Polytope of Type {16,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,10,4}*1280
Also Known As : {{16,10|2},{10,4|2}}. if this polytope has another name.
Group : SmallGroup(1280,326216)
Rank : 4
Schlafli Type : {16,10,4}
Number of vertices, edges, etc : 16, 80, 20, 4
Order of s0s1s2s3 : 80
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 : {8,10,4}*640, {16,10,2}*640
4-fold quotients : {4,10,4}*320, {8,10,2}*320
5-fold quotients : {16,2,4}*256
8-fold quotients : {2,10,4}*160, {4,10,2}*160
10-fold quotients : {8,2,4}*128, {16,2,2}*128
16-fold quotients : {2,10,2}*80
20-fold quotients : {4,2,4}*64, {8,2,2}*64
32-fold quotients : {2,5,2}*40
40-fold quotients : {2,2,4}*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 := ( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)( 8,328)
( 9,329)( 10,330)( 11,336)( 12,337)( 13,338)( 14,339)( 15,340)( 16,331)
( 17,332)( 18,333)( 19,334)( 20,335)( 21,341)( 22,342)( 23,343)( 24,344)
( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,356)( 32,357)
( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)( 40,355)
( 41,371)( 42,372)( 43,373)( 44,374)( 45,375)( 46,376)( 47,377)( 48,378)
( 49,379)( 50,380)( 51,361)( 52,362)( 53,363)( 54,364)( 55,365)( 56,366)
( 57,367)( 58,368)( 59,369)( 60,370)( 61,391)( 62,392)( 63,393)( 64,394)
( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)( 72,382)
( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)( 80,390)
( 81,441)( 82,442)( 83,443)( 84,444)( 85,445)( 86,446)( 87,447)( 88,448)
( 89,449)( 90,450)( 91,456)( 92,457)( 93,458)( 94,459)( 95,460)( 96,451)
( 97,452)( 98,453)( 99,454)(100,455)(101,461)(102,462)(103,463)(104,464)
(105,465)(106,466)(107,467)(108,468)(109,469)(110,470)(111,476)(112,477)
(113,478)(114,479)(115,480)(116,471)(117,472)(118,473)(119,474)(120,475)
(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)(128,408)
(129,409)(130,410)(131,416)(132,417)(133,418)(134,419)(135,420)(136,411)
(137,412)(138,413)(139,414)(140,415)(141,421)(142,422)(143,423)(144,424)
(145,425)(146,426)(147,427)(148,428)(149,429)(150,430)(151,436)(152,437)
(153,438)(154,439)(155,440)(156,431)(157,432)(158,433)(159,434)(160,435)
(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)
(169,489)(170,490)(171,496)(172,497)(173,498)(174,499)(175,500)(176,491)
(177,492)(178,493)(179,494)(180,495)(181,501)(182,502)(183,503)(184,504)
(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,516)(192,517)
(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)(200,515)
(201,531)(202,532)(203,533)(204,534)(205,535)(206,536)(207,537)(208,538)
(209,539)(210,540)(211,521)(212,522)(213,523)(214,524)(215,525)(216,526)
(217,527)(218,528)(219,529)(220,530)(221,551)(222,552)(223,553)(224,554)
(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)(232,542)
(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)(240,550)
(241,601)(242,602)(243,603)(244,604)(245,605)(246,606)(247,607)(248,608)
(249,609)(250,610)(251,616)(252,617)(253,618)(254,619)(255,620)(256,611)
