Polytope of Type {4,10,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,4,4}*1280
Also Known As : {{4,10|2},{10,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1280,364857)
Rank : 5
Schlafli Type : {4,10,4,4}
Number of vertices, edges, etc : 4, 20, 20, 8, 4
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 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 : {2,10,4,4}*640, {4,10,4,2}*640, {4,10,2,4}*640
   4-fold quotients : {2,10,2,4}*320, {2,10,4,2}*320, {4,10,2,2}*320
   5-fold quotients : {4,2,4,4}*256
   8-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
   10-fold quotients : {2,2,4,4}*128, {4,2,2,4}*128, {4,2,4,2}*128
   16-fold quotients : {2,5,2,2}*80
   20-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)
(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)
( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)( 24,104)
( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)
( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)
( 41,126)( 42,127)( 43,128)( 44,129)( 45,130)( 46,121)( 47,122)( 48,123)
( 49,124)( 50,125)( 51,136)( 52,137)( 53,138)( 54,139)( 55,140)( 56,131)
( 57,132)( 58,133)( 59,134)( 60,135)( 61,146)( 62,147)( 63,148)( 64,149)
( 65,150)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,156)( 72,157)
( 73,158)( 74,159)( 75,160)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)
(161,241)(162,242)(163,243)(164,244)(165,245)(166,246)(167,247)(168,248)
(169,249)(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)(176,256)
(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)(184,264)
(185,265)(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)(192,272)
(193,273)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)
(201,286)(202,287)(203,288)(204,289)(205,290)(206,281)(207,282)(208,283)
(209,284)(210,285)(211,296)(212,297)(213,298)(214,299)(215,300)(216,291)
(217,292)(218,293)(219,294)(220,295)(221,306)(222,307)(223,308)(224,309)
(225,310)(226,301)(227,302)(228,303)(229,304)(230,305)(231,316)(232,317)
(233,318)(234,319)(235,320)(236,311)(237,312)(238,313)(239,314)(240,315)
(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)(328,408)
(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)(336,416)
(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)(344,424)
(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)(352,432)
(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)(360,440)
(361,446)(362,447)(363,448)(364,449)(365,450)(366,441)(367,442)(368,443)
(369,444)(370,445)(371,456)(372,457)(373,458)(374,459)(375,460)(376,451)
(377,452)(378,453)(379,454)(380,455)(381,466)(382,467)(383,468)(384,469)
(385,470)(386,461)(387,462)(388,463)(389,464)(390,465)(391,476)(392,477)
(393,478)(394,479)(395,480)(396,471)(397,472)(398,473)(399,474)(400,475)
(481,561)(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)(488,568)
(489,569)(490,570)(491,571)(492,572)(493,573)(494,574)(495,575)(496,576)
(497,577)(498,578)(499,579)(500,580)(501,581)(502,582)(503,583)(504,584)
(505,585)(506,586)(507,587)(508,588)(509,589)(510,590)(511,591)(512,592)
(513,593)(514,594)(515,595)(516,596)(517,597)(518,598)(519,599)(520,600)
