Polytope of Type {8,51}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,51}*1632
if this polytope has a name.
Group : SmallGroup(1632,1033)
Rank : 3
Schlafli Type : {8,51}
Number of vertices, edges, etc : 16, 408, 102
Order of s0s1s2 : 204
Order of s0s1s2s1 : 8
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 : {4,51}*816
4-fold quotients : {4,51}*408
8-fold quotients : {2,51}*204
17-fold quotients : {8,3}*96
24-fold quotients : {2,17}*68
34-fold quotients : {4,3}*48
68-fold quotients : {4,3}*24
136-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,413)( 2,414)( 3,416)( 4,415)( 5,410)( 6,409)( 7,411)( 8,412)
( 9,421)( 10,422)( 11,424)( 12,423)( 13,418)( 14,417)( 15,419)( 16,420)
( 17,429)( 18,430)( 19,432)( 20,431)( 21,426)( 22,425)( 23,427)( 24,428)
( 25,437)( 26,438)( 27,440)( 28,439)( 29,434)( 30,433)( 31,435)( 32,436)
( 33,445)( 34,446)( 35,448)( 36,447)( 37,442)( 38,441)( 39,443)( 40,444)
( 41,453)( 42,454)( 43,456)( 44,455)( 45,450)( 46,449)( 47,451)( 48,452)
( 49,461)( 50,462)( 51,464)( 52,463)( 53,458)( 54,457)( 55,459)( 56,460)
( 57,469)( 58,470)( 59,472)( 60,471)( 61,466)( 62,465)( 63,467)( 64,468)
( 65,477)( 66,478)( 67,480)( 68,479)( 69,474)( 70,473)( 71,475)( 72,476)
( 73,485)( 74,486)( 75,488)( 76,487)( 77,482)( 78,481)( 79,483)( 80,484)
( 81,493)( 82,494)( 83,496)( 84,495)( 85,490)( 86,489)( 87,491)( 88,492)
( 89,501)( 90,502)( 91,504)( 92,503)( 93,498)( 94,497)( 95,499)( 96,500)
( 97,509)( 98,510)( 99,512)(100,511)(101,506)(102,505)(103,507)(104,508)
(105,517)(106,518)(107,520)(108,519)(109,514)(110,513)(111,515)(112,516)
(113,525)(114,526)(115,528)(116,527)(117,522)(118,521)(119,523)(120,524)
(121,533)(122,534)(123,536)(124,535)(125,530)(126,529)(127,531)(128,532)
(129,541)(130,542)(131,544)(132,543)(133,538)(134,537)(135,539)(136,540)
(137,549)(138,550)(139,552)(140,551)(141,546)(142,545)(143,547)(144,548)
(145,557)(146,558)(147,560)(148,559)(149,554)(150,553)(151,555)(152,556)
(153,565)(154,566)(155,568)(156,567)(157,562)(158,561)(159,563)(160,564)
(161,573)(162,574)(163,576)(164,575)(165,570)(166,569)(167,571)(168,572)
(169,581)(170,582)(171,584)(172,583)(173,578)(174,577)(175,579)(176,580)
(177,589)(178,590)(179,592)(180,591)(181,586)(182,585)(183,587)(184,588)
(185,597)(186,598)(187,600)(188,599)(189,594)(190,593)(191,595)(192,596)
(193,605)(194,606)(195,608)(196,607)(197,602)(198,601)(199,603)(200,604)
(201,613)(202,614)(203,616)(204,615)(205,610)(206,609)(207,611)(208,612)
(209,621)(210,622)(211,624)(212,623)(213,618)(214,617)(215,619)(216,620)
(217,629)(218,630)(219,632)(220,631)(221,626)(222,625)(223,627)(224,628)
(225,637)(226,638)(227,640)(228,639)(229,634)(230,633)(231,635)(232,636)
(233,645)(234,646)(235,648)(236,647)(237,642)(238,641)(239,643)(240,644)
(241,653)(242,654)(243,656)(244,655)(245,650)(246,649)(247,651)(248,652)
(249,661)(250,662)(251,664)(252,663)(253,658)(254,657)(255,659)(256,660)
