Polytope of Type {8,10,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10,8}*1280
Also Known As : {{8,10|2},{10,8|2}}. if this polytope has another name.
Group : SmallGroup(1280,161912)
Rank : 4
Schlafli Type : {8,10,8}
Number of vertices, edges, etc : 8, 40, 40, 8
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Self-Dual
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 : {4,10,8}*640, {8,10,4}*640
4-fold quotients : {4,10,4}*320, {2,10,8}*320, {8,10,2}*320
5-fold quotients : {8,2,8}*256
8-fold quotients : {2,10,4}*160, {4,10,2}*160
10-fold quotients : {4,2,8}*128, {8,2,4}*128
16-fold quotients : {2,10,2}*80
20-fold quotients : {4,2,4}*64, {2,2,8}*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)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)( 16,336)
( 17,337)( 18,338)( 19,339)( 20,340)( 21,341)( 22,342)( 23,343)( 24,344)
( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)( 32,352)
( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)( 40,360)
( 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)( 91,451)( 92,452)( 93,453)( 94,454)( 95,455)( 96,456)
( 97,457)( 98,458)( 99,459)(100,460)(101,461)(102,462)(103,463)(104,464)
(105,465)(106,466)(107,467)(108,468)(109,469)(110,470)(111,471)(112,472)
(113,473)(114,474)(115,475)(116,476)(117,477)(118,478)(119,479)(120,480)
(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)(128,408)
(129,409)(130,410)(131,411)(132,412)(133,413)(134,414)(135,415)(136,416)
(137,417)(138,418)(139,419)(140,420)(141,421)(142,422)(143,423)(144,424)
(145,425)(146,426)(147,427)(148,428)(149,429)(150,430)(151,431)(152,432)
(153,433)(154,434)(155,435)(156,436)(157,437)(158,438)(159,439)(160,440)
(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)
(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)(176,496)
(177,497)(178,498)(179,499)(180,500)(181,501)(182,502)(183,503)(184,504)
(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,511)(192,512)
(193,513)(194,514)(195,515)(196,516)(197,517)(198,518)(199,519)(200,520)
(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)(251,611)(252,612)(253,613)(254,614)(255,615)(256,616)
(257,617)(258,618)(259,619)(260,620)(261,621)(262,622)(263,623)(264,624)
(265,625)(266,626)(267,627)(268,628)(269,629)(270,630)(271,631)(272,632)
(273,633)(274,634)(275,635)(276,636)(277,637)(278,638)(279,639)(280,640)
(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)(288,568)
(289,569)(290,570)(291,571)(292,572)(293,573)(294,574)(295,575)(296,576)
(297,577)(298,578)(299,579)(300,580)(301,581)(302,582)(303,583)(304,584)
(305,585)(306,586)(307,587)(308,588)(309,589)(310,590)(311,591)(312,592)
(313,593)(314,594)(315,595)(316,596)(317,597)(318,598)(319,599)(320,600);;
s1 := ( 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)
( 41,131)( 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)(171,251)(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)
(201,291)(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)(331,411)(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)
(361,451)(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)(491,571)(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)
(521,611)(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 := ( 1,133)( 2,132)( 3,131)( 4,135)( 5,134)( 6,138)( 7,137)( 8,136)
( 9,140)( 10,139)( 11,123)( 12,122)( 13,121)( 14,125)( 15,124)( 16,128)
( 17,127)( 18,126)( 19,130)( 20,129)( 21,158)( 22,157)( 23,156)( 24,160)
( 25,159)( 26,153)( 27,152)( 28,151)( 29,155)( 30,154)( 31,148)( 32,147)
( 33,146)( 34,150)( 35,149)( 36,143)( 37,142)( 38,141)( 39,145)( 40,144)
( 41, 83)( 42, 82)( 43, 81)( 44, 85)( 45, 84)( 46, 88)( 47, 87)( 48, 86)
( 49, 90)( 50, 89)( 51, 93)( 52, 92)( 53, 91)( 54, 95)( 55, 94)( 56, 98)
( 57, 97)( 58, 96)( 59,100)( 60, 99)( 61,108)( 62,107)( 63,106)( 64,110)
( 65,109)( 66,103)( 67,102)( 68,101)( 69,105)( 70,104)( 71,118)( 72,117)
( 73,116)( 74,120)( 75,119)( 76,113)( 77,112)( 78,111)( 79,115)( 80,114)
(161,313)(162,312)(163,311)(164,315)(165,314)(166,318)(167,317)(168,316)
(169,320)(170,319)(171,303)(172,302)(173,301)(174,305)(175,304)(176,308)
(177,307)(178,306)(179,310)(180,309)(181,293)(182,292)(183,291)(184,295)
(185,294)(186,298)(187,297)(188,296)(189,300)(190,299)(191,283)(192,282)
(193,281)(194,285)(195,284)(196,288)(197,287)(198,286)(199,290)(200,289)
(201,263)(202,262)(203,261)(204,265)(205,264)(206,268)(207,267)(208,266)
(209,270)(210,269)(211,273)(212,272)(213,271)(214,275)(215,274)(216,278)
(217,277)(218,276)(219,280)(220,279)(221,243)(222,242)(223,241)(224,245)
(225,244)(226,248)(227,247)(228,246)(229,250)(230,249)(231,253)(232,252)
(233,251)(234,255)(235,254)(236,258)(237,257)(238,256)(239,260)(240,259)
(321,413)(322,412)(323,411)(324,415)(325,414)(326,418)(327,417)(328,416)
(329,420)(330,419)(331,403)(332,402)(333,401)(334,405)(335,404)(336,408)
(337,407)(338,406)(339,410)(340,409)(341,438)(342,437)(343,436)(344,440)
(345,439)(346,433)(347,432)(348,431)(349,435)(350,434)(351,428)(352,427)
(353,426)(354,430)(355,429)(356,423)(357,422)(358,421)(359,425)(360,424)
(361,453)(362,452)(363,451)(364,455)(365,454)(366,458)(367,457)(368,456)
(369,460)(370,459)(371,443)(372,442)(373,441)(374,445)(375,444)(376,448)
(377,447)(378,446)(379,450)(380,449)(381,478)(382,477)(383,476)(384,480)
(385,479)(386,473)(387,472)(388,471)(389,475)(390,474)(391,468)(392,467)
(393,466)(394,470)(395,469)(396,463)(397,462)(398,461)(399,465)(400,464)
(481,593)(482,592)(483,591)(484,595)(485,594)(486,598)(487,597)(488,596)
(489,600)(490,599)(491,583)(492,582)(493,581)(494,585)(495,584)(496,588)
(497,587)(498,586)(499,590)(500,589)(501,573)(502,572)(503,571)(504,575)
(505,574)(506,578)(507,577)(508,576)(509,580)(510,579)(511,563)(512,562)
(513,561)(514,565)(515,564)(516,568)(517,567)(518,566)(519,570)(520,569)
(521,633)(522,632)(523,631)(524,635)(525,634)(526,638)(527,637)(528,636)
(529,640)(530,639)(531,623)(532,622)(533,621)(534,625)(535,624)(536,628)
(537,627)(538,626)(539,630)(540,629)(541,613)(542,612)(543,611)(544,615)
(545,614)(546,618)(547,617)(548,616)(549,620)(550,619)(551,603)(552,602)
(553,601)(554,605)(555,604)(556,608)(557,607)(558,606)(559,610)(560,609);;
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)( 21,186)( 22,187)( 23,188)( 24,189)
( 25,190)( 26,181)( 27,182)( 28,183)( 29,184)( 30,185)( 31,196)( 32,197)
( 33,198)( 34,199)( 35,200)( 36,191)( 37,192)( 38,193)( 39,194)( 40,195)
( 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)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,221)( 67,222)( 68,223)( 69,224)( 70,225)( 71,236)( 72,237)
( 73,238)( 74,239)( 75,240)( 76,231)( 77,232)( 78,233)( 79,234)( 80,235)
( 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)(101,266)(102,267)(103,268)(104,269)
(105,270)(106,261)(107,262)(108,263)(109,264)(110,265)(111,276)(112,277)
(113,278)(114,279)(115,280)(116,271)(117,272)(118,273)(119,274)(120,275)
(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)(141,306)(142,307)(143,308)(144,309)
(145,310)(146,301)(147,302)(148,303)(149,304)(150,305)(151,316)(152,317)
(153,318)(154,319)(155,320)(156,311)(157,312)(158,313)(159,314)(160,315)
(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)(341,506)(342,507)(343,508)(344,509)
(345,510)(346,501)(347,502)(348,503)(349,504)(350,505)(351,516)(352,517)
(353,518)(354,519)(355,520)(356,511)(357,512)(358,513)(359,514)(360,515)
(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)(381,546)(382,547)(383,548)(384,549)
(385,550)(386,541)(387,542)(388,543)(389,544)(390,545)(391,556)(392,557)
(393,558)(394,559)(395,560)(396,551)(397,552)(398,553)(399,554)(400,555)
(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)(421,586)(422,587)(423,588)(424,589)
(425,590)(426,581)(427,582)(428,583)(429,584)(430,585)(431,596)(432,597)
(433,598)(434,599)(435,600)(436,591)(437,592)(438,593)(439,594)(440,595)
(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)(461,626)(462,627)(463,628)(464,629)
(465,630)(466,621)(467,622)(468,623)(469,624)(470,625)(471,636)(472,637)
(473,638)(474,639)(475,640)(476,631)(477,632)(478,633)(479,634)(480,635);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*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 ];;
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)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)
( 16,336)( 17,337)( 18,338)( 19,339)( 20,340)( 21,341)( 22,342)( 23,343)
( 24,344)( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)
( 32,352)( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)
( 40,360)( 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)( 91,451)( 92,452)( 93,453)( 94,454)( 95,455)
( 96,456)( 97,457)( 98,458)( 99,459)(100,460)(101,461)(102,462)(103,463)
(104,464)(105,465)(106,466)(107,467)(108,468)(109,469)(110,470)(111,471)
(112,472)(113,473)(114,474)(115,475)(116,476)(117,477)(118,478)(119,479)
(120,480)(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)
(128,408)(129,409)(130,410)(131,411)(132,412)(133,413)(134,414)(135,415)
(136,416)(137,417)(138,418)(139,419)(140,420)(141,421)(142,422)(143,423)
(144,424)(145,425)(146,426)(147,427)(148,428)(149,429)(150,430)(151,431)
(152,432)(153,433)(154,434)(155,435)(156,436)(157,437)(158,438)(159,439)
(160,440)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)
(168,488)(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)
(176,496)(177,497)(178,498)(179,499)(180,500)(181,501)(182,502)(183,503)
(184,504)(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,511)
(192,512)(193,513)(194,514)(195,515)(196,516)(197,517)(198,518)(199,519)
(200,520)(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)(251,611)(252,612)(253,613)(254,614)(255,615)
(256,616)(257,617)(258,618)(259,619)(260,620)(261,621)(262,622)(263,623)
(264,624)(265,625)(266,626)(267,627)(268,628)(269,629)(270,630)(271,631)
(272,632)(273,633)(274,634)(275,635)(276,636)(277,637)(278,638)(279,639)
(280,640)(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)
(288,568)(289,569)(290,570)(291,571)(292,572)(293,573)(294,574)(295,575)
(296,576)(297,577)(298,578)(299,579)(300,580)(301,581)(302,582)(303,583)
(304,584)(305,585)(306,586)(307,587)(308,588)(309,589)(310,590)(311,591)
(312,592)(313,593)(314,594)(315,595)(316,596)(317,597)(318,598)(319,599)
(320,600);
s1 := 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)( 41,131)( 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)(171,251)(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)(201,291)(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)(331,411)(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)(361,451)(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)(491,571)(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)(521,611)(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)!( 1,133)( 2,132)( 3,131)( 4,135)( 5,134)( 6,138)( 7,137)
( 8,136)( 9,140)( 10,139)( 11,123)( 12,122)( 13,121)( 14,125)( 15,124)
( 16,128)( 17,127)( 18,126)( 19,130)( 20,129)( 21,158)( 22,157)( 23,156)
( 24,160)( 25,159)( 26,153)( 27,152)( 28,151)( 29,155)( 30,154)( 31,148)
( 32,147)( 33,146)( 34,150)( 35,149)( 36,143)( 37,142)( 38,141)( 39,145)
( 40,144)( 41, 83)( 42, 82)( 43, 81)( 44, 85)( 45, 84)( 46, 88)( 47, 87)
( 48, 86)( 49, 90)( 50, 89)( 51, 93)( 52, 92)( 53, 91)( 54, 95)( 55, 94)
( 56, 98)( 57, 97)( 58, 96)( 59,100)( 60, 99)( 61,108)( 62,107)( 63,106)
( 64,110)( 65,109)( 66,103)( 67,102)( 68,101)( 69,105)( 70,104)( 71,118)
( 72,117)( 73,116)( 74,120)( 75,119)( 76,113)( 77,112)( 78,111)( 79,115)
( 80,114)(161,313)(162,312)(163,311)(164,315)(165,314)(166,318)(167,317)
(168,316)(169,320)(170,319)(171,303)(172,302)(173,301)(174,305)(175,304)
(176,308)(177,307)(178,306)(179,310)(180,309)(181,293)(182,292)(183,291)
(184,295)(185,294)(186,298)(187,297)(188,296)(189,300)(190,299)(191,283)
(192,282)(193,281)(194,285)(195,284)(196,288)(197,287)(198,286)(199,290)
(200,289)(201,263)(202,262)(203,261)(204,265)(205,264)(206,268)(207,267)
(208,266)(209,270)(210,269)(211,273)(212,272)(213,271)(214,275)(215,274)
(216,278)(217,277)(218,276)(219,280)(220,279)(221,243)(222,242)(223,241)
(224,245)(225,244)(226,248)(227,247)(228,246)(229,250)(230,249)(231,253)
(232,252)(233,251)(234,255)(235,254)(236,258)(237,257)(238,256)(239,260)
(240,259)(321,413)(322,412)(323,411)(324,415)(325,414)(326,418)(327,417)
(328,416)(329,420)(330,419)(331,403)(332,402)(333,401)(334,405)(335,404)
(336,408)(337,407)(338,406)(339,410)(340,409)(341,438)(342,437)(343,436)
(344,440)(345,439)(346,433)(347,432)(348,431)(349,435)(350,434)(351,428)
(352,427)(353,426)(354,430)(355,429)(356,423)(357,422)(358,421)(359,425)
(360,424)(361,453)(362,452)(363,451)(364,455)(365,454)(366,458)(367,457)
(368,456)(369,460)(370,459)(371,443)(372,442)(373,441)(374,445)(375,444)
(376,448)(377,447)(378,446)(379,450)(380,449)(381,478)(382,477)(383,476)
(384,480)(385,479)(386,473)(387,472)(388,471)(389,475)(390,474)(391,468)
(392,467)(393,466)(394,470)(395,469)(396,463)(397,462)(398,461)(399,465)
(400,464)(481,593)(482,592)(483,591)(484,595)(485,594)(486,598)(487,597)
(488,596)(489,600)(490,599)(491,583)(492,582)(493,581)(494,585)(495,584)
(496,588)(497,587)(498,586)(499,590)(500,589)(501,573)(502,572)(503,571)
(504,575)(505,574)(506,578)(507,577)(508,576)(509,580)(510,579)(511,563)
(512,562)(513,561)(514,565)(515,564)(516,568)(517,567)(518,566)(519,570)
(520,569)(521,633)(522,632)(523,631)(524,635)(525,634)(526,638)(527,637)
(528,636)(529,640)(530,639)(531,623)(532,622)(533,621)(534,625)(535,624)
(536,628)(537,627)(538,626)(539,630)(540,629)(541,613)(542,612)(543,611)
(544,615)(545,614)(546,618)(547,617)(548,616)(549,620)(550,619)(551,603)
(552,602)(553,601)(554,605)(555,604)(556,608)(557,607)(558,606)(559,610)
(560,609);
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)( 21,186)( 22,187)( 23,188)
( 24,189)( 25,190)( 26,181)( 27,182)( 28,183)( 29,184)( 30,185)( 31,196)
( 32,197)( 33,198)( 34,199)( 35,200)( 36,191)( 37,192)( 38,193)( 39,194)
( 40,195)( 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)( 61,226)( 62,227)( 63,228)
( 64,229)( 65,230)( 66,221)( 67,222)( 68,223)( 69,224)( 70,225)( 71,236)
( 72,237)( 73,238)( 74,239)( 75,240)( 76,231)( 77,232)( 78,233)( 79,234)
( 80,235)( 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)(101,266)(102,267)(103,268)
(104,269)(105,270)(106,261)(107,262)(108,263)(109,264)(110,265)(111,276)
(112,277)(113,278)(114,279)(115,280)(116,271)(117,272)(118,273)(119,274)
(120,275)(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)(141,306)(142,307)(143,308)
(144,309)(145,310)(146,301)(147,302)(148,303)(149,304)(150,305)(151,316)
(152,317)(153,318)(154,319)(155,320)(156,311)(157,312)(158,313)(159,314)
(160,315)(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)(341,506)(342,507)(343,508)
(344,509)(345,510)(346,501)(347,502)(348,503)(349,504)(350,505)(351,516)
(352,517)(353,518)(354,519)(355,520)(356,511)(357,512)(358,513)(359,514)
(360,515)(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)(381,546)(382,547)(383,548)
(384,549)(385,550)(386,541)(387,542)(388,543)(389,544)(390,545)(391,556)
(392,557)(393,558)(394,559)(395,560)(396,551)(397,552)(398,553)(399,554)
(400,555)(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)(421,586)(422,587)(423,588)
(424,589)(425,590)(426,581)(427,582)(428,583)(429,584)(430,585)(431,596)
(432,597)(433,598)(434,599)(435,600)(436,591)(437,592)(438,593)(439,594)
(440,595)(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)(461,626)(462,627)(463,628)
(464,629)(465,630)(466,621)(467,622)(468,623)(469,624)(470,625)(471,636)
(472,637)(473,638)(474,639)(475,640)(476,631)(477,632)(478,633)(479,634)
(480,635);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*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 >;
References : None.
to this polytope