,511)(262,512)(263,513)(264,514)
(265,515)(266,516)(267,517)(268,518)(269,519)(270,520)(271,501)(272,502)
(273,503)(274,504)(275,505)(276,506)(277,507)(278,508)(279,509)(280,510)
(281,531)(282,532)(283,533)(284,534)(285,535)(286,536)(287,537)(288,538)
(289,539)(290,540)(291,521)(292,522)(293,523)(294,524)(295,525)(296,526)
(297,527)(298,528)(299,529)(300,530)(301,551)(302,552)(303,553)(304,554)
(305,555)(306,556)(307,557)(308,558)(309,559)(310,560)(311,541)(312,542)
(313,543)(314,544)(315,545)(316,546)(317,547)(318,548)(319,549)(320,550);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)
( 8, 89)( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)
( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)
( 24,103)( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)
( 32,115)( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,126)( 42,130)( 43,129)( 44,128)( 45,127)( 46,121)( 47,125)
( 48,124)( 49,123)( 50,122)( 51,136)( 52,140)( 53,139)( 54,138)( 55,137)
( 56,131)( 57,135)( 58,134)( 59,133)( 60,132)( 61,146)( 62,150)( 63,149)
( 64,148)( 65,147)( 66,141)( 67,145)( 68,144)( 69,143)( 70,142)( 71,156)
( 72,160)( 73,159)( 74,158)( 75,157)( 76,151)( 77,155)( 78,154)( 79,153)
( 80,152)(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)
(168,249)(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)
(176,256)(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)
(184,263)(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)
(192,275)(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)
(200,277)(201,286)(202,290)(203,289)(204,288)(205,287)(206,281)(207,285)
(208,284)(209,283)(210,282)(211,296)(212,300)(213,299)(214,298)(215,297)
(216,291)(217,295)(218,294)(219,293)(220,292)(221,306)(222,310)(223,309)
(224,308)(225,307)(226,301)(227,305)(228,304)(229,303)(230,302)(231,316)
(232,320)(233,319)(234,318)(235,317)(236,311)(237,315)(238,314)(239,313)
(240,312)(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)(341,421)(342,425)(343,424)
(344,423)(345,422)(346,426)(347,430)(348,429)(349,428)(350,427)(351,431)
(352,435)(353,434)(354,433)(355,432)(356,436)(357,440)(358,439)(359,438)
(360,437)(361,446)(362,450)(363,449)(364,448)(365,447)(366,441)(367,445)
(368,444)(369,443)(370,442)(371,456)(372,460)(373,459)(374,458)(375,457)
(376,451)(377,455)(378,454)(379,453)(380,452)(381,466)(382,470)(383,469)
(384,468)(385,467)(386,461)(387,465)(388,464)(389,463)(390,462)(391,476)
(392,480)(393,479)(394,478)(395,477)(396,471)(397,475)(398,474)(399,473)
(400,472)(481,561)(482,565)(483,564)(484,563)(485,562)(486,566)(487,570)
(488,569)(489,568)(490,567)(491,571)(492,575)(493,574)(494,573)(495,572)
(496,576)(497,580)(498,579)(499,578)(500,577)(501,581)(502,585)(503,584)
(504,583)(505,582)(506,586)(507,590)(508,589)(509,588)(510,587)(511,591)
(512,595)(513,594)(514,593)(515,592)(516,596)(517,600)(518,599)(519,598)
(520,597)(521,606)(522,610)(523,609)(524,608)(525,607)(526,601)(527,605)
(528,604)(529,603)(530,602)(531,616)(532,620)(533,619)(534,618)(535,617)
(536,611)(537,615)(538,614)(539,613)(540,612)(541,626)(542,630)(543,629)
(544,628)(545,627)(546,621)(547,625)(548,624)(549,623)(550,622)(551,636)
(552,640)(553,639)(554,638)(555,637)(556,631)(557,635)(558,634)(559,633)
(560,632);
s1 := Sym(640)!( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 13)( 14, 15)( 16, 18)
( 19, 20)( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 33)( 34, 35)( 36, 38)
( 39, 40)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 58)( 52, 57)
( 53, 56)( 54, 60)( 55, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 70)( 65, 69)
( 71, 78)( 72, 77)( 73, 76)( 74, 80)( 75, 79)( 81,123)( 82,122)( 83,121)
( 84,125)( 85,124)( 86,128)( 87,127)( 88,126)( 89,130)( 90,129)( 91,133)
( 92,132)( 93,131)( 94,135)( 95,134)( 96,138)( 97,137)( 98,136)( 99,140)
(100,139)(101,143)(102,142)(103,141)(104,145)(105,144)(106,148)(107,147)
(108,146)(109,150)(110,149)(111,153)(112,152)(113,151)(114,155)(115,154)
(116,158)(117,157)(118,156)(119,160)(120,159)(161,183)(162,182)(163,181)
(164,185)(165,184)(166,188)(167,187)(168,186)(169,190)(170,189)(171,193)
(172,192)(173,191)(174,195)(175,194)(176,198)(177,197)(178,196)(179,200)
(180,199)(201,228)(202,227)(203,226)(204,230)(205,229)(206,223)(207,222)
(208,221)(209,225)(210,224)(211,238)(212,237)(213,236)(214,240)(215,239)
(216,233)(217,232)(218,231)(219,235)(220,234)(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)(321,363)(322,362)(323,361)
(324,365)(325,364)(326,368)(327,367)(328,366)(329,370)(330,369)(331,373)
(332,372)(333,371)(334,375)(335,374)(336,378)(337,377)(338,376)(339,380)
(340,379)(341,383)(342,382)(343,381)(344,385)(345,384)(346,388)(347,387)
(348,386)(349,390)(350,389)(351,393)(352,392)(353,391)(354,395)(355,394)
(356,398)(357,397)(358,396)(359,400)(360,399)(401,403)(404,405)(406,408)
(409,410)(411,413)(414,415)(416,418)(419,420)(421,423)(424,425)(426,428)
(429,430)(431,433)(434,435)(436,438)(439,440)(441,448)(442,447)(443,446)
(444,450)(445,449)(451,458)(452,457)(453,456)(454,460)(455,459)(461,468)
(462,467)(463,466)(464,470)(465,469)(471,478)(472,477)(473,476)(474,480)
(475,479)(481,543)(482,542)(483,541)(484,545)(485,544)(486,548)(487,547)
(488,546)(489,550)(490,549)(491,553)(492,552)(493,551)(494,555)(495,554)
(496,558)(497,557)(498,556)(499,560)(500,559)(501,523)(502,522)(503,521)
(504,525)(505,524)(506,528)(507,527)(508,526)(509,530)(510,529)(511,533)
(512,532)(513,531)(514,535)(515,534)(516,538)(517,537)(518,536)(519,540)
(520,539)(561,583)(562,582)(563,581)(564,585)(565,584)(566,588)(567,587)
(568,586)(569,590)(570,589)(571,593)(572,592)(573,591)(574,595)(575,594)
(576,598)(577,597)(578,596)(579,600)(580,599)(601,628)(602,627)(603,626)
(604,630)(605,629)(606,623)(607,622)(608,621)(609,625)(610,624)(611,638)
(612,637)(613,636)(614,640)(615,639)(616,633)(617,632)(618,631)(619,635)
(620,634);
s2 := Sym(640)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)
( 8,168)( 9,169)( 10,170)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)
( 16,176)( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)
( 24,184)( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 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)( 51,211)( 52,212)( 53,213)( 54,214)( 55,215)
( 56,216)( 57,217)( 58,218)( 59,219)( 60,220)( 61,221)( 62,222)( 63,223)
( 64,224)( 65,225)( 66,226)( 67,227)( 68,228)( 69,229)( 70,230)( 71,231)
( 72,232)( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)
( 80,240)( 81,241)( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)
( 88,248)( 89,249)( 90,250)( 91,251)( 92,252)( 93,253)( 94,254)( 95,255)
( 96,256)( 97,257)( 98,258)( 99,259)(100,260)(101,261)(102,262)(103,263)
(104,264)(105,265)(106,266)(107,267)(108,268)(109,269)(110,270)(111,271)
(112,272)(113,273)(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)
(120,280)(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)
(128,288)(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)
(136,296)(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)
(144,304)(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)
(152,312)(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)
(160,320)(321,481)(322,482)(323,483)(324,484)(325,485)(326,486)(327,487)
(328,488)(329,489)(330,490)(331,491)(332,492)(333,493)(334,494)(335,495)
(336,496)(337,497)(338,498)(339,499)(340,500)(341,501)(342,502)(343,503)
(344,504)(345,505)(346,506)(347,507)(348,508)(349,509)(350,510)(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)(371,531)(372,532)(373,533)(374,534)(375,535)
(376,536)(377,537)(378,538)(379,539)(380,540)(381,541)(382,542)(383,543)
(384,544)(385,545)(386,546)(387,547)(388,548)(389,549)(390,550)(391,551)
(392,552)(393,553)(394,554)(395,555)(396,556)(397,557)(398,558)(399,559)
(400,560)(401,561)(402,562)(403,563)(404,564)(405,565)(406,566)(407,567)
(408,568)(409,569)(410,570)(411,571)(412,572)(413,573)(414,574)(415,575)
(416,576)(417,577)(418,578)(419,579)(420,580)(421,581)(422,582)(423,583)
(424,584)(425,585)(426,586)(427,587)(428,588)(429,589)(430,590)(431,591)
(432,592)(433,593)(434,594)(435,595)(436,596)(437,597)(438,598)(439,599)
(440,600)(441,601)(442,602)(443,603)(444,604)(445,605)(446,606)(447,607)
(448,608)(449,609)(450,610)(451,611)(452,612)(453,613)(454,614)(455,615)
(456,616)(457,617)(458,618)(459,619)(460,620)(461,621)(462,622)(463,623)
(464,624)(465,625)(466,626)(467,627)(468,628)(469,629)(470,630)(471,631)
(472,632)(473,633)(474,634)(475,635)(476,636)(477,637)(478,638)(479,639)
(480,640);
s3 := Sym(640)!( 1,401)( 2,402)( 3,403)( 4,404)( 5,405)( 6,406)( 7,407)
( 8,408)( 9,409)( 10,410)( 11,411)( 12,412)( 13,413)( 14,414)( 15,415)
( 16,416)( 17,417)( 18,418)( 19,419)( 20,420)( 21,421)( 22,422)( 23,423)
( 24,424)( 25,425)( 26,426)( 27,427)( 28,428)( 29,429)( 30,430)( 31,431)
( 32,432)( 33,433)( 34,434)( 35,435)( 36,436)( 37,437)( 38,438)( 39,439)
( 40,440)( 41,441)( 42,442)( 43,443)( 44,444)( 45,445)( 46,446)( 47,447)
( 48,448)( 49,449)( 50,450)( 51,451)( 52,452)( 53,453)( 54,454)( 55,455)
( 56,456)( 57,457)( 58,458)( 59,459)( 60,460)( 61,461)( 62,462)( 63,463)
( 64,464)( 65,465)( 66,466)( 67,467)( 68,468)( 69,469)( 70,470)( 71,471)
( 72,472)( 73,473)( 74,474)( 75,475)( 76,476)( 77,477)( 78,478)( 79,479)
( 80,480)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,571)(162,572)(163,573)(164,574)(165,575)(166,576)(167,577)
(168,578)(169,579)(170,580)(171,561)(172,562)(173,563)(174,564)(175,565)
(176,566)(177,567)(178,568)(179,569)(180,570)(181,591)(182,592)(183,593)
(184,594)(185,595)(186,596)(187,597)(188,598)(189,599)(190,600)(191,581)
(192,582)(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)
(200,590)(201,611)(202,612)(203,613)(204,614)(205,615)(206,616)(207,617)
(208,618)(209,619)(210,620)(211,601)(212,602)(213,603)(214,604)(215,605)
(216,606)(217,607)(218,608)(219,609)(220,610)(221,631)(222,632)(223,633)
(224,634)(225,635)(226,636)(227,637)(228,638)(229,639)(230,640)(231,621)
(232,622)(233,623)(234,624)(235,625)(236,626)(237,627)(238,628)(239,629)
(240,630)(241,491)(242,492)(243,493)(244,494)(245,495)(246,496)(247,497)
(248,498)(249,499)(250,500)(251,481)(252,482)(253,483)(254,484)(255,485)
(256,486)(257,487)(258,488)(259,489)(260,490)(261,511)(262,512)(263,513)
(264,514)(265,515)(266,516)(267,517)(268,518)(269,519)(270,520)(271,501)
(272,502)(273,503)(274,504)(275,505)(276,506)(277,507)(278,508)(279,509)
(280,510)(281,531)(282,532)(283,533)(284,534)(285,535)(286,536)(287,537)
(288,538)(289,539)(290,540)(291,521)(292,522)(293,523)(294,524)(295,525)
(296,526)(297,527)(298,528)(299,529)(300,530)(301,551)(302,552)(303,553)
(304,554)(305,555)(306,556)(307,557)(308,558)(309,559)(310,560)(311,541)
(312,542)(313,543)(314,544)(315,545)(316,546)(317,547)(318,548)(319,549)
(320,550);
poly := sub<Sym(640)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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