(257,612)(258,613)(259,614)(260,615)(261,621)(262,622)(263,623)(264,624)
(265,625)(266,626)(267,627)(268,628)(269,629)(270,630)(271,636)(272,637)
(273,638)(274,639)(275,640)(276,631)(277,632)(278,633)(279,634)(280,635)
(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)(288,568)
(289,569)(290,570)(291,576)(292,577)(293,578)(294,579)(295,580)(296,571)
(297,572)(298,573)(299,574)(300,575)(301,581)(302,582)(303,583)(304,584)
(305,585)(306,586)(307,587)(308,588)(309,589)(310,590)(311,596)(312,597)
(313,598)(314,599)(315,600)(316,591)(317,592)(318,593)(319,594)(320,595);;
s1 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)( 8, 89)
( 9, 88)( 10, 87)( 11, 96)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16, 91)
( 17, 95)( 18, 94)( 19, 93)( 20, 92)( 21,101)( 22,105)( 23,104)( 24,103)
( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,116)( 32,120)
( 33,119)( 34,118)( 35,117)( 36,111)( 37,115)( 38,114)( 39,113)( 40,112)
( 41,131)( 42,135)( 43,134)( 44,133)( 45,132)( 46,136)( 47,140)( 48,139)
( 49,138)( 50,137)( 51,121)( 52,125)( 53,124)( 54,123)( 55,122)( 56,126)
( 57,130)( 58,129)( 59,128)( 60,127)( 61,151)( 62,155)( 63,154)( 64,153)
( 65,152)( 66,156)( 67,160)( 68,159)( 69,158)( 70,157)( 71,141)( 72,145)
( 73,144)( 74,143)( 75,142)( 76,146)( 77,150)( 78,149)( 79,148)( 80,147)
(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)(168,249)
(169,248)(170,247)(171,256)(172,260)(173,259)(174,258)(175,257)(176,251)
(177,255)(178,254)(179,253)(180,252)(181,261)(182,265)(183,264)(184,263)
(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,276)(192,280)
(193,279)(194,278)(195,277)(196,271)(197,275)(198,274)(199,273)(200,272)
(201,291)(202,295)(203,294)(204,293)(205,292)(206,296)(207,300)(208,299)
(209,298)(210,297)(211,281)(212,285)(213,284)(214,283)(215,282)(216,286)
(217,290)(218,289)(219,288)(220,287)(221,311)(222,315)(223,314)(224,313)
(225,312)(226,316)(227,320)(228,319)(229,318)(230,317)(231,301)(232,305)
(233,304)(234,303)(235,302)(236,306)(237,310)(238,309)(239,308)(240,307)
(321,401)(322,405)(323,404)(324,403)(325,402)(326,406)(327,410)(328,409)
(329,408)(330,407)(331,416)(332,420)(333,419)(334,418)(335,417)(336,411)
(337,415)(338,414)(339,413)(340,412)(341,421)(342,425)(343,424)(344,423)
(345,422)(346,426)(347,430)(348,429)(349,428)(350,427)(351,436)(352,440)
(353,439)(354,438)(355,437)(356,431)(357,435)(358,434)(359,433)(360,432)
(361,451)(362,455)(363,454)(364,453)(365,452)(366,456)(367,460)(368,459)
(369,458)(370,457)(371,441)(372,445)(373,444)(374,443)(375,442)(376,446)
(377,450)(378,449)(379,448)(380,447)(381,471)(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)
(481,561)(482,565)(483,564)(484,563)(485,562)(486,566)(487,570)(488,569)
(489,568)(490,567)(491,576)(492,580)(493,579)(494,578)(495,577)(496,571)
(497,575)(498,574)(499,573)(500,572)(501,581)(502,585)(503,584)(504,583)
(505,582)(506,586)(507,590)(508,589)(509,588)(510,587)(511,596)(512,600)
(513,599)(514,598)(515,597)(516,591)(517,595)(518,594)(519,593)(520,592)
(521,611)(522,615)(523,614)(524,613)(525,612)(526,616)(527,620)(528,619)
(529,618)(530,617)(531,601)(532,605)(533,604)(534,603)(535,602)(536,606)
(537,610)(538,609)(539,608)(540,607)(541,631)(542,635)(543,634)(544,633)
(545,632)(546,636)(547,640)(548,639)(549,638)(550,637)(551,621)(552,625)
(553,624)(554,623)(555,622)(556,626)(557,630)(558,629)(559,628)(560,627);;
s2 := ( 1,123)( 2,122)( 3,121)( 4,125)( 5,124)( 6,128)( 7,127)( 8,126)
( 9,130)( 10,129)( 11,133)( 12,132)( 13,131)( 14,135)( 15,134)( 16,138)
( 17,137)( 18,136)( 19,140)( 20,139)( 21,143)( 22,142)( 23,141)( 24,145)
( 25,144)( 26,148)( 27,147)( 28,146)( 29,150)( 30,149)( 31,153)( 32,152)
( 33,151)( 34,155)( 35,154)( 36,158)( 37,157)( 38,156)( 39,160)( 40,159)
( 41, 98)( 42, 97)( 43, 96)( 44,100)( 45, 99)( 46, 93)( 47, 92)( 48, 91)
( 49, 95)( 50, 94)( 51, 83)( 52, 82)( 53, 81)( 54, 85)( 55, 84)( 56, 88)
( 57, 87)( 58, 86)( 59, 90)( 60, 89)( 61,118)( 62,117)( 63,116)( 64,120)
( 65,119)( 66,113)( 67,112)( 68,111)( 69,115)( 70,114)( 71,103)( 72,102)
( 73,101)( 74,105)( 75,104)( 76,108)( 77,107)( 78,106)( 79,110)( 80,109)
(161,303)(162,302)(163,301)(164,305)(165,304)(166,308)(167,307)(168,306)
(169,310)(170,309)(171,313)(172,312)(173,311)(174,315)(175,314)(176,318)
(177,317)(178,316)(179,320)(180,319)(181,283)(182,282)(183,281)(184,285)
(185,284)(186,288)(187,287)(188,286)(189,290)(190,289)(191,293)(192,292)
(193,291)(194,295)(195,294)(196,298)(197,297)(198,296)(199,300)(200,299)
(201,278)(202,277)(203,276)(204,280)(205,279)(206,273)(207,272)(208,271)
(209,275)(210,274)(211,263)(212,262)(213,261)(214,265)(215,264)(216,268)
(217,267)(218,266)(219,270)(220,269)(221,258)(222,257)(223,256)(224,260)
(225,259)(226,253)(227,252)(228,251)(229,255)(230,254)(231,243)(232,242)
(233,241)(234,245)(235,244)(236,248)(237,247)(238,246)(239,250)(240,249)
(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)(341,423)(342,422)(343,421)(344,425)
(345,424)(346,428)(347,427)(348,426)(349,430)(350,429)(351,433)(352,432)
(353,431)(354,435)(355,434)(356,438)(357,437)(358,436)(359,440)(360,439)
(361,443)(362,442)(363,441)(364,445)(365,444)(366,448)(367,447)(368,446)
(369,450)(370,449)(371,453)(372,452)(373,451)(374,455)(375,454)(376,458)
(377,457)(378,456)(379,460)(380,459)(381,463)(382,462)(383,461)(384,465)
(385,464)(386,468)(387,467)(388,466)(389,470)(390,469)(391,473)(392,472)
(393,471)(394,475)(395,474)(396,478)(397,477)(398,476)(399,480)(400,479)
(481,583)(482,582)(483,581)(484,585)(485,584)(486,588)(487,587)(488,586)
(489,590)(490,589)(491,593)(492,592)(493,591)(494,595)(495,594)(496,598)
(497,597)(498,596)(499,600)(500,599)(501,563)(502,562)(503,561)(504,565)
(505,564)(506,568)(507,567)(508,566)(509,570)(510,569)(511,573)(512,572)
(513,571)(514,575)(515,574)(516,578)(517,577)(518,576)(519,580)(520,579)
(521,623)(522,622)(523,621)(524,625)(525,624)(526,628)(527,627)(528,626)
(529,630)(530,629)(531,633)(532,632)(533,631)(534,635)(535,634)(536,638)
(537,637)(538,636)(539,640)(540,639)(541,603)(542,602)(543,601)(544,605)
(545,604)(546,608)(547,607)(548,606)(549,610)(550,609)(551,613)(552,612)
(553,611)(554,615)(555,614)(556,618)(557,617)(558,616)(559,620)(560,619);;
s3 := ( 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);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)
( 8,328)( 9,329)( 10,330)( 11,336)( 12,337)( 13,338)( 14,339)( 15,340)
( 16,331)( 17,332)( 18,333)( 19,334)( 20,335)( 21,341)( 22,342)( 23,343)
( 24,344)( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,356)
( 32,357)( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)
( 40,355)( 41,371)( 42,372)( 43,373)( 44,374)( 45,375)( 46,376)( 47,377)
( 48,378)( 49,379)( 50,380)( 51,361)( 52,362)( 53,363)( 54,364)( 55,365)
( 56,366)( 57,367)( 58,368)( 59,369)( 60,370)( 61,391)( 62,392)( 63,393)
( 64,394)( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)
( 72,382)( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)
( 80,390)( 81,441)( 82,442)( 83,443)( 84,444)( 85,445)( 86,446)( 87,447)
( 88,448)( 89,449)( 90,450)( 91,456)( 92,457)( 93,458)( 94,459)( 95,460)
( 96,451)( 97,452)( 98,453)( 99,454)(100,455)(101,461)(102,462)(103,463)
(104,464)(105,465)(106,466)(107,467)(108,468)(109,469)(110,470)(111,476)
(112,477)(113,478)(114,479)(115,480)(116,471)(117,472)(118,473)(119,474)
(120,475)(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)
(128,408)(129,409)(130,410)(131,416)(132,417)(133,418)(134,419)(135,420)
(136,411)(137,412)(138,413)(139,414)(140,415)(141,421)(142,422)(143,423)
(144,424)(145,425)(146,426)(147,427)(148,428)(149,429)(150,430)(151,436)
(152,437)(153,438)(154,439)(155,440)(156,431)(157,432)(158,433)(159,434)
(160,435)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)
(168,488)(169,489)(170,490)(171,496)(172,497)(173,498)(174,499)(175,500)
(176,491)(177,492)(178,493)(179,494)(180,495)(181,501)(182,502)(183,503)
(184,504)(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,516)
(192,517)(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)
(200,515)(201,531)(202,532)(203,533)(204,534)(205,535)(206,536)(207,537)
(208,538)(209,539)(210,540)(211,521)(212,522)(213,523)(214,524)(215,525)
(216,526)(217,527)(218,528)(219,529)(220,530)(221,551)(222,552)(223,553)
(224,554)(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)
(232,542)(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)
(240,550)(241,601)(242,602)(243,603)(244,604)(245,605)(246,606)(247,607)
(248,608)(249,609)(250,610)(251,616)(252,617)(253,618)(254,619)(255,620)
(256,611)(257,612)(258,613)(259,614)(260,615)(261,621)(262,622)(263,623)
(264,624)(265,625)(266,626)(267,627)(268,628)(269,629)(270,630)(271,636)
(272,637)(273,638)(274,639)(275,640)(276,631)(277,632)(278,633)(279,634)
(280,635)(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)
(288,568)(289,569)(290,570)(291,576)(292,577)(293,578)(294,579)(295,580)
(296,571)(297,572)(298,573)(299,574)(300,575)(301,581)(302,582)(303,583)