(257,669)(258,670)(259,672)(260,671)(261,666)(262,665)(263,667)(264,668)
(265,677)(266,678)(267,680)(268,679)(269,674)(270,673)(271,675)(272,676)
(273,685)(274,686)(275,688)(276,687)(277,682)(278,681)(279,683)(280,684)
(281,693)(282,694)(283,696)(284,695)(285,690)(286,689)(287,691)(288,692)
(289,701)(290,702)(291,704)(292,703)(293,698)(294,697)(295,699)(296,700)
(297,709)(298,710)(299,712)(300,711)(301,706)(302,705)(303,707)(304,708)
(305,717)(306,718)(307,720)(308,719)(309,714)(310,713)(311,715)(312,716)
(313,725)(314,726)(315,728)(316,727)(317,722)(318,721)(319,723)(320,724)
(321,733)(322,734)(323,736)(324,735)(325,730)(326,729)(327,731)(328,732)
(329,741)(330,742)(331,744)(332,743)(333,738)(334,737)(335,739)(336,740)
(337,749)(338,750)(339,752)(340,751)(341,746)(342,745)(343,747)(344,748)
(345,757)(346,758)(347,760)(348,759)(349,754)(350,753)(351,755)(352,756)
(353,765)(354,766)(355,768)(356,767)(357,762)(358,761)(359,763)(360,764)
(361,773)(362,774)(363,776)(364,775)(365,770)(366,769)(367,771)(368,772)
(369,781)(370,782)(371,784)(372,783)(373,778)(374,777)(375,779)(376,780)
(377,789)(378,790)(379,792)(380,791)(381,786)(382,785)(383,787)(384,788)
(385,797)(386,798)(387,800)(388,799)(389,794)(390,793)(391,795)(392,796)
(393,805)(394,806)(395,808)(396,807)(397,802)(398,801)(399,803)(400,804)
(401,813)(402,814)(403,816)(404,815)(405,810)(406,809)(407,811)(408,812);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 9,129)( 10,130)( 11,132)( 12,131)( 13,135)
( 14,136)( 15,133)( 16,134)( 17,121)( 18,122)( 19,124)( 20,123)( 21,127)
( 22,128)( 23,125)( 24,126)( 25,113)( 26,114)( 27,116)( 28,115)( 29,119)
( 30,120)( 31,117)( 32,118)( 33,105)( 34,106)( 35,108)( 36,107)( 37,111)
( 38,112)( 39,109)( 40,110)( 41, 97)( 42, 98)( 43,100)( 44, 99)( 45,103)
( 46,104)( 47,101)( 48,102)( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53, 95)
( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 84)( 60, 83)( 61, 87)
( 62, 88)( 63, 85)( 64, 86)( 65, 73)( 66, 74)( 67, 76)( 68, 75)( 69, 79)
( 70, 80)( 71, 77)( 72, 78)(137,273)(138,274)(139,276)(140,275)(141,279)
(142,280)(143,277)(144,278)(145,401)(146,402)(147,404)(148,403)(149,407)
(150,408)(151,405)(152,406)(153,393)(154,394)(155,396)(156,395)(157,399)
(158,400)(159,397)(160,398)(161,385)(162,386)(163,388)(164,387)(165,391)
(166,392)(167,389)(168,390)(169,377)(170,378)(171,380)(172,379)(173,383)
(174,384)(175,381)(176,382)(177,369)(178,370)(179,372)(180,371)(181,375)
(182,376)(183,373)(184,374)(185,361)(186,362)(187,364)(188,363)(189,367)
(190,368)(191,365)(192,366)(193,353)(194,354)(195,356)(196,355)(197,359)
(198,360)(199,357)(200,358)(201,345)(202,346)(203,348)(204,347)(205,351)
(206,352)(207,349)(208,350)(209,337)(210,338)(211,340)(212,339)(213,343)
(214,344)(215,341)(216,342)(217,329)(218,330)(219,332)(220,331)(221,335)
(222,336)(223,333)(224,334)(225,321)(226,322)(227,324)(228,323)(229,327)
(230,328)(231,325)(232,326)(233,313)(234,314)(235,316)(236,315)(237,319)
(238,320)(239,317)(240,318)(241,305)(242,306)(243,308)(244,307)(245,311)
(246,312)(247,309)(248,310)(249,297)(250,298)(251,300)(252,299)(253,303)
(254,304)(255,301)(256,302)(257,289)(258,290)(259,292)(260,291)(261,295)
(262,296)(263,293)(264,294)(265,281)(266,282)(267,284)(268,283)(269,287)
(270,288)(271,285)(272,286)(409,410)(413,416)(414,415)(417,538)(418,537)
(419,539)(420,540)(421,544)(422,543)(423,542)(424,541)(425,530)(426,529)
(427,531)(428,532)(429,536)(430,535)(431,534)(432,533)(433,522)(434,521)
(435,523)(436,524)(437,528)(438,527)(439,526)(440,525)(441,514)(442,513)
(443,515)(444,516)(445,520)(446,519)(447,518)(448,517)(449,506)(450,505)
(451,507)(452,508)(453,512)(454,511)(455,510)(456,509)(457,498)(458,497)
(459,499)(460,500)(461,504)(462,503)(463,502)(464,501)(465,490)(466,489)
(467,491)(468,492)(469,496)(470,495)(471,494)(472,493)(473,482)(474,481)
(475,483)(476,484)(477,488)(478,487)(479,486)(480,485)(545,682)(546,681)
(547,683)(548,684)(549,688)(550,687)(551,686)(552,685)(553,810)(554,809)
(555,811)(556,812)(557,816)(558,815)(559,814)(560,813)(561,802)(562,801)
(563,803)(564,804)(565,808)(566,807)(567,806)(568,805)(569,794)(570,793)
(571,795)(572,796)(573,800)(574,799)(575,798)(576,797)(577,786)(578,785)
(579,787)(580,788)(581,792)(582,791)(583,790)(584,789)(585,778)(586,777)
(587,779)(588,780)(589,784)(590,783)(591,782)(592,781)(593,770)(594,769)
(595,771)(596,772)(597,776)(598,775)(599,774)(600,773)(601,762)(602,761)
(603,763)(604,764)(605,768)(606,767)(607,766)(608,765)(609,754)(610,753)
(611,755)(612,756)(613,760)(614,759)(615,758)(616,757)(617,746)(618,745)
(619,747)(620,748)(621,752)(622,751)(623,750)(624,749)(625,738)(626,737)
(627,739)(628,740)(629,744)(630,743)(631,742)(632,741)(633,730)(634,729)
(635,731)(636,732)(637,736)(638,735)(639,734)(640,733)(641,722)(642,721)
(643,723)(644,724)(645,728)(646,727)(647,726)(648,725)(649,714)(650,713)
(651,715)(652,716)(653,720)(654,719)(655,718)(656,717)(657,706)(658,705)
(659,707)(660,708)(661,712)(662,711)(663,710)(664,709)(665,698)(666,697)
(667,699)(668,700)(669,704)(670,703)(671,702)(672,701)(673,690)(674,689)
(675,691)(676,692)(677,696)(678,695)(679,694)(680,693);;
s2 := ( 1,145)( 2,146)( 3,151)( 4,152)( 5,150)( 6,149)( 7,147)( 8,148)
( 9,137)( 10,138)( 11,143)( 12,144)( 13,142)( 14,141)( 15,139)( 16,140)
( 17,265)( 18,266)( 19,271)( 20,272)( 21,270)( 22,269)( 23,267)( 24,268)
( 25,257)( 26,258)( 27,263)( 28,264)( 29,262)( 30,261)( 31,259)( 32,260)
( 33,249)( 34,250)( 35,255)( 36,256)( 37,254)( 38,253)( 39,251)( 40,252)
( 41,241)( 42,242)( 43,247)( 44,248)( 45,246)( 46,245)( 47,243)( 48,244)
( 49,233)( 50,234)( 51,239)( 52,240)( 53,238)( 54,237)( 55,235)( 56,236)
( 57,225)( 58,226)( 59,231)( 60,232)( 61,230)( 62,229)( 63,227)( 64,228)
( 65,217)( 66,218)( 67,223)( 68,224)( 69,222)( 70,221)( 71,219)( 72,220)
( 73,209)( 74,210)( 75,215)( 76,216)( 77,214)( 78,213)( 79,211)( 80,212)
