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Polytope of Type {8,40}

Atlas Canonical Name : {8,40}*1280a
if this polytope has a name.
Group : SmallGroup(1280,58267)
Rank : 3
Schlafli Type : {8,40}
Number of vertices, edges, etc : 16, 320, 80
Order of s0s1s2 : 40
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,40}*640a, {8,40}*640a, {8,40}*640b, {8,20}*640a, {8,40}*640c, {8,40}*640d
4-fold quotients : {4,40}*320a, {4,20}*320, {4,40}*320b, {8,20}*320a, {8,20}*320b
5-fold quotients : {8,8}*256a
8-fold quotients : {4,20}*160, {2,40}*160, {8,10}*160
10-fold quotients : {4,8}*128a, {8,4}*128a, {8,8}*128a, {8,8}*128b, {8,8}*128c, {8,8}*128d
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,8}*64a, {8,4}*64a, {4,8}*64b, {8,4}*64b, {4,4}*64
32-fold quotients : {2,10}*40
40-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
64-fold quotients : {2,5}*20
80-fold quotients : {2,4}*16, {4,2}*16
160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,321)(  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)
( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)( 88,428)
( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)( 96,436)
( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)(104,404)
(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)(112,412)
(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)(120,420)
(121,471)(122,472)(123,473)(124,474)(125,475)(126,476)(127,477)(128,478)
(129,479)(130,480)(131,461)(132,462)(133,463)(134,464)(135,465)(136,466)
(137,467)(138,468)(139,469)(140,470)(141,451)(142,452)(143,453)(144,454)
(145,455)(146,456)(147,457)(148,458)(149,459)(150,460)(151,441)(152,442)
(153,443)(154,444)(155,445)(156,446)(157,447)(158,448)(159,449)(160,450)
(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)
(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)(248,588)
(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)(256,596)
(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)(264,564)
(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)(272,572)
(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)(280,580)
(281,631)(282,632)(283,633)(284,634)(285,635)(286,636)(287,637)(288,638)
(289,639)(290,640)(291,621)(292,622)(293,623)(294,624)(295,625)(296,626)
(297,627)(298,628)(299,629)(300,630)(301,611)(302,612)(303,613)(304,614)
(305,615)(306,616)(307,617)(308,618)(309,619)(310,620)(311,601)(312,602)
(313,603)(314,604)(315,605)(316,606)(317,607)(318,608)(319,609)(320,610);;
s1 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 41, 46)( 42, 50)( 43, 49)( 44, 48)( 45, 47)( 51, 56)( 52, 60)( 53, 59)
( 54, 58)( 55, 57)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 71, 76)
( 72, 80)( 73, 79)( 74, 78)( 75, 77)( 81,101)( 82,105)( 83,104)( 84,103)
( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,111)( 92,115)
( 93,114)( 94,113)( 95,112)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)
(121,146)(122,150)(123,149)(124,148)(125,147)(126,141)(127,145)(128,144)
(129,143)(130,142)(131,156)(132,160)(133,159)(134,158)(135,157)(136,151)
(137,155)(138,154)(139,153)(140,152)(161,201)(162,205)(163,204)(164,203)
(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,211)(172,215)
(173,214)(174,213)(175,212)(176,216)(177,220)(178,219)(179,218)(180,217)
(181,221)(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)(241,301)(242,305)(243,304)(244,303)
(245,302)(246,306)(247,310)(248,309)(249,308)(250,307)(251,311)(252,315)
(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)(260,317)
(261,281)(262,285)(263,284)(264,283)(265,282)(266,286)(267,290)(268,289)
(269,288)(270,287)(271,291)(272,295)(273,294)(274,293)(275,292)(276,296)
(277,300)(278,299)(279,298)(280,297)(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)(481,611)(482,615)(483,614)(484,613)
(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,601)(492,605)
(493,604)(494,603)(495,602)(496,606)(497,610)(498,609)(499,608)(500,607)
(501,631)(502,635)(503,634)(504,633)(505,632)(506,636)(507,640)(508,639)
(509,638)(510,637)(511,621)(512,625)(513,624)(514,623)(515,622)(516,626)
(517,630)(518,629)(519,628)(520,627)(521,571)(522,575)(523,574)(524,573)
(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,561)(532,565)
(533,564)(534,563)(535,562)(536,566)(537,570)(538,569)(539,568)(540,567)
(541,591)(542,595)(543,594)(544,593)(545,592)(546,596)(547,600)(548,599)
(549,598)(550,597)(551,581)(552,585)(553,584)(554,583)(555,582)(556,586)
(557,590)(558,589)(559,588)(560,587);;
s2 := (  1,163)(  2,162)(  3,161)(  4,165)(  5,164)(  6,168)(  7,167)(  8,166)
(  9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)( 16,178)
( 17,177)( 18,176)( 19,180)( 20,179)( 21,183)( 22,182)( 23,181)( 24,185)
( 25,184)( 26,188)( 27,187)( 28,186)( 29,190)( 30,189)( 31,193)( 32,192)
( 33,191)( 34,195)( 35,194)( 36,198)( 37,197)( 38,196)( 39,200)( 40,199)
( 41,208)( 42,207)( 43,206)( 44,210)( 45,209)( 46,203)( 47,202)( 48,201)
( 49,205)( 50,204)( 51,218)( 52,217)( 53,216)( 54,220)( 55,219)( 56,213)
( 57,212)( 58,211)( 59,215)( 60,214)( 61,228)( 62,227)( 63,226)( 64,230)
( 65,229)( 66,223)( 67,222)( 68,221)( 69,225)( 70,224)( 71,238)( 72,237)
( 73,236)( 74,240)( 75,239)( 76,233)( 77,232)( 78,231)( 79,235)( 80,234)
( 81,253)( 82,252)( 83,251)( 84,255)( 85,254)( 86,258)( 87,257)( 88,256)
( 89,260)( 90,259)( 91,243)( 92,242)( 93,241)( 94,245)( 95,244)( 96,248)
( 97,247)( 98,246)( 99,250)(100,249)(101,273)(102,272)(103,271)(104,275)
(105,274)(106,278)(107,277)(108,276)(109,280)(110,279)(111,263)(112,262)
(113,261)(114,265)(115,264)(116,268)(117,267)(118,266)(119,270)(120,269)
(121,298)(122,297)(123,296)(124,300)(125,299)(126,293)(127,292)(128,291)
(129,295)(130,294)(131,288)(132,287)(133,286)(134,290)(135,289)(136,283)
(137,282)(138,281)(139,285)(140,284)(141,318)(142,317)(143,316)(144,320)
(145,319)(146,313)(147,312)(148,311)(149,315)(150,314)(151,308)(152,307)
(153,306)(154,310)(155,309)(156,303)(157,302)(158,301)(159,305)(160,304)
(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)(328,486)
(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)(336,498)
(337,497)(338,496)(339,500)(340,499)(341,503)(342,502)(343,501)(344,505)
(345,504)(346,508)(347,507)(348,506)(349,510)(350,509)(351,513)(352,512)
(353,511)(354,515)(355,514)(356,518)(357,517)(358,516)(359,520)(360,519)
(361,528)(362,527)(363,526)(364,530)(365,529)(366,523)(367,522)(368,521)
(369,525)(370,524)(371,538)(372,537)(373,536)(374,540)(375,539)(376,533)
(377,532)(378,531)(379,535)(380,534)(381,548)(382,547)(383,546)(384,550)
(385,549)(386,543)(387,542)(388,541)(389,545)(390,544)(391,558)(392,557)
(393,556)(394,560)(395,559)(396,553)(397,552)(398,551)(399,555)(400,554)
(401,573)(402,572)(403,571)(404,575)(405,574)(406,578)(407,577)(408,576)
(409,580)(410,579)(411,563)(412,562)(413,561)(414,565)(415,564)(416,568)
(417,567)(418,566)(419,570)(420,569)(421,593)(422,592)(423,591)(424,595)
(425,594)(426,598)(427,597)(428,596)(429,600)(430,599)(431,583)(432,582)
(433,581)(434,585)(435,584)(436,588)(437,587)(438,586)(439,590)(440,589)
(441,618)(442,617)(443,616)(444,620)(445,619)(446,613)(447,612)(448,611)
(449,615)(450,614)(451,608)(452,607)(453,606)(454,610)(455,609)(456,603)
(457,602)(458,601)(459,605)(460,604)(461,638)(462,637)(463,636)(464,640)
(465,639)(466,633)(467,632)(468,631)(469,635)(470,634)(471,628)(472,627)
(473,626)(474,630)(475,629)(476,623)(477,622)(478,621)(479,625)(480,624);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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)( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)
( 88,428)( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)
( 96,436)( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)
(104,404)(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)
(112,412)(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)
(120,420)(121,471)(122,472)(123,473)(124,474)(125,475)(126,476)(127,477)
(128,478)(129,479)(130,480)(131,461)(132,462)(133,463)(134,464)(135,465)
(136,466)(137,467)(138,468)(139,469)(140,470)(141,451)(142,452)(143,453)
(144,454)(145,455)(146,456)(147,457)(148,458)(149,459)(150,460)(151,441)
(152,442)(153,443)(154,444)(155,445)(156,446)(157,447)(158,448)(159,449)
(160,450)(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)(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)
(248,588)(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)
(256,596)(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)
(264,564)(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)
(272,572)(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)
(280,580)(281,631)(282,632)(283,633)(284,634)(285,635)(286,636)(287,637)
(288,638)(289,639)(290,640)(291,621)(292,622)(293,623)(294,624)(295,625)
(296,626)(297,627)(298,628)(299,629)(300,630)(301,611)(302,612)(303,613)
(304,614)(305,615)(306,616)(307,617)(308,618)(309,619)(310,620)(311,601)
(312,602)(313,603)(314,604)(315,605)(316,606)(317,607)(318,608)(319,609)
(320,610);
s1 := Sym(640)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 41, 46)( 42, 50)( 43, 49)( 44, 48)( 45, 47)( 51, 56)( 52, 60)
( 53, 59)( 54, 58)( 55, 57)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)
( 71, 76)( 72, 80)( 73, 79)( 74, 78)( 75, 77)( 81,101)( 82,105)( 83,104)
( 84,103)( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,111)
( 92,115)( 93,114)( 94,113)( 95,112)( 96,116)( 97,120)( 98,119)( 99,118)
(100,117)(121,146)(122,150)(123,149)(124,148)(125,147)(126,141)(127,145)
(128,144)(129,143)(130,142)(131,156)(132,160)(133,159)(134,158)(135,157)
(136,151)(137,155)(138,154)(139,153)(140,152)(161,201)(162,205)(163,204)
(164,203)(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,211)
(172,215)(173,214)(174,213)(175,212)(176,216)(177,220)(178,219)(179,218)
(180,217)(181,221)(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)(241,301)(242,305)(243,304)
(244,303)(245,302)(246,306)(247,310)(248,309)(249,308)(250,307)(251,311)
(252,315)(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)
(260,317)(261,281)(262,285)(263,284)(264,283)(265,282)(266,286)(267,290)
(268,289)(269,288)(270,287)(271,291)(272,295)(273,294)(274,293)(275,292)
(276,296)(277,300)(278,299)(279,298)(280,297)(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)(481,611)(482,615)(483,614)
(484,613)(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,601)
(492,605)(493,604)(494,603)(495,602)(496,606)(497,610)(498,609)(499,608)
(500,607)(501,631)(502,635)(503,634)(504,633)(505,632)(506,636)(507,640)