(521,606)(522,607)(523,608)(524,609)(525,610)(526,601)(527,602)(528,603)
(529,604)(530,605)(531,616)(532,617)(533,618)(534,619)(535,620)(536,611)
(537,612)(538,613)(539,614)(540,615)(541,626)(542,627)(543,628)(544,629)
(545,630)(546,621)(547,622)(548,623)(549,624)(550,625)(551,636)(552,637)
(553,638)(554,639)(555,640)(556,631)(557,632)(558,633)(559,634)(560,635);;
s1 := (  1, 41)(  2, 45)(  3, 44)(  4, 43)(  5, 42)(  6, 46)(  7, 50)(  8, 49)
(  9, 48)( 10, 47)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 56)
( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 61)( 22, 65)( 23, 64)( 24, 63)
( 25, 62)( 26, 66)( 27, 70)( 28, 69)( 29, 68)( 30, 67)( 31, 71)( 32, 75)
( 33, 74)( 34, 73)( 35, 72)( 36, 76)( 37, 80)( 38, 79)( 39, 78)( 40, 77)
( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)
( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)( 96,136)
( 97,140)( 98,139)( 99,138)(100,137)(101,141)(102,145)(103,144)(104,143)
(105,142)(106,146)(107,150)(108,149)(109,148)(110,147)(111,151)(112,155)
(113,154)(114,153)(115,152)(116,156)(117,160)(118,159)(119,158)(120,157)
(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)(181,221)(182,225)(183,224)(184,223)
(185,222)(186,226)(187,230)(188,229)(189,228)(190,227)(191,231)(192,235)
(193,234)(194,233)(195,232)(196,236)(197,240)(198,239)(199,238)(200,237)
(241,281)(242,285)(243,284)(244,283)(245,282)(246,286)(247,290)(248,289)
(249,288)(250,287)(251,291)(252,295)(253,294)(254,293)(255,292)(256,296)
(257,300)(258,299)(259,298)(260,297)(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)
(321,361)(322,365)(323,364)(324,363)(325,362)(326,366)(327,370)(328,369)
(329,368)(330,367)(331,371)(332,375)(333,374)(334,373)(335,372)(336,376)
(337,380)(338,379)(339,378)(340,377)(341,381)(342,385)(343,384)(344,383)
(345,382)(346,386)(347,390)(348,389)(349,388)(350,387)(351,391)(352,395)
(353,394)(354,393)(355,392)(356,396)(357,400)(358,399)(359,398)(360,397)
(401,441)(402,445)(403,444)(404,443)(405,442)(406,446)(407,450)(408,449)
(409,448)(410,447)(411,451)(412,455)(413,454)(414,453)(415,452)(416,456)
(417,460)(418,459)(419,458)(420,457)(421,461)(422,465)(423,464)(424,463)
(425,462)(426,466)(427,470)(428,469)(429,468)(430,467)(431,471)(432,475)
(433,474)(434,473)(435,472)(436,476)(437,480)(438,479)(439,478)(440,477)
(481,521)(482,525)(483,524)(484,523)(485,522)(486,526)(487,530)(488,529)
(489,528)(490,527)(491,531)(492,535)(493,534)(494,533)(495,532)(496,536)
(497,540)(498,539)(499,538)(500,537)(501,541)(502,545)(503,544)(504,543)
(505,542)(506,546)(507,550)(508,549)(509,548)(510,547)(511,551)(512,555)
(513,554)(514,553)(515,552)(516,556)(517,560)(518,559)(519,558)(520,557)
(561,601)(562,605)(563,604)(564,603)(565,602)(566,606)(567,610)(568,609)
(569,608)(570,607)(571,611)(572,615)(573,614)(574,613)(575,612)(576,616)
(577,620)(578,619)(579,618)(580,617)(581,621)(582,625)(583,624)(584,623)
(585,622)(586,626)(587,630)(588,629)(589,628)(590,627)(591,631)(592,635)
(593,634)(594,633)(595,632)(596,636)(597,640)(598,639)(599,638)(600,637);;
s2 := (  1,203)(  2,202)(  3,201)(  4,205)(  5,204)(  6,208)(  7,207)(  8,206)
(  9,210)( 10,209)( 11,213)( 12,212)( 13,211)( 14,215)( 15,214)( 16,218)
