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# Polytope of Type {8,80}

Atlas Canonical Name : {8,80}*1280f
if this polytope has a name.
Group : SmallGroup(1280,83050)
Rank : 3
Schlafli Type : {8,80}
Number of vertices, edges, etc : 8, 320, 80
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {8,40}*640b, {4,80}*640b
4-fold quotients : {4,40}*320a, {8,20}*320a
5-fold quotients : {8,16}*256f
8-fold quotients : {4,20}*160, {2,40}*160, {8,10}*160
10-fold quotients : {8,8}*128b, {4,16}*128b
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,8}*64a, {8,4}*64a
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 := (  1,161)(  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)
( 41,216)( 42,217)( 43,218)( 44,219)( 45,220)( 46,211)( 47,212)( 48,213)
( 49,214)( 50,215)( 51,206)( 52,207)( 53,208)( 54,209)( 55,210)( 56,201)
( 57,202)( 58,203)( 59,204)( 60,205)( 61,236)( 62,237)( 63,238)( 64,239)
( 65,240)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,226)( 72,227)
( 73,228)( 74,229)( 75,230)( 76,221)( 77,222)( 78,223)( 79,224)( 80,225)
( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,256)( 87,257)( 88,258)
( 89,259)( 90,260)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,246)
( 97,247)( 98,248)( 99,249)(100,250)(101,271)(102,272)(103,273)(104,274)
(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,261)(112,262)
(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)
(121,286)(122,287)(123,288)(124,289)(125,290)(126,281)(127,282)(128,283)
(129,284)(130,285)(131,296)(132,297)(133,298)(134,299)(135,300)(136,291)
(137,292)(138,293)(139,294)(140,295)(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)(341,501)(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)
(361,536)(362,537)(363,538)(364,539)(365,540)(366,531)(367,532)(368,533)
(369,534)(370,535)(371,526)(372,527)(373,528)(374,529)(375,530)(376,521)
(377,522)(378,523)(379,524)(380,525)(381,556)(382,557)(383,558)(384,559)
(385,560)(386,551)(387,552)(388,553)(389,554)(390,555)(391,546)(392,547)
(393,548)(394,549)(395,550)(396,541)(397,542)(398,543)(399,544)(400,545)
(401,571)(402,572)(403,573)(404,574)(405,575)(406,576)(407,577)(408,578)
(409,579)(410,580)(411,561)(412,562)(413,563)(414,564)(415,565)(416,566)
(417,567)(418,568)(419,569)(420,570)(421,591)(422,592)(423,593)(424,594)
(425,595)(426,596)(427,597)(428,598)(429,599)(430,600)(431,581)(432,582)
(433,583)(434,584)(435,585)(436,586)(437,587)(438,588)(439,589)(440,590)
(441,606)(442,607)(443,608)(444,609)(445,610)(446,601)(447,602)(448,603)
(449,604)(450,605)(451,616)(452,617)(453,618)(454,619)(455,620)(456,611)
(457,612)(458,613)(459,614)(460,615)(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);;
s1 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 36)( 32, 40)( 33, 39)
( 34, 38)( 35, 37)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 46, 51)
( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 61, 71)( 62, 75)( 63, 74)( 64, 73)
( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 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)(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)
(127,155)(128,154)(129,153)(130,152)(131,146)(132,150)(133,149)(134,148)
(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(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)(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)
(187,225)(188,224)(189,223)(190,222)(191,236)(192,240)(193,239)(194,238)
(195,237)(196,231)(197,235)(198,234)(199,233)(200,232)(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)(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)
(347,425)(348,424)(349,423)(350,422)(351,436)(352,440)(353,439)(354,438)
(355,437)(356,431)(357,435)(358,434)(359,433)(360,432)(361,456)(362,460)
(363,459)(364,458)(365,457)(366,451)(367,455)(368,454)(369,453)(370,452)
(371,446)(372,450)(373,449)(374,448)(375,447)(376,441)(377,445)(378,444)
(379,443)(380,442)(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)(481,611)(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)(501,636)(502,640)(503,639)(504,638)(505,637)(506,631)
(507,635)(508,634)(509,633)(510,632)(511,626)(512,630)(513,629)(514,628)
(515,627)(516,621)(517,625)(518,624)(519,623)(520,622)(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)(541,596)(542,600)(543,599)(544,598)(545,597)(546,591)
(547,595)(548,594)(549,593)(550,592)(551,586)(552,590)(553,589)(554,588)
(555,587)(556,581)(557,585)(558,584)(559,583)(560,582);;
s2 := (  1,483)(  2,482)(  3,481)(  4,485)(  5,484)(  6,488)(  7,487)(  8,486)
(  9,490)( 10,489)( 11,493)( 12,492)( 13,491)( 14,495)( 15,494)( 16,498)
( 17,497)( 18,496)( 19,500)( 20,499)( 21,508)( 22,507)( 23,506)( 24,510)
( 25,509)( 26,503)( 27,502)( 28,501)( 29,505)( 30,504)( 31,518)( 32,517)
( 33,516)( 34,520)( 35,519)( 36,513)( 37,512)( 38,511)( 39,515)( 40,514)
( 41,528)( 42,527)( 43,526)( 44,530)( 45,529)( 46,523)( 47,522)( 48,521)
( 49,525)( 50,524)( 51,538)( 52,537)( 53,536)( 54,540)( 55,539)( 56,533)
( 57,532)( 58,531)( 59,535)( 60,534)( 61,543)( 62,542)( 63,541)( 64,545)
( 65,544)( 66,548)( 67,547)( 68,546)( 69,550)( 70,549)( 71,553)( 72,552)
( 73,551)( 74,555)( 75,554)( 76,558)( 77,557)( 78,556)( 79,560)( 80,559)
( 81,593)( 82,592)( 83,591)( 84,595)( 85,594)( 86,598)( 87,597)( 88,596)
( 89,600)( 90,599)( 91,583)( 92,582)( 93,581)( 94,585)( 95,584)( 96,588)
( 97,587)( 98,586)( 99,590)(100,589)(101,573)(102,572)(103,571)(104,575)
(105,574)(106,578)(107,577)(108,576)(109,580)(110,579)(111,563)(112,562)
(113,561)(114,565)(115,564)(116,568)(117,567)(118,566)(119,570)(120,569)
(121,638)(122,637)(123,636)(124,640)(125,639)(126,633)(127,632)(128,631)
(129,635)(130,634)(131,628)(132,627)(133,626)(134,630)(135,629)(136,623)
(137,622)(138,621)(139,625)(140,624)(141,618)(142,617)(143,616)(144,620)
(145,619)(146,613)(147,612)(148,611)(149,615)(150,614)(151,608)(152,607)
(153,606)(154,610)(155,609)(156,603)(157,602)(158,601)(159,605)(160,604)
(161,323)(162,322)(163,321)(164,325)(165,324)(166,328)(167,327)(168,326)
(169,330)(170,329)(171,333)(172,332)(173,331)(174,335)(175,334)(176,338)
(177,337)(178,336)(179,340)(180,339)(181,348)(182,347)(183,346)(184,350)
(185,349)(186,343)(187,342)(188,341)(189,345)(190,344)(191,358)(192,357)
(193,356)(194,360)(195,359)(196,353)(197,352)(198,351)(199,355)(200,354)
(201,368)(202,367)(203,366)(204,370)(205,369)(206,363)(207,362)(208,361)
(209,365)(210,364)(211,378)(212,377)(213,376)(214,380)(215,379)(216,373)
(217,372)(218,371)(219,375)(220,374)(221,383)(222,382)(223,381)(224,385)
(225,384)(226,388)(227,387)(228,386)(229,390)(230,389)(231,393)(232,392)
(233,391)(234,395)(235,394)(236,398)(237,397)(238,396)(239,400)(240,399)
(241,433)(242,432)(243,431)(244,435)(245,434)(246,438)(247,437)(248,436)
(249,440)(250,439)(251,423)(252,422)(253,421)(254,425)(255,424)(256,428)
(257,427)(258,426)(259,430)(260,429)(261,413)(262,412)(263,411)(264,415)
(265,414)(266,418)(267,417)(268,416)(269,420)(270,419)(271,403)(272,402)
(273,401)(274,405)(275,404)(276,408)(277,407)(278,406)(279,410)(280,409)
(281,478)(282,477)(283,476)(284,480)(285,479)(286,473)(287,472)(288,471)
(289,475)(290,474)(291,468)(292,467)(293,466)(294,470)(295,469)(296,463)
(297,462)(298,461)(299,465)(300,464)(301,458)(302,457)(303,456)(304,460)
(305,459)(306,453)(307,452)(308,451)(309,455)(310,454)(311,448)(312,447)
(313,446)(314,450)(315,449)(316,443)(317,442)(318,441)(319,445)(320,444);;
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,
s2*s0*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*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope