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