( 81,201)( 82,202)( 83,207)( 84,208)( 85,206)( 86,205)( 87,203)( 88,204)
( 89,193)( 90,194)( 91,199)( 92,200)( 93,198)( 94,197)( 95,195)( 96,196)
( 97,185)( 98,186)( 99,191)(100,192)(101,190)(102,189)(103,187)(104,188)
(105,177)(106,178)(107,183)(108,184)(109,182)(110,181)(111,179)(112,180)
(113,169)(114,170)(115,175)(116,176)(117,174)(118,173)(119,171)(120,172)
(121,161)(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)
(129,153)(130,154)(131,159)(132,160)(133,158)(134,157)(135,155)(136,156)
(273,281)(274,282)(275,287)(276,288)(277,286)(278,285)(279,283)(280,284)
(289,401)(290,402)(291,407)(292,408)(293,406)(294,405)(295,403)(296,404)
(297,393)(298,394)(299,399)(300,400)(301,398)(302,397)(303,395)(304,396)
(305,385)(306,386)(307,391)(308,392)(309,390)(310,389)(311,387)(312,388)
(313,377)(314,378)(315,383)(316,384)(317,382)(318,381)(319,379)(320,380)
(321,369)(322,370)(323,375)(324,376)(325,374)(326,373)(327,371)(328,372)
(329,361)(330,362)(331,367)(332,368)(333,366)(334,365)(335,363)(336,364)
(337,353)(338,354)(339,359)(340,360)(341,358)(342,357)(343,355)(344,356)
(347,351)(348,352)(349,350)(409,554)(410,553)(411,560)(412,559)(413,557)
(414,558)(415,556)(416,555)(417,546)(418,545)(419,552)(420,551)(421,549)
(422,550)(423,548)(424,547)(425,674)(426,673)(427,680)(428,679)(429,677)
(430,678)(431,676)(432,675)(433,666)(434,665)(435,672)(436,671)(437,669)
(438,670)(439,668)(440,667)(441,658)(442,657)(443,664)(444,663)(445,661)
(446,662)(447,660)(448,659)(449,650)(450,649)(451,656)(452,655)(453,653)
(454,654)(455,652)(456,651)(457,642)(458,641)(459,648)(460,647)(461,645)
(462,646)(463,644)(464,643)(465,634)(466,633)(467,640)(468,639)(469,637)
(470,638)(471,636)(472,635)(473,626)(474,625)(475,632)(476,631)(477,629)
(478,630)(479,628)(480,627)(481,618)(482,617)(483,624)(484,623)(485,621)
(486,622)(487,620)(488,619)(489,610)(490,609)(491,616)(492,615)(493,613)
(494,614)(495,612)(496,611)(497,602)(498,601)(499,608)(500,607)(501,605)
(502,606)(503,604)(504,603)(505,594)(506,593)(507,600)(508,599)(509,597)
(510,598)(511,596)(512,595)(513,586)(514,585)(515,592)(516,591)(517,589)
(518,590)(519,588)(520,587)(521,578)(522,577)(523,584)(524,583)(525,581)
(526,582)(527,580)(528,579)(529,570)(530,569)(531,576)(532,575)(533,573)
(534,574)(535,572)(536,571)(537,562)(538,561)(539,568)(540,567)(541,565)
(542,566)(543,564)(544,563)(681,690)(682,689)(683,696)(684,695)(685,693)
(686,694)(687,692)(688,691)(697,810)(698,809)(699,816)(700,815)(701,813)
(702,814)(703,812)(704,811)(705,802)(706,801)(707,808)(708,807)(709,805)
(710,806)(711,804)(712,803)(713,794)(714,793)(715,800)(716,799)(717,797)
(718,798)(719,796)(720,795)(721,786)(722,785)(723,792)(724,791)(725,789)
(726,790)(727,788)(728,787)(729,778)(730,777)(731,784)(732,783)(733,781)
(734,782)(735,780)(736,779)(737,770)(738,769)(739,776)(740,775)(741,773)