(508,639)(509,638)(510,637)(511,621)(512,625)(513,624)(514,623)(515,622)
(516,626)(517,630)(518,629)(519,628)(520,627)(521,571)(522,575)(523,574)
(524,573)(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,561)
(532,565)(533,564)(534,563)(535,562)(536,566)(537,570)(538,569)(539,568)
(540,567)(541,591)(542,595)(543,594)(544,593)(545,592)(546,596)(547,600)
(548,599)(549,598)(550,597)(551,581)(552,585)(553,584)(554,583)(555,582)
(556,586)(557,590)(558,589)(559,588)(560,587);
s2 := Sym(640)!(  1,163)(  2,162)(  3,161)(  4,165)(  5,164)(  6,168)(  7,167)
(  8,166)(  9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)
( 16,178)( 17,177)( 18,176)( 19,180)( 20,179)( 21,183)( 22,182)( 23,181)
( 24,185)( 25,184)( 26,188)( 27,187)( 28,186)( 29,190)( 30,189)( 31,193)
( 32,192)( 33,191)( 34,195)( 35,194)( 36,198)( 37,197)( 38,196)( 39,200)
( 40,199)( 41,208)( 42,207)( 43,206)( 44,210)( 45,209)( 46,203)( 47,202)
( 48,201)( 49,205)( 50,204)( 51,218)( 52,217)( 53,216)( 54,220)( 55,219)
( 56,213)( 57,212)( 58,211)( 59,215)( 60,214)( 61,228)( 62,227)( 63,226)
( 64,230)( 65,229)( 66,223)( 67,222)( 68,221)( 69,225)( 70,224)( 71,238)
( 72,237)( 73,236)( 74,240)( 75,239)( 76,233)( 77,232)( 78,231)( 79,235)
( 80,234)( 81,253)( 82,252)( 83,251)( 84,255)( 85,254)( 86,258)( 87,257)
( 88,256)( 89,260)( 90,259)( 91,243)( 92,242)( 93,241)( 94,245)( 95,244)
( 96,248)( 97,247)( 98,246)( 99,250)(100,249)(101,273)(102,272)(103,271)
(104,275)(105,274)(106,278)(107,277)(108,276)(109,280)(110,279)(111,263)
(112,262)(113,261)(114,265)(115,264)(116,268)(117,267)(118,266)(119,270)
(120,269)(121,298)(122,297)(123,296)(124,300)(125,299)(126,293)(127,292)
(128,291)(129,295)(130,294)(131,288)(132,287)(133,286)(134,290)(135,289)
(136,283)(137,282)(138,281)(139,285)(140,284)(141,318)(142,317)(143,316)
(144,320)(145,319)(146,313)(147,312)(148,311)(149,315)(150,314)(151,308)
(152,307)(153,306)(154,310)(155,309)(156,303)(157,302)(158,301)(159,305)
(160,304)(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)
(328,486)(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)
(336,498)(337,497)(338,496)(339,500)(340,499)(341,503)(342,502)(343,501)
(344,505)(345,504)(346,508)(347,507)(348,506)(349,510)(350,509)(351,513)
(352,512)(353,511)(354,515)(355,514)(356,518)(357,517)(358,516)(359,520)
(360,519)(361,528)(362,527)(363,526)(364,530)(365,529)(366,523)(367,522)
(368,521)(369,525)(370,524)(371,538)(372,537)(373,536)(374,540)(375,539)
(376,533)(377,532)(378,531)(379,535)(380,534)(381,548)(382,547)(383,546)
(384,550)(385,549)(386,543)(387,542)(388,541)(389,545)(390,544)(391,558)
(392,557)(393,556)(394,560)(395,559)(396,553)(397,552)(398,551)(399,555)
(400,554)(401,573)(402,572)(403,571)(404,575)(405,574)(406,578)(407,577)
(408,576)(409,580)(410,579)(411,563)(412,562)(413,561)(414,565)(415,564)
(416,568)(417,567)(418,566)(419,570)(420,569)(421,593)(422,592)(423,591)
(424,595)(425,594)(426,598)(427,597)(428,596)(429,600)(430,599)(431,583)
(432,582)(433,581)(434,585)(435,584)(436,588)(437,587)(438,586)(439,590)
(440,589)(441,618)(442,617)(443,616)(444,620)(445,619)(446,613)(447,612)
(448,611)(449,615)(450,614)(451,608)(452,607)(453,606)(454,610)(455,609)
(456,603)(457,602)(458,601)(459,605)(460,604)(461,638)(462,637)(463,636)
(464,640)(465,639)(466,633)(467,632)(468,631)(469,635)(470,634)(471,628)
(472,627)(473,626)(474,630)(475,629)(476,623)(477,622)(478,621)(479,625)
(480,624);
poly := sub<Sym(640)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope