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# Polytope of Type {8,80}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,80}*1280d
Also Known As : {8,80|2}. if this polytope has another name.
Group : SmallGroup(1280,82994)
Rank : 3
Schlafli Type : {8,80}
Number of vertices, edges, etc : 8, 320, 80
Order of s0s1s2 : 80
Order of s0s1s2s1 : 2
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}*640a
4-fold quotients : {4,40}*320a, {8,20}*320a, {2,80}*320
5-fold quotients : {8,16}*256d
8-fold quotients : {4,20}*160, {2,40}*160, {8,10}*160
10-fold quotients : {8,8}*128b, {4,16}*128a
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,8}*64a, {8,4}*64a, {2,16}*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 := (  1,161)(  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)
( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,216)( 47,217)( 48,218)
( 49,219)( 50,220)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)( 56,206)
( 57,207)( 58,208)( 59,209)( 60,210)( 61,231)( 62,232)( 63,233)( 64,234)
( 65,235)( 66,236)( 67,237)( 68,238)( 69,239)( 70,240)( 71,221)( 72,222)
( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)
( 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)
(121,281)(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)
(361,531)(362,532)(363,533)(364,534)(365,535)(366,536)(367,537)(368,538)
(369,539)(370,540)(371,521)(372,522)(373,523)(374,524)(375,525)(376,526)
(377,527)(378,528)(379,529)(380,530)(381,551)(382,552)(383,553)(384,554)
(385,555)(386,556)(387,557)(388,558)(389,559)(390,560)(391,541)(392,542)
(393,543)(394,544)(395,545)(396,546)(397,547)(398,548)(399,549)(400,550)
(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)
(441,601)(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);;
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, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 46, 56)
( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 61, 76)( 62, 80)( 63, 79)( 64, 78)
( 65, 77)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 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)(121,151)(122,155)(123,154)(124,153)(125,152)(126,156)
(127,160)(128,159)(129,158)(130,157)(131,141)(132,145)(133,144)(134,143)
(135,142)(136,146)(137,150)(138,149)(139,148)(140,147)(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)(361,451)(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)(381,476)(382,480)(383,479)(384,478)(385,477)(386,471)
(387,475)(388,474)(389,473)(390,472)(391,466)(392,470)(393,469)(394,468)
(395,467)(396,461)(397,465)(398,464)(399,463)(400,462)(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)
( 41,523)( 42,522)( 43,521)( 44,525)( 45,524)( 46,528)( 47,527)( 48,526)
( 49,530)( 50,529)( 51,533)( 52,532)( 53,531)( 54,535)( 55,534)( 56,538)
( 57,537)( 58,536)( 59,540)( 60,539)( 61,548)( 62,547)( 63,546)( 64,550)
( 65,549)( 66,543)( 67,542)( 68,541)( 69,545)( 70,544)( 71,558)( 72,557)
( 73,556)( 74,560)( 75,559)( 76,553)( 77,552)( 78,551)( 79,555)( 80,554)
( 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)
(121,633)(122,632)(123,631)(124,635)(125,634)(126,638)(127,637)(128,636)
(129,640)(130,639)(131,623)(132,622)(133,621)(134,625)(135,624)(136,628)
(137,627)(138,626)(139,630)(140,629)(141,613)(142,612)(143,611)(144,615)
(145,614)(146,618)(147,617)(148,616)(149,620)(150,619)(151,603)(152,602)
(153,601)(154,605)(155,604)(156,608)(157,607)(158,606)(159,610)(160,609)
(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)
(201,363)(202,362)(203,361)(204,365)(205,364)(206,368)(207,367)(208,366)
(209,370)(210,369)(211,373)(212,372)(213,371)(214,375)(215,374)(216,378)
(217,377)(218,376)(219,380)(220,379)(221,388)(222,387)(223,386)(224,390)
(225,389)(226,383)(227,382)(228,381)(229,385)(230,384)(231,398)(232,397)
(233,396)(234,400)(235,399)(236,393)(237,392)(238,391)(239,395)(240,394)
(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)
(281,473)(282,472)(283,471)(284,475)(285,474)(286,478)(287,477)(288,476)
(289,480)(290,479)(291,463)(292,462)(293,461)(294,465)(295,464)(296,468)
(297,467)(298,466)(299,470)(300,469)(301,453)(302,452)(303,451)(304,455)
(305,454)(306,458)(307,457)(308,456)(309,460)(310,459)(311,443)(312,442)
(313,441)(314,445)(315,444)(316,448)(317,447)(318,446)(319,450)(320,449);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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)!(  1,161)(  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)( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,216)( 47,217)
( 48,218)( 49,219)( 50,220)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)
( 56,206)( 57,207)( 58,208)( 59,209)( 60,210)( 61,231)( 62,232)( 63,233)
( 64,234)( 65,235)( 66,236)( 67,237)( 68,238)( 69,239)( 70,240)( 71,221)
( 72,222)( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)
( 80,230)( 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)(121,281)(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)(361,531)(362,532)(363,533)(364,534)(365,535)(366,536)(367,537)
(368,538)(369,539)(370,540)(371,521)(372,522)(373,523)(374,524)(375,525)
(376,526)(377,527)(378,528)(379,529)(380,530)(381,551)(382,552)(383,553)
(384,554)(385,555)(386,556)(387,557)(388,558)(389,559)(390,560)(391,541)
(392,542)(393,543)(394,544)(395,545)(396,546)(397,547)(398,548)(399,549)
(400,550)(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)(441,601)(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);
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, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 56)( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 61, 76)( 62, 80)( 63, 79)
( 64, 78)( 65, 77)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 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)(121,151)(122,155)(123,154)(124,153)(125,152)
(126,156)(127,160)(128,159)(129,158)(130,157)(131,141)(132,145)(133,144)
(134,143)(135,142)(136,146)(137,150)(138,149)(139,148)(140,147)(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)(361,451)
(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)(381,476)(382,480)(383,479)(384,478)(385,477)
(386,471)(387,475)(388,474)(389,473)(390,472)(391,466)(392,470)(393,469)
(394,468)(395,467)(396,461)(397,465)(398,464)(399,463)(400,462)(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)( 41,523)( 42,522)( 43,521)( 44,525)( 45,524)( 46,528)( 47,527)
( 48,526)( 49,530)( 50,529)( 51,533)( 52,532)( 53,531)( 54,535)( 55,534)
( 56,538)( 57,537)( 58,536)( 59,540)( 60,539)( 61,548)( 62,547)( 63,546)
( 64,550)( 65,549)( 66,543)( 67,542)( 68,541)( 69,545)( 70,544)( 71,558)
( 72,557)( 73,556)( 74,560)( 75,559)( 76,553)( 77,552)( 78,551)( 79,555)
( 80,554)( 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)(121,633)(122,632)(123,631)(124,635)(125,634)(126,638)(127,637)
(128,636)(129,640)(130,639)(131,623)(132,622)(133,621)(134,625)(135,624)
(136,628)(137,627)(138,626)(139,630)(140,629)(141,613)(142,612)(143,611)
(144,615)(145,614)(146,618)(147,617)(148,616)(149,620)(150,619)(151,603)
(152,602)(153,601)(154,605)(155,604)(156,608)(157,607)(158,606)(159,610)
(160,609)(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)(201,363)(202,362)(203,361)(204,365)(205,364)(206,368)(207,367)
(208,366)(209,370)(210,369)(211,373)(212,372)(213,371)(214,375)(215,374)
(216,378)(217,377)(218,376)(219,380)(220,379)(221,388)(222,387)(223,386)
(224,390)(225,389)(226,383)(227,382)(228,381)(229,385)(230,384)(231,398)
(232,397)(233,396)(234,400)(235,399)(236,393)(237,392)(238,391)(239,395)
(240,394)(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)(281,473)(282,472)(283,471)(284,475)(285,474)(286,478)(287,477)
(288,476)(289,480)(290,479)(291,463)(292,462)(293,461)(294,465)(295,464)
(296,468)(297,467)(298,466)(299,470)(300,469)(301,453)(302,452)(303,451)
(304,455)(305,454)(306,458)(307,457)(308,456)(309,460)(310,459)(311,443)
(312,442)(313,441)(314,445)(315,444)(316,448)(317,447)(318,446)(319,450)
(320,449);
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, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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