( 17,217)( 18,216)( 19,220)( 20,219)( 21,223)( 22,222)( 23,221)( 24,225)
( 25,224)( 26,228)( 27,227)( 28,226)( 29,230)( 30,229)( 31,233)( 32,232)
( 33,231)( 34,235)( 35,234)( 36,238)( 37,237)( 38,236)( 39,240)( 40,239)
( 41,163)( 42,162)( 43,161)( 44,165)( 45,164)( 46,168)( 47,167)( 48,166)
( 49,170)( 50,169)( 51,173)( 52,172)( 53,171)( 54,175)( 55,174)( 56,178)
( 57,177)( 58,176)( 59,180)( 60,179)( 61,183)( 62,182)( 63,181)( 64,185)
( 65,184)( 66,188)( 67,187)( 68,186)( 69,190)( 70,189)( 71,193)( 72,192)
( 73,191)( 74,195)( 75,194)( 76,198)( 77,197)( 78,196)( 79,200)( 80,199)
( 81,288)( 82,287)( 83,286)( 84,290)( 85,289)( 86,283)( 87,282)( 88,281)
( 89,285)( 90,284)( 91,298)( 92,297)( 93,296)( 94,300)( 95,299)( 96,293)
( 97,292)( 98,291)( 99,295)(100,294)(101,308)(102,307)(103,306)(104,310)
(105,309)(106,303)(107,302)(108,301)(109,305)(110,304)(111,318)(112,317)
(113,316)(114,320)(115,319)(116,313)(117,312)(118,311)(119,315)(120,314)
(121,248)(122,247)(123,246)(124,250)(125,249)(126,243)(127,242)(128,241)
(129,245)(130,244)(131,258)(132,257)(133,256)(134,260)(135,259)(136,253)
(137,252)(138,251)(139,255)(140,254)(141,268)(142,267)(143,266)(144,270)
(145,269)(146,263)(147,262)(148,261)(149,265)(150,264)(151,278)(152,277)
(153,276)(154,280)(155,279)(156,273)(157,272)(158,271)(159,275)(160,274)
(321,523)(322,522)(323,521)(324,525)(325,524)(326,528)(327,527)(328,526)
(329,530)(330,529)(331,533)(332,532)(333,531)(334,535)(335,534)(336,538)
(337,537)(338,536)(339,540)(340,539)(341,543)(342,542)(343,541)(344,545)
(345,544)(346,548)(347,547)(348,546)(349,550)(350,549)(351,553)(352,552)
(353,551)(354,555)(355,554)(356,558)(357,557)(358,556)(359,560)(360,559)
(361,483)(362,482)(363,481)(364,485)(365,484)(366,488)(367,487)(368,486)
(369,490)(370,489)(371,493)(372,492)(373,491)(374,495)(375,494)(376,498)
(377,497)(378,496)(379,500)(380,499)(381,503)(382,502)(383,501)(384,505)
(385,504)(386,508)(387,507)(388,506)(389,510)(390,509)(391,513)(392,512)
(393,511)(394,515)(395,514)(396,518)(397,517)(398,516)(399,520)(400,519)
(401,608)(402,607)(403,606)(404,610)(405,609)(406,603)(407,602)(408,601)
(409,605)(410,604)(411,618)(412,617)(413,616)(414,620)(415,619)(416,613)
(417,612)(418,611)(419,615)(420,614)(421,628)(422,627)(423,626)(424,630)
(425,629)(426,623)(427,622)(428,621)(429,625)(430,624)(431,638)(432,637)
(433,636)(434,640)(435,639)(436,633)(437,632)(438,631)(439,635)(440,634)
(441,568)(442,567)(443,566)(444,570)(445,569)(446,563)(447,562)(448,561)
(449,565)(450,564)(451,578)(452,577)(453,576)(454,580)(455,579)(456,573)
(457,572)(458,571)(459,575)(460,574)(461,588)(462,587)(463,586)(464,590)
(465,589)(466,583)(467,582)(468,581)(469,585)(470,584)(471,598)(472,597)
(473,596)(474,600)(475,599)(476,593)(477,592)(478,591)(479,595)(480,594);;
s3 := (161,171)(162,172)(163,173)(164,174)(165,175)(166,176)(167,177)(168,178)
(169,179)(170,180)(181,191)(182,192)(183,193)(184,194)(185,195)(186,196)
(187,197)(188,198)(189,199)(190,200)(201,211)(202,212)(203,213)(204,214)
(205,215)(206,216)(207,217)(208,218)(209,219)(210,220)(221,231)(222,232)