(304,584)(305,585)(306,586)(307,587)(308,588)(309,589)(310,590)(311,596)
(312,597)(313,598)(314,599)(315,600)(316,591)(317,592)(318,593)(319,594)
(320,595);
s1 := Sym(640)!( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)
( 8, 89)( 9, 88)( 10, 87)( 11, 96)( 12,100)( 13, 99)( 14, 98)( 15, 97)
( 16, 91)( 17, 95)( 18, 94)( 19, 93)( 20, 92)( 21,101)( 22,105)( 23,104)
( 24,103)( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,116)
( 32,120)( 33,119)( 34,118)( 35,117)( 36,111)( 37,115)( 38,114)( 39,113)
( 40,112)( 41,131)( 42,135)( 43,134)( 44,133)( 45,132)( 46,136)( 47,140)
( 48,139)( 49,138)( 50,137)( 51,121)( 52,125)( 53,124)( 54,123)( 55,122)
( 56,126)( 57,130)( 58,129)( 59,128)( 60,127)( 61,151)( 62,155)( 63,154)
( 64,153)( 65,152)( 66,156)( 67,160)( 68,159)( 69,158)( 70,157)( 71,141)
( 72,145)( 73,144)( 74,143)( 75,142)( 76,146)( 77,150)( 78,149)( 79,148)
( 80,147)(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)
(168,249)(169,248)(170,247)(171,256)(172,260)(173,259)(174,258)(175,257)
(176,251)(177,255)(178,254)(179,253)(180,252)(181,261)(182,265)(183,264)
(184,263)(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,276)
(192,280)(193,279)(194,278)(195,277)(196,271)(197,275)(198,274)(199,273)
(200,272)(201,291)(202,295)(203,294)(204,293)(205,292)(206,296)(207,300)
(208,299)(209,298)(210,297)(211,281)(212,285)(213,284)(214,283)(215,282)
(216,286)(217,290)(218,289)(219,288)(220,287)(221,311)(222,315)(223,314)
(224,313)(225,312)(226,316)(227,320)(228,319)(229,318)(230,317)(231,301)
(232,305)(233,304)(234,303)(235,302)(236,306)(237,310)(238,309)(239,308)
(240,307)(321,401)(322,405)(323,404)(324,403)(325,402)(326,406)(327,410)
(328,409)(329,408)(330,407)(331,416)(332,420)(333,419)(334,418)(335,417)
(336,411)(337,415)(338,414)(339,413)(340,412)(341,421)(342,425)(343,424)
(344,423)(345,422)(346,426)(347,430)(348,429)(349,428)(350,427)(351,436)
(352,440)(353,439)(354,438)(355,437)(356,431)(357,435)(358,434)(359,433)
(360,432)(361,451)(362,455)(363,454)(364,453)(365,452)(366,456)(367,460)
(368,459)(369,458)(370,457)(371,441)(372,445)(373,444)(374,443)(375,442)
(376,446)(377,450)(378,449)(379,448)(380,447)(381,471)(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)(481,561)(482,565)(483,564)(484,563)(485,562)(486,566)(487,570)
(488,569)(489,568)(490,567)(491,576)(492,580)(493,579)(494,578)(495,577)
(496,571)(497,575)(498,574)(499,573)(500,572)(501,581)(502,585)(503,584)
(504,583)(505,582)(506,586)(507,590)(508,589)(509,588)(510,587)(511,596)
(512,600)(513,599)(514,598)(515,597)(516,591)(517,595)(518,594)(519,593)
(520,592)(521,611)(522,615)(523,614)(524,613)(525,612)(526,616)(527,620)
(528,619)(529,618)(530,617)(531,601)(532,605)(533,604)(534,603)(535,602)
(536,606)(537,610)(538,609)(539,608)(540,607)(541,631)(542,635)(543,634)
(544,633)(545,632)(546,636)(547,640)(548,639)(549,638)(550,637)(551,621)
(552,625)(553,624)(554,623)(555,622)(556,626)(557,630)(558,629)(559,628)
(560,627);
s2 := Sym(640)!( 1,123)( 2,122)( 3,121)( 4,125)( 5,124)( 6,128)( 7,127)
( 8,126)( 9,130)( 10,129)( 11,133)( 12,132)( 13,131)( 14,135)( 15,134)
( 16,138)( 17,137)( 18,136)( 19,140)( 20,139)( 21,143)( 22,142)( 23,141)
( 24,145)( 25,144)( 26,148)( 27,147)( 28,146)( 29,150)( 30,149)( 31,153)
( 32,152)( 33,151)( 34,155)( 35,154)( 36,158)( 37,157)( 38,156)( 39,160)
( 40,159)( 41, 98)( 42, 97)( 43, 96)( 44,100)( 45, 99)( 46, 93)( 47, 92)
( 48, 91)( 49, 95)( 50, 94)( 51, 83)( 52, 82)( 53, 81)( 54, 85)( 55, 84)
( 56, 88)( 57, 87)( 58, 86)( 59, 90)( 60, 89)( 61,118)( 62,117)( 63,116)
( 64,120)( 65,119)( 66,113)( 67,112)( 68,111)( 69,115)( 70,114)( 71,103)
( 72,102)( 73,101)( 74,105)( 75,104)( 76,108)( 77,107)( 78,106)( 79,110)
( 80,109)(161,303)(162,302)(163,301)(164,305)(165,304)(166,308)(167,307)
(168,306)(169,310)(170,309)(171,313)(172,312)(173,311)(174,315)(175,314)
(176,318)(177,317)(178,316)(179,320)(180,319)(181,283)(182,282)(183,281)
(184,285)(185,284)(186,288)(187,287)(188,286)(189,290)(190,289)(191,293)
(192,292)(193,291)(194,295)(195,294)(196,298)(197,297)(198,296)(199,300)
(200,299)(201,278)(202,277)(203,276)(204,280)(205,279)(206,273)(207,272)
(208,271)(209,275)(210,274)(211,263)(212,262)(213,261)(214,265)(215,264)
(216,268)(217,267)(218,266)(219,270)(220,269)(221,258)(222,257)(223,256)
(224,260)(225,259)(226,253)(227,252)(228,251)(229,255)(230,254)(231,243)
(232,242)(233,241)(234,245)(235,244)(236,248)(237,247)(238,246)(239,250)
(240,249)(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)(341,423)(342,422)(343,421)
(344,425)(345,424)(346,428)(347,427)(348,426)(349,430)(350,429)(351,433)
(352,432)(353,431)(354,435)(355,434)(356,438)(357,437)(358,436)(359,440)
(360,439)(361,443)(362,442)(363,441)(364,445)(365,444)(366,448)(367,447)
(368,446)(369,450)(370,449)(371,453)(372,452)(373,451)(374,455)(375,454)
(376,458)(377,457)(378,456)(379,460)(380,459)(381,463)(382,462)(383,461)
(384,465)(385,464)(386,468)(387,467)(388,466)(389,470)(390,469)(391,473)
(392,472)(393,471)(394,475)(395,474)(396,478)(397,477)(398,476)(399,480)
(400,479)(481,583)(482,582)(483,581)(484,585)(485,584)(486,588)(487,587)
(488,586)(489,590)(490,589)(491,593)(492,592)(493,591)(494,595)(495,594)
(496,598)(497,597)(498,596)(499,600)(500,599)(501,563)(502,562)(503,561)
(504,565)(505,564)(506,568)(507,567)(508,566)(509,570)(510,569)(511,573)
(512,572)(513,571)(514,575)(515,574)(516,578)(517,577)(518,576)(519,580)
(520,579)(521,623)(522,622)(523,621)(524,625)(525,624)(526,628)(527,627)
(528,626)(529,630)(530,629)(531,633)(532,632)(533,631)(534,635)(535,634)
(536,638)(537,637)(538,636)(539,640)(540,639)(541,603)(542,602)(543,601)
(544,605)(545,604)(546,608)(547,607)(548,606)(549,610)(550,609)(551,613)
(552,612)(553,611)(554,615)(555,614)(556,618)(557,617)(558,616)(559,620)
(560,619);
s3 := 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);
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*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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