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# Polytope of Type {16,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,40}*1280c
if this polytope has a name.
Group : SmallGroup(1280,82993)
Rank : 3
Schlafli Type : {16,40}
Number of vertices, edges, etc : 16, 320, 40
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}*640d, {16,20}*640a
4-fold quotients : {4,40}*320b, {8,20}*320a, {16,10}*320
5-fold quotients : {16,8}*256c
8-fold quotients : {4,20}*160, {8,10}*160
10-fold quotients : {8,8}*128c, {16,4}*128a
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {8,4}*64a, {4,8}*64b, {16,2}*64
32-fold quotients : {2,10}*40
40-fold quotients : {4,4}*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)( 21,346)( 22,347)( 23,348)( 24,349)
( 25,350)( 26,341)( 27,342)( 28,343)( 29,344)( 30,345)( 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)( 61,396)( 62,397)( 63,398)( 64,399)
( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)( 72,387)
( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)( 80,385)
( 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)(181,506)(182,507)(183,508)(184,509)
(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(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)(221,556)(222,557)(223,558)(224,559)
(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)(232,547)
(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)(240,545)
(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)
( 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 := (  1,163)(  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)
( 41,213)( 42,212)( 43,211)( 44,215)( 45,214)( 46,218)( 47,217)( 48,216)
( 49,220)( 50,219)( 51,203)( 52,202)( 53,201)( 54,205)( 55,204)( 56,208)
( 57,207)( 58,206)( 59,210)( 60,209)( 61,233)( 62,232)( 63,231)( 64,235)
( 65,234)( 66,238)( 67,237)( 68,236)( 69,240)( 70,239)( 71,223)( 72,222)
( 73,221)( 74,225)( 75,224)( 76,228)( 77,227)( 78,226)( 79,230)( 80,229)
( 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)
(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)(128,286)
(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)(136,298)
(137,297)(138,296)(139,300)(140,299)(141,303)(142,302)(143,301)(144,305)
(145,304)(146,308)(147,307)(148,306)(149,310)(150,309)(151,313)(152,312)
(153,311)(154,315)(155,314)(156,318)(157,317)(158,316)(159,320)(160,319)
(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)
(361,533)(362,532)(363,531)(364,535)(365,534)(366,538)(367,537)(368,536)
(369,540)(370,539)(371,523)(372,522)(373,521)(374,525)(375,524)(376,528)
(377,527)(378,526)(379,530)(380,529)(381,553)(382,552)(383,551)(384,555)
(385,554)(386,558)(387,557)(388,556)(389,560)(390,559)(391,543)(392,542)
(393,541)(394,545)(395,544)(396,548)(397,547)(398,546)(399,550)(400,549)
(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)
(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)(448,606)
(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)(456,618)
(457,617)(458,616)(459,620)(460,619)(461,623)(462,622)(463,621)(464,625)
(465,624)(466,628)(467,627)(468,626)(469,630)(470,629)(471,633)(472,632)
(473,631)(474,635)(475,634)(476,638)(477,637)(478,636)(479,640)(480,639);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*s0*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*s0*s1*s2*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)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)
( 16,336)( 17,337)( 18,338)( 19,339)( 20,340)( 21,346)( 22,347)( 23,348)
( 24,349)( 25,350)( 26,341)( 27,342)( 28,343)( 29,344)( 30,345)( 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)( 61,396)( 62,397)( 63,398)
( 64,399)( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)
( 72,387)( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)
( 80,385)( 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)(181,506)(182,507)(183,508)
(184,509)(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(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)(221,556)(222,557)(223,558)
(224,559)(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)
(232,547)(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)
(240,545)(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)( 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)!(  1,163)(  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)( 41,213)( 42,212)( 43,211)( 44,215)( 45,214)( 46,218)( 47,217)
( 48,216)( 49,220)( 50,219)( 51,203)( 52,202)( 53,201)( 54,205)( 55,204)
( 56,208)( 57,207)( 58,206)( 59,210)( 60,209)( 61,233)( 62,232)( 63,231)
( 64,235)( 65,234)( 66,238)( 67,237)( 68,236)( 69,240)( 70,239)( 71,223)
( 72,222)( 73,221)( 74,225)( 75,224)( 76,228)( 77,227)( 78,226)( 79,230)
( 80,229)( 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)(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)
(128,286)(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)
(136,298)(137,297)(138,296)(139,300)(140,299)(141,303)(142,302)(143,301)
(144,305)(145,304)(146,308)(147,307)(148,306)(149,310)(150,309)(151,313)
(152,312)(153,311)(154,315)(155,314)(156,318)(157,317)(158,316)(159,320)
(160,319)(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)(361,533)(362,532)(363,531)(364,535)(365,534)(366,538)(367,537)
(368,536)(369,540)(370,539)(371,523)(372,522)(373,521)(374,525)(375,524)
(376,528)(377,527)(378,526)(379,530)(380,529)(381,553)(382,552)(383,551)
(384,555)(385,554)(386,558)(387,557)(388,556)(389,560)(390,559)(391,543)
(392,542)(393,541)(394,545)(395,544)(396,548)(397,547)(398,546)(399,550)
(400,549)(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)(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)
(448,606)(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)
(456,618)(457,617)(458,616)(459,620)(460,619)(461,623)(462,622)(463,621)
(464,625)(465,624)(466,628)(467,627)(468,626)(469,630)(470,629)(471,633)
(472,632)(473,631)(474,635)(475,634)(476,638)(477,637)(478,636)(479,640)
(480,639);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*s0*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*s0*s1*s2*s1 >;

```
References : None.
to this polytope