(223,233)(224,234)(225,235)(226,236)(227,237)(228,238)(229,239)(230,240)
(241,251)(242,252)(243,253)(244,254)(245,255)(246,256)(247,257)(248,258)
(249,259)(250,260)(261,271)(262,272)(263,273)(264,274)(265,275)(266,276)
(267,277)(268,278)(269,279)(270,280)(281,291)(282,292)(283,293)(284,294)
(285,295)(286,296)(287,297)(288,298)(289,299)(290,300)(301,311)(302,312)
(303,313)(304,314)(305,315)(306,316)(307,317)(308,318)(309,319)(310,320)
(321,341)(322,342)(323,343)(324,344)(325,345)(326,346)(327,347)(328,348)
(329,349)(330,350)(331,351)(332,352)(333,353)(334,354)(335,355)(336,356)
(337,357)(338,358)(339,359)(340,360)(361,381)(362,382)(363,383)(364,384)
(365,385)(366,386)(367,387)(368,388)(369,389)(370,390)(371,391)(372,392)
(373,393)(374,394)(375,395)(376,396)(377,397)(378,398)(379,399)(380,400)
(401,421)(402,422)(403,423)(404,424)(405,425)(406,426)(407,427)(408,428)
(409,429)(410,430)(411,431)(412,432)(413,433)(414,434)(415,435)(416,436)
(417,437)(418,438)(419,439)(420,440)(441,461)(442,462)(443,463)(444,464)
(445,465)(446,466)(447,467)(448,468)(449,469)(450,470)(451,471)(452,472)
(453,473)(454,474)(455,475)(456,476)(457,477)(458,478)(459,479)(460,480)
(481,511)(482,512)(483,513)(484,514)(485,515)(486,516)(487,517)(488,518)
(489,519)(490,520)(491,501)(492,502)(493,503)(494,504)(495,505)(496,506)
(497,507)(498,508)(499,509)(500,510)(521,551)(522,552)(523,553)(524,554)
(525,555)(526,556)(527,557)(528,558)(529,559)(530,560)(531,541)(532,542)
(533,543)(534,544)(535,545)(536,546)(537,547)(538,548)(539,549)(540,550)
(561,591)(562,592)(563,593)(564,594)(565,595)(566,596)(567,597)(568,598)
(569,599)(570,600)(571,581)(572,582)(573,583)(574,584)(575,585)(576,586)
(577,587)(578,588)(579,589)(580,590)(601,631)(602,632)(603,633)(604,634)
(605,635)(606,636)(607,637)(608,638)(609,639)(610,640)(611,621)(612,622)
(613,623)(614,624)(615,625)(616,626)(617,627)(618,628)(619,629)(620,630);;
s4 := (  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)
(161,566)(162,567)(163,568)(164,569)(165,570)(166,561)(167,562)(168,563)
(169,564)(170,565)(171,576)(172,577)(173,578)(174,579)(175,580)(176,571)
(177,572)(178,573)(179,574)(180,575)(181,586)(182,587)(183,588)(184,589)
(185,590)(186,581)(187,582)(188,583)(189,584)(190,585)(191,596)(192,597)
(193,598)(194,599)(195,600)(196,591)(197,592)(198,593)(199,594)(200,595)
(201,606)(202,607)(203,608)(204,609)(205,610)(206,601)(207,602)(208,603)
(209,604)(210,605)(211,616)(212,617)(213,618)(214,619)(215,620)(216,611)
(217,612)(218,613)(219,614)(220,615)(221,626)(222,627)(223,628)(224,629)
(225,630)(226,621)(227,622)(228,623)(229,624)(230,625)(231,636)(232,637)
(233,638)(234,639)(235,640)(236,631)(237,632)(238,633)(239,634)(240,635)
(241,486)(242,487)(243,488)(244,489)(245,490)(246,481)(247,482)(248,483)
(249,484)(250,485)(251,496)(252,497)(253,498)(254,499)(255,500)(256,491)
(257,492)(258,493)(259,494)(260,495)(261,506)(262,507)(263,508)(264,509)
(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,516)(272,517)
(273,518)(274,519)(275,520)(276,511)(277,512)(278,513)(279,514)(280,515)
(281,526)(282,527)(283,528)(284,529)(285,530)(286,521)(287,522)(288,523)
(289,524)(290,525)(291,536)(292,537)(293,538)(294,539)(295,540)(296,531)
(297,532)(298,533)(299,534)(300,535)(301,546)(302,547)(303,548)(304,549)
(305,550)(306,541)(307,542)(308,543)(309,544)(310,545)(311,556)(312,557)
(313,558)(314,559)(315,560)(316,551)(317,552)(318,553)(319,554)(320,555);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)
(  8, 88)(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)
( 16, 96)( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)
( 24,104)( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)
( 32,112)( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)
( 40,120)( 41,126)( 42,127)( 43,128)( 44,129)( 45,130)( 46,121)( 47,122)
( 48,123)( 49,124)( 50,125)( 51,136)( 52,137)( 53,138)( 54,139)( 55,140)
( 56,131)( 57,132)( 58,133)( 59,134)( 60,135)( 61,146)( 62,147)( 63,148)
( 64,149)( 65,150)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,156)
( 72,157)( 73,158)( 74,159)( 75,160)( 76,151)( 77,152)( 78,153)( 79,154)
( 80,155)(161,241)(162,242)(163,243)(164,244)(165,245)(166,246)(167,247)
(168,248)(169,249)(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)
(176,256)(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)
(184,264)(185,265)(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)
(192,272)(193,273)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)
(200,280)(201,286)(202,287)(203,288)(204,289)(205,290)(206,281)(207,282)
(208,283)(209,284)(210,285)(211,296)(212,297)(213,298)(214,299)(215,300)
(216,291)(217,292)(218,293)(219,294)(220,295)(221,306)(222,307)(223,308)
(224,309)(225,310)(226,301)(227,302)(228,303)(229,304)(230,305)(231,316)
(232,317)(233,318)(234,319)(235,320)(236,311)(237,312)(238,313)(239,314)
(240,315)(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)
(328,408)(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)
(336,416)(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)
(344,424)(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)
(352,432)(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)
(360,440)(361,446)(362,447)(363,448)(364,449)(365,450)(366,441)(367,442)
(368,443)(369,444)(370,445)(371,456)(372,457)(373,458)(374,459)(375,460)
(376,451)(377,452)(378,453)(379,454)(380,455)(381,466)(382,467)(383,468)
(384,469)(385,470)(386,461)(387,462)(388,463)(389,464)(390,465)(391,476)
(392,477)(393,478)(394,479)(395,480)(396,471)(397,472)(398,473)(399,474)
(400,475)(481,561)(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)
(488,568)(489,569)(490,570)(491,571)(492,572)(493,573)(494,574)(495,575)
(496,576)(497,577)(498,578)(499,579)(500,580)(501,581)(502,582)(503,583)
(504,584)(505,585)(506,586)(507,587)(508,588)(509,589)(510,590)(511,591)
(512,592)(513,593)(514,594)(515,595)(516,596)(517,597)(518,598)(519,599)
(520,600)(521,606)(522,607)(523,608)(524,609)(525,610)(526,601)(527,602)
(528,603)(529,604)(530,605)(531,616)(532,617)(533,618)(534,619)(535,620)
(536,611)(537,612)(538,613)(539,614)(540,615)(541,626)(542,627)(543,628)
(544,629)(545,630)(546,621)(547,622)(548,623)(549,624)(550,625)(551,636)
(552,637)(553,638)(554,639)(555,640)(556,631)(557,632)(558,633)(559,634)
(560,635);
s1 := Sym(640)!(  1, 41)(  2, 45)(  3, 44)(  4, 43)(  5, 42)(  6, 46)(  7, 50)
(  8, 49)(  9, 48)( 10, 47)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)
( 16, 56)( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 61)( 22, 65)( 23, 64)
( 24, 63)( 25, 62)( 26, 66)( 27, 70)( 28, 69)( 29, 68)( 30, 67)( 31, 71)
( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 76)( 37, 80)( 38, 79)( 39, 78)
( 40, 77)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)
( 88,129)( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)
( 96,136)( 97,140)( 98,139)( 99,138)(100,137)(101,141)(102,145)(103,144)
(104,143)(105,142)(106,146)(107,150)(108,149)(109,148)(110,147)(111,151)
(112,155)(113,154)(114,153)(115,152)(116,156)(117,160)(118,159)(119,158)
(120,157)(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)(181,221)(182,225)(183,224)
(184,223)(185,222)(186,226)(187,230)(188,229)(189,228)(190,227)(191,231)
(192,235)(193,234)(194,233)(195,232)(196,236)(197,240)(198,239)(199,238)
(200,237)(241,281)(242,285)(243,284)(244,283)(245,282)(246,286)(247,290)
(248,289)(249,288)(250,287)(251,291)(252,295)(253,294)(254,293)(255,292)
(256,296)(257,300)(258,299)(259,298)(260,297)(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)(321,361)(322,365)(323,364)(324,363)(325,362)(326,366)(327,370)
(328,369)(329,368)(330,367)(331,371)(332,375)(333,374)(334,373)(335,372)
(336,376)(337,380)(338,379)(339,378)(340,377)(341,381)(342,385)(343,384)
(344,383)(345,382)(346,386)(347,390)(348,389)(349,388)(350,387)(351,391)
(352,395)(353,394)(354,393)(355,392)(356,396)(357,400)(358,399)(359,398)
(360,397)(401,441)(402,445)(403,444)(404,443)(405,442)(406,446)(407,450)
(408,449)(409,448)(410,447)(411,451)(412,455)(413,454)(414,453)(415,452)
(416,456)(417,460)(418,459)(419,458)(420,457)(421,461)(422,465)(423,464)
(424,463)(425,462)(426,466)(427,470)(428,469)(429,468)(430,467)(431,471)
(432,475)(433,474)(434,473)(435,472)(436,476)(437,480)(438,479)(439,478)
(440,477)(481,521)(482,525)(483,524)(484,523)(485,522)(486,526)(487,530)
(488,529)(489,528)(490,527)(491,531)(492,535)(493,534)(494,533)(495,532)
(496,536)(497,540)(498,539)(499,538)(500,537)(501,541)(502,545)(503,544)
(504,543)(505,542)(506,546)(507,550)(508,549)(509,548)(510,547)(511,551)
(512,555)(513,554)(514,553)(515,552)(516,556)(517,560)(518,559)(519,558)
(520,557)(561,601)(562,605)(563,604)(564,603)(565,602)(566,606)(567,610)
(568,609)(569,608)(570,607)(571,611)(572,615)(573,614)(574,613)(575,612)
(576,616)(577,620)(578,619)(579,618)(580,617)(581,621)(582,625)(583,624)
(584,623)(585,622)(586,626)(587,630)(588,629)(589,628)(590,627)(591,631)
(592,635)(593,634)(594,633)(595,632)(596,636)(597,640)(598,639)(599,638)
(600,637);
s2 := Sym(640)!(  1,203)(  2,202)(  3,201)(  4,205)(  5,204)(  6,208)(  7,207)
(  8,206)(  9,210)( 10,209)( 11,213)( 12,212)( 13,211)( 14,215)( 15,214)
( 16,218)( 17,217)( 18,216)( 19,220)( 20,219)( 21,223)( 22,222)( 23,221)
( 24,225)( 25,224)( 26,228)( 27,227)( 28,226)( 29,230)( 30,229)( 31,233)
( 32,232)( 33,231)( 34,235)( 35,234)( 36,238)( 37,237)( 38,236)( 39,240)
( 40,239)( 41,163)( 42,162)( 43,161)( 44,165)( 45,164)( 46,168)( 47,167)
( 48,166)( 49,170)( 50,169)( 51,173)( 52,172)( 53,171)( 54,175)( 55,174)
( 56,178)( 57,177)( 58,176)( 59,180)( 60,179)( 61,183)( 62,182)( 63,181)
( 64,185)( 65,184)( 66,188)( 67,187)( 68,186)( 69,190)( 70,189)( 71,193)
( 72,192)( 73,191)( 74,195)( 75,194)( 76,198)( 77,197)( 78,196)( 79,200)
( 80,199)( 81,288)( 82,287)( 83,286)( 84,290)( 85,289)( 86,283)( 87,282)
( 88,281)( 89,285)( 90,284)( 91,298)( 92,297)( 93,296)( 94,300)( 95,299)
( 96,293)( 97,292)( 98,291)( 99,295)(100,294)(101,308)(102,307)(103,306)
(104,310)(105,309)(106,303)(107,302)(108,301)(109,305)(110,304)(111,318)
(112,317)(113,316)(114,320)(115,319)(116,313)(117,312)(118,311)(119,315)
(120,314)(121,248)(122,247)(123,246)(124,250)(125,249)(126,243)(127,242)
(128,241)(129,245)(130,244)(131,258)(132,257)(133,256)(134,260)(135,259)
(136,253)(137,252)(138,251)(139,255)(140,254)(141,268)(142,267)(143,266)
(144,270)(145,269)(146,263)(147,262)(148,261)(149,265)(150,264)(151,278)
(152,277)(153,276)(154,280)(155,279)(156,273)(157,272)(158,271)(159,275)
(160,274)(321,523)(322,522)(323,521)(324,525)(325,524)(326,528)(327,527)
(328,526)(329,530)(330,529)(331,533)(332,532)(333,531)(334,535)(335,534)
(336,538)(337,537)(338,536)(339,540)(340,539)(341,543)(342,542)(343,541)
(344,545)(345,544)(346,548)(347,547)(348,546)(349,550)(350,549)(351,553)
(352,552)(353,551)(354,555)(355,554)(356,558)(357,557)(358,556)(359,560)
(360,559)(361,483)(362,482)(363,481)(364,485)(365,484)(366,488)(367,487)
(368,486)(369,490)(370,489)(371,493)(372,492)(373,491)(374,495)(375,494)
(376,498)(377,497)(378,496)(379,500)(380,499)(381,503)(382,502)(383,501)
(384,505)(385,504)(386,508)(387,507)(388,506)(389,510)(390,509)(391,513)
(392,512)(393,511)(394,515)(395,514)(396,518)(397,517)(398,516)(399,520)
(400,519)(401,608)(402,607)(403,606)(404,610)(405,609)(406,603)(407,602)
(408,601)(409,605)(410,604)(411,618)(412,617)(413,616)(414,620)(415,619)
(416,613)(417,612)(418,611)(419,615)(420,614)(421,628)(422,627)(423,626)
(424,630)(425,629)(426,623)(427,622)(428,621)(429,625)(430,624)(431,638)
(432,637)(433,636)(434,640)(435,639)(436,633)(437,632)(438,631)(439,635)
(440,634)(441,568)(442,567)(443,566)(444,570)(445,569)(446,563)(447,562)
(448,561)(449,565)(450,564)(451,578)(452,577)(453,576)(454,580)(455,579)
(456,573)(457,572)(458,571)(459,575)(460,574)(461,588)(462,587)(463,586)
(464,590)(465,589)(466,583)(467,582)(468,581)(469,585)(470,584)(471,598)
(472,597)(473,596)(474,600)(475,599)(476,593)(477,592)(478,591)(479,595)
(480,594);
s3 := Sym(640)!(161,171)(162,172)(163,173)(164,174)(165,175)(166,176)(167,177)
(168,178)(169,179)(170,180)(181,191)(182,192)(183,193)(184,194)(185,195)
(186,196)(187,197)(188,198)(189,199)(190,200)(201,211)(202,212)(203,213)
(204,214)(205,215)(206,216)(207,217)(208,218)(209,219)(210,220)(221,231)
(222,232)(223,233)(224,234)(225,235)(226,236)(227,237)(228,238)(229,239)
(230,240)(241,251)(242,252)(243,253)(244,254)(245,255)(246,256)(247,257)
(248,258)(249,259)(250,260)(261,271)(262,272)(263,273)(264,274)(265,275)
(266,276)(267,277)(268,278)(269,279)(270,280)(281,291)(282,292)(283,293)
(284,294)(285,295)(286,296)(287,297)(288,298)(289,299)(290,300)(301,311)
(302,312)(303,313)(304,314)(305,315)(306,316)(307,317)(308,318)(309,319)
(310,320)(321,341)(322,342)(323,343)(324,344)(325,345)(326,346)(327,347)
(328,348)(329,349)(330,350)(331,351)(332,352)(333,353)(334,354)(335,355)
(336,356)(337,357)(338,358)(339,359)(340,360)(361,381)(362,382)(363,383)
(364,384)(365,385)(366,386)(367,387)(368,388)(369,389)(370,390)(371,391)
(372,392)(373,393)(374,394)(375,395)(376,396)(377,397)(378,398)(379,399)
(380,400)(401,421)(402,422)(403,423)(404,424)(405,425)(406,426)(407,427)
(408,428)(409,429)(410,430)(411,431)(412,432)(413,433)(414,434)(415,435)
(416,436)(417,437)(418,438)(419,439)(420,440)(441,461)(442,462)(443,463)
(444,464)(445,465)(446,466)(447,467)(448,468)(449,469)(450,470)(451,471)
(452,472)(453,473)(454,474)(455,475)(456,476)(457,477)(458,478)(459,479)
(460,480)(481,511)(482,512)(483,513)(484,514)(485,515)(486,516)(487,517)
(488,518)(489,519)(490,520)(491,501)(492,502)(493,503)(494,504)(495,505)
(496,506)(497,507)(498,508)(499,509)(500,510)(521,551)(522,552)(523,553)
(524,554)(525,555)(526,556)(527,557)(528,558)(529,559)(530,560)(531,541)
(532,542)(533,543)(534,544)(535,545)(536,546)(537,547)(538,548)(539,549)
(540,550)(561,591)(562,592)(563,593)(564,594)(565,595)(566,596)(567,597)
(568,598)(569,599)(570,600)(571,581)(572,582)(573,583)(574,584)(575,585)
(576,586)(577,587)(578,588)(579,589)(580,590)(601,631)(602,632)(603,633)
(604,634)(605,635)(606,636)(607,637)(608,638)(609,639)(610,640)(611,621)
(612,622)(613,623)(614,624)(615,625)(616,626)(617,627)(618,628)(619,629)
(620,630);
s4 := 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)(161,566)(162,567)(163,568)(164,569)(165,570)(166,561)(167,562)
(168,563)(169,564)(170,565)(171,576)(172,577)(173,578)(174,579)(175,580)
(176,571)(177,572)(178,573)(179,574)(180,575)(181,586)(182,587)(183,588)
(184,589)(185,590)(186,581)(187,582)(188,583)(189,584)(190,585)(191,596)
(192,597)(193,598)(194,599)(195,600)(196,591)(197,592)(198,593)(199,594)
(200,595)(201,606)(202,607)(203,608)(204,609)(205,610)(206,601)(207,602)
(208,603)(209,604)(210,605)(211,616)(212,617)(213,618)(214,619)(215,620)
(216,611)(217,612)(218,613)(219,614)(220,615)(221,626)(222,627)(223,628)
(224,629)(225,630)(226,621)(227,622)(228,623)(229,624)(230,625)(231,636)
(232,637)(233,638)(234,639)(235,640)(236,631)(237,632)(238,633)(239,634)
(240,635)(241,486)(242,487)(243,488)(244,489)(245,490)(246,481)(247,482)
(248,483)(249,484)(250,485)(251,496)(252,497)(253,498)(254,499)(255,500)
(256,491)(257,492)(258,493)(259,494)(260,495)(261,506)(262,507)(263,508)
(264,509)(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,516)
(272,517)(273,518)(274,519)(275,520)(276,511)(277,512)(278,513)(279,514)
(280,515)(281,526)(282,527)(283,528)(284,529)(285,530)(286,521)(287,522)
(288,523)(289,524)(290,525)(291,536)(292,537)(293,538)(294,539)(295,540)
(296,531)(297,532)(298,533)(299,534)(300,535)(301,546)(302,547)(303,548)
(304,549)(305,550)(306,541)(307,542)(308,543)(309,544)(310,545)(311,556)
(312,557)(313,558)(314,559)(315,560)(316,551)(317,552)(318,553)(319,554)
(320,555);
poly := sub<Sym(640)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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