(742,774)(743,772)(744,771)(745,762)(746,761)(747,768)(748,767)(749,765)
(750,766)(751,764)(752,763)(753,754)(755,760)(756,759);;
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*s2*s1*s0*s1*s2*s1*s2*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*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(816)!( 1,413)( 2,414)( 3,416)( 4,415)( 5,410)( 6,409)( 7,411)
( 8,412)( 9,421)( 10,422)( 11,424)( 12,423)( 13,418)( 14,417)( 15,419)
( 16,420)( 17,429)( 18,430)( 19,432)( 20,431)( 21,426)( 22,425)( 23,427)
( 24,428)( 25,437)( 26,438)( 27,440)( 28,439)( 29,434)( 30,433)( 31,435)
( 32,436)( 33,445)( 34,446)( 35,448)( 36,447)( 37,442)( 38,441)( 39,443)
( 40,444)( 41,453)( 42,454)( 43,456)( 44,455)( 45,450)( 46,449)( 47,451)
( 48,452)( 49,461)( 50,462)( 51,464)( 52,463)( 53,458)( 54,457)( 55,459)
( 56,460)( 57,469)( 58,470)( 59,472)( 60,471)( 61,466)( 62,465)( 63,467)
( 64,468)( 65,477)( 66,478)( 67,480)( 68,479)( 69,474)( 70,473)( 71,475)
( 72,476)( 73,485)( 74,486)( 75,488)( 76,487)( 77,482)( 78,481)( 79,483)
( 80,484)( 81,493)( 82,494)( 83,496)( 84,495)( 85,490)( 86,489)( 87,491)
( 88,492)( 89,501)( 90,502)( 91,504)( 92,503)( 93,498)( 94,497)( 95,499)
( 96,500)( 97,509)( 98,510)( 99,512)(100,511)(101,506)(102,505)(103,507)
(104,508)(105,517)(106,518)(107,520)(108,519)(109,514)(110,513)(111,515)
(112,516)(113,525)(114,526)(115,528)(116,527)(117,522)(118,521)(119,523)
(120,524)(121,533)(122,534)(123,536)(124,535)(125,530)(126,529)(127,531)
(128,532)(129,541)(130,542)(131,544)(132,543)(133,538)(134,537)(135,539)
(136,540)(137,549)(138,550)(139,552)(140,551)(141,546)(142,545)(143,547)
(144,548)(145,557)(146,558)(147,560)(148,559)(149,554)(150,553)(151,555)
(152,556)(153,565)(154,566)(155,568)(156,567)(157,562)(158,561)(159,563)
(160,564)(161,573)(162,574)(163,576)(164,575)(165,570)(166,569)(167,571)
(168,572)(169,581)(170,582)(171,584)(172,583)(173,578)(174,577)(175,579)
(176,580)(177,589)(178,590)(179,592)(180,591)(181,586)(182,585)(183,587)
(184,588)(185,597)(186,598)(187,600)(188,599)(189,594)(190,593)(191,595)
(192,596)(193,605)(194,606)(195,608)(196,607)(197,602)(198,601)(199,603)
(200,604)(201,613)(202,614)(203,616)(204,615)(205,610)(206,609)(207,611)
(208,612)(209,621)(210,622)(211,624)(212,623)(213,618)(214,617)(215,619)
(216,620)(217,629)(218,630)(219,632)(220,631)(221,626)(222,625)(223,627)
(224,628)(225,637)(226,638)(227,640)(228,639)(229,634)(230,633)(231,635)
(232,636)(233,645)(234,646)(235,648)(236,647)(237,642)(238,641)(239,643)
(240,644)(241,653)(242,654)(243,656)(244,655)(245,650)(246,649)(247,651)
(248,652)(249,661)(250,662)(251,664)(252,663)(253,658)(254,657)(255,659)
(256,660)(257,669)(258,670)(259,672)(260,671)(261,666)(262,665)(263,667)
(264,668)(265,677)(266,678)(267,680)(268,679)(269,674)(270,673)(271,675)
(272,676)(273,685)(274,686)(275,688)(276,687)(277,682)(278,681)(279,683)
(280,684)(281,693)(282,694)(283,696)(284,695)(285,690)(286,689)(287,691)
(288,692)(289,701)(290,702)(291,704)(292,703)(293,698)(294,697)(295,699)
(296,700)(297,709)(298,710)(299,712)(300,711)(301,706)(302,705)(303,707)
(304,708)(305,717)(306,718)(307,720)(308,719)(309,714)(310,713)(311,715)
(312,716)(313,725)(314,726)(315,728)(316,727)(317,722)(318,721)(319,723)
(320,724)(321,733)(322,734)(323,736)(324,735)(325,730)(326,729)(327,731)
(328,732)(329,741)(330,742)(331,744)(332,743)(333,738)(334,737)(335,739)
(336,740)(337,749)(338,750)(339,752)(340,751)(341,746)(342,745)(343,747)
(344,748)(345,757)(346,758)(347,760)(348,759)(349,754)(350,753)(351,755)
(352,756)(353,765)(354,766)(355,768)(356,767)(357,762)(358,761)(359,763)
(360,764)(361,773)(362,774)(363,776)(364,775)(365,770)(366,769)(367,771)
(368,772)(369,781)(370,782)(371,784)(372,783)(373,778)(374,777)(375,779)
(376,780)(377,789)(378,790)(379,792)(380,791)(381,786)(382,785)(383,787)
(384,788)(385,797)(386,798)(387,800)(388,799)(389,794)(390,793)(391,795)
(392,796)(393,805)(394,806)(395,808)(396,807)(397,802)(398,801)(399,803)
(400,804)(401,813)(402,814)(403,816)(404,815)(405,810)(406,809)(407,811)
(408,812);
s1 := Sym(816)!( 3, 4)( 5, 7)( 6, 8)( 9,129)( 10,130)( 11,132)( 12,131)
( 13,135)( 14,136)( 15,133)( 16,134)( 17,121)( 18,122)( 19,124)( 20,123)
( 21,127)( 22,128)( 23,125)( 24,126)( 25,113)( 26,114)( 27,116)( 28,115)
( 29,119)( 30,120)( 31,117)( 32,118)( 33,105)( 34,106)( 35,108)( 36,107)
( 37,111)( 38,112)( 39,109)( 40,110)( 41, 97)( 42, 98)( 43,100)( 44, 99)
( 45,103)( 46,104)( 47,101)( 48,102)( 49, 89)( 50, 90)( 51, 92)( 52, 91)
( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 84)( 60, 83)
( 61, 87)( 62, 88)( 63, 85)( 64, 86)( 65, 73)( 66, 74)( 67, 76)( 68, 75)
( 69, 79)( 70, 80)( 71, 77)( 72, 78)(137,273)(138,274)(139,276)(140,275)
(141,279)(142,280)(143,277)(144,278)(145,401)(146,402)(147,404)(148,403)
(149,407)(150,408)(151,405)(152,406)(153,393)(154,394)(155,396)(156,395)
(157,399)(158,400)(159,397)(160,398)(161,385)(162,386)(163,388)(164,387)
(165,391)(166,392)(167,389)(168,390)(169,377)(170,378)(171,380)(172,379)
(173,383)(174,384)(175,381)(176,382)(177,369)(178,370)(179,372)(180,371)
(181,375)(182,376)(183,373)(184,374)(185,361)(186,362)(187,364)(188,363)
(189,367)(190,368)(191,365)(192,366)(193,353)(194,354)(195,356)(196,355)
(197,359)(198,360)(199,357)(200,358)(201,345)(202,346)(203,348)(204,347)
(205,351)(206,352)(207,349)(208,350)(209,337)(210,338)(211,340)(212,339)
(213,343)(214,344)(215,341)(216,342)(217,329)(218,330)(219,332)(220,331)
(221,335)(222,336)(223,333)(224,334)(225,321)(226,322)(227,324)(228,323)
(229,327)(230,328)(231,325)(232,326)(233,313)(234,314)(235,316)(236,315)
(237,319)(238,320)(239,317)(240,318)(241,305)(242,306)(243,308)(244,307)
(245,311)(246,312)(247,309)(248,310)(249,297)(250,298)(251,300)(252,299)
(253,303)(254,304)(255,301)(256,302)(257,289)(258,290)(259,292)(260,291)
(261,295)(262,296)(263,293)(264,294)(265,281)(266,282)(267,284)(268,283)
(269,287)(270,288)(271,285)(272,286)(409,410)(413,416)(414,415)(417,538)
(418,537)(419,539)(420,540)(421,544)(422,543)(423,542)(424,541)(425,530)
(426,529)(427,531)(428,532)(429,536)(430,535)(431,534)(432,533)(433,522)
(434,521)(435,523)(436,524)(437,528)(438,527)(439,526)(440,525)(441,514)
(442,513)(443,515)(444,516)(445,520)(446,519)(447,518)(448,517)(449,506)
(450,505)(451,507)(452,508)(453,512)(454,511)(455,510)(456,509)(457,498)
(458,497)(459,499)(460,500)(461,504)(462,503)(463,502)(464,501)(465,490)
(466,489)(467,491)(468,492)(469,496)(470,495)(471,494)(472,493)(473,482)
(474,481)(475,483)(476,484)(477,488)(478,487)(479,486)(480,485)(545,682)
(546,681)(547,683)(548,684)(549,688)(550,687)(551,686)(552,685)(553,810)
(554,809)(555,811)(556,812)(557,816)(558,815)(559,814)(560,813)(561,802)
(562,801)(563,803)(564,804)(565,808)(566,807)(567,806)(568,805)(569,794)
(570,793)(571,795)(572,796)(573,800)(574,799)(575,798)(576,797)(577,786)
(578,785)(579,787)(580,788)(581,792)(582,791)(583,790)(584,789)(585,778)
(586,777)(587,779)(588,780)(589,784)(590,783)(591,782)(592,781)(593,770)
(594,769)(595,771)(596,772)(597,776)(598,775)(599,774)(600,773)(601,762)
(602,761)(603,763)(604,764)(605,768)(606,767)(607,766)(608,765)(609,754)
(610,753)(611,755)(612,756)(613,760)(614,759)(615,758)(616,757)(617,746)
(618,745)(619,747)(620,748)(621,752)(622,751)(623,750)(624,749)(625,738)
(626,737)(627,739)(628,740)(629,744)(630,743)(631,742)(632,741)(633,730)
(634,729)(635,731)(636,732)(637,736)(638,735)(639,734)(640,733)(641,722)
(642,721)(643,723)(644,724)(645,728)(646,727)(647,726)(648,725)(649,714)
(650,713)(651,715)(652,716)(653,720)(654,719)(655,718)(656,717)(657,706)
(658,705)(659,707)(660,708)(661,712)(662,711)(663,710)(664,709)(665,698)
(666,697)(667,699)(668,700)(669,704)(670,703)(671,702)(672,701)(673,690)
(674,689)(675,691)(676,692)(677,696)(678,695)(679,694)(680,693);
s2 := Sym(816)!( 1,145)( 2,146)( 3,151)( 4,152)( 5,150)( 6,149)( 7,147)
( 8,148)( 9,137)( 10,138)( 11,143)( 12,144)( 13,142)( 14,141)( 15,139)
( 16,140)( 17,265)( 18,266)( 19,271)( 20,272)( 21,270)( 22,269)( 23,267)
( 24,268)( 25,257)( 26,258)( 27,263)( 28,264)( 29,262)( 30,261)( 31,259)
( 32,260)( 33,249)( 34,250)( 35,255)( 36,256)( 37,254)( 38,253)( 39,251)
( 40,252)( 41,241)( 42,242)( 43,247)( 44,248)( 45,246)( 46,245)( 47,243)
( 48,244)( 49,233)( 50,234)( 51,239)( 52,240)( 53,238)( 54,237)( 55,235)
( 56,236)( 57,225)( 58,226)( 59,231)( 60,232)( 61,230)( 62,229)( 63,227)
( 64,228)( 65,217)( 66,218)( 67,223)( 68,224)( 69,222)( 70,221)( 71,219)
( 72,220)( 73,209)( 74,210)( 75,215)( 76,216)( 77,214)( 78,213)( 79,211)
( 80,212)( 81,201)( 82,202)( 83,207)( 84,208)( 85,206)( 86,205)( 87,203)
( 88,204)( 89,193)( 90,194)( 91,199)( 92,200)( 93,198)( 94,197)( 95,195)
( 96,196)( 97,185)( 98,186)( 99,191)(100,192)(101,190)(102,189)(103,187)
(104,188)(105,177)(106,178)(107,183)(108,184)(109,182)(110,181)(111,179)
(112,180)(113,169)(114,170)(115,175)(116,176)(117,174)(118,173)(119,171)
(120,172)(121,161)(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)
(128,164)(129,153)(130,154)(131,159)(132,160)(133,158)(134,157)(135,155)
(136,156)(273,281)(274,282)(275,287)(276,288)(277,286)(278,285)(279,283)
(280,284)(289,401)(290,402)(291,407)(292,408)(293,406)(294,405)(295,403)
(296,404)(297,393)(298,394)(299,399)(300,400)(301,398)(302,397)(303,395)
(304,396)(305,385)(306,386)(307,391)(308,392)(309,390)(310,389)(311,387)
(312,388)(313,377)(314,378)(315,383)(316,384)(317,382)(318,381)(319,379)
(320,380)(321,369)(322,370)(323,375)(324,376)(325,374)(326,373)(327,371)
(328,372)(329,361)(330,362)(331,367)(332,368)(333,366)(334,365)(335,363)
(336,364)(337,353)(338,354)(339,359)(340,360)(341,358)(342,357)(343,355)
(344,356)(347,351)(348,352)(349,350)(409,554)(410,553)(411,560)(412,559)
(413,557)(414,558)(415,556)(416,555)(417,546)(418,545)(419,552)(420,551)
(421,549)(422,550)(423,548)(424,547)(425,674)(426,673)(427,680)(428,679)
(429,677)(430,678)(431,676)(432,675)(433,666)(434,665)(435,672)(436,671)
(437,669)(438,670)(439,668)(440,667)(441,658)(442,657)(443,664)(444,663)
(445,661)(446,662)(447,660)(448,659)(449,650)(450,649)(451,656)(452,655)
(453,653)(454,654)(455,652)(456,651)(457,642)(458,641)(459,648)(460,647)
(461,645)(462,646)(463,644)(464,643)(465,634)(466,633)(467,640)(468,639)
(469,637)(470,638)(471,636)(472,635)(473,626)(474,625)(475,632)(476,631)
(477,629)(478,630)(479,628)(480,627)(481,618)(482,617)(483,624)(484,623)
(485,621)(486,622)(487,620)(488,619)(489,610)(490,609)(491,616)(492,615)
(493,613)(494,614)(495,612)(496,611)(497,602)(498,601)(499,608)(500,607)
(501,605)(502,606)(503,604)(504,603)(505,594)(506,593)(507,600)(508,599)
(509,597)(510,598)(511,596)(512,595)(513,586)(514,585)(515,592)(516,591)
(517,589)(518,590)(519,588)(520,587)(521,578)(522,577)(523,584)(524,583)
(525,581)(526,582)(527,580)(528,579)(529,570)(530,569)(531,576)(532,575)
(533,573)(534,574)(535,572)(536,571)(537,562)(538,561)(539,568)(540,567)
(541,565)(542,566)(543,564)(544,563)(681,690)(682,689)(683,696)(684,695)
(685,693)(686,694)(687,692)(688,691)(697,810)(698,809)(699,816)(700,815)
(701,813)(702,814)(703,812)(704,811)(705,802)(706,801)(707,808)(708,807)
(709,805)(710,806)(711,804)(712,803)(713,794)(714,793)(715,800)(716,799)
(717,797)(718,798)(719,796)(720,795)(721,786)(722,785)(723,792)(724,791)
(725,789)(726,790)(727,788)(728,787)(729,778)(730,777)(731,784)(732,783)
(733,781)(734,782)(735,780)(736,779)(737,770)(738,769)(739,776)(740,775)
(741,773)(742,774)(743,772)(744,771)(745,762)(746,761)(747,768)(748,767)
(749,765)(750,766)(751,764)(752,763)(753,754)(755,760)(756,759);
poly := sub<Sym(816)|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*s2*s1*s0*s1*s2*s1*s2*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*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