Polytope of Type {106,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {106,8}*1696
Also Known As : {106,8|2}. if this polytope has another name.
Group : SmallGroup(1696,155)
Rank : 3
Schlafli Type : {106,8}
Number of vertices, edges, etc : 106, 424, 8
Order of s0s1s2 : 424
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 : {106,4}*848
4-fold quotients : {106,2}*424
8-fold quotients : {53,2}*212
53-fold quotients : {2,8}*32
106-fold quotients : {2,4}*16
212-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,213)( 2,265)( 3,264)( 4,263)( 5,262)( 6,261)( 7,260)( 8,259)
( 9,258)( 10,257)( 11,256)( 12,255)( 13,254)( 14,253)( 15,252)( 16,251)
( 17,250)( 18,249)( 19,248)( 20,247)( 21,246)( 22,245)( 23,244)( 24,243)
( 25,242)( 26,241)( 27,240)( 28,239)( 29,238)( 30,237)( 31,236)( 32,235)
( 33,234)( 34,233)( 35,232)( 36,231)( 37,230)( 38,229)( 39,228)( 40,227)
( 41,226)( 42,225)( 43,224)( 44,223)( 45,222)( 46,221)( 47,220)( 48,219)
( 49,218)( 50,217)( 51,216)( 52,215)( 53,214)( 54,266)( 55,318)( 56,317)
( 57,316)( 58,315)( 59,314)( 60,313)( 61,312)( 62,311)( 63,310)( 64,309)
( 65,308)( 66,307)( 67,306)( 68,305)( 69,304)( 70,303)( 71,302)( 72,301)
( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,295)( 79,294)( 80,293)
( 81,292)( 82,291)( 83,290)( 84,289)( 85,288)( 86,287)( 87,286)( 88,285)
( 89,284)( 90,283)( 91,282)( 92,281)( 93,280)( 94,279)( 95,278)( 96,277)
( 97,276)( 98,275)( 99,274)(100,273)(101,272)(102,271)(103,270)(104,269)
(105,268)(106,267)(107,319)(108,371)(109,370)(110,369)(111,368)(112,367)
(113,366)(114,365)(115,364)(116,363)(117,362)(118,361)(119,360)(120,359)
(121,358)(122,357)(123,356)(124,355)(125,354)(126,353)(127,352)(128,351)
(129,350)(130,349)(131,348)(132,347)(133,346)(134,345)(135,344)(136,343)
(137,342)(138,341)(139,340)(140,339)(141,338)(142,337)(143,336)(144,335)
(145,334)(146,333)(147,332)(148,331)(149,330)(150,329)(151,328)(152,327)
(153,326)(154,325)(155,324)(156,323)(157,322)(158,321)(159,320)(160,372)
(161,424)(162,423)(163,422)(164,421)(165,420)(166,419)(167,418)(168,417)
(169,416)(170,415)(171,414)(172,413)(173,412)(174,411)(175,410)(176,409)
(177,408)(178,407)(179,406)(180,405)(181,404)(182,403)(183,402)(184,401)
(185,400)(186,399)(187,398)(188,397)(189,396)(190,395)(191,394)(192,393)
(193,392)(194,391)(195,390)(196,389)(197,388)(198,387)(199,386)(200,385)
(201,384)(202,383)(203,382)(204,381)(205,380)(206,379)(207,378)(208,377)
(209,376)(210,375)(211,374)(212,373)(425,637)(426,689)(427,688)(428,687)
(429,686)(430,685)(431,684)(432,683)(433,682)(434,681)(435,680)(436,679)
(437,678)(438,677)(439,676)(440,675)(441,674)(442,673)(443,672)(444,671)
(445,670)(446,669)(447,668)(448,667)(449,666)(450,665)(451,664)(452,663)
(453,662)(454,661)(455,660)(456,659)(457,658)(458,657)(459,656)(460,655)
(461,654)(462,653)(463,652)(464,651)(465,650)(466,649)(467,648)(468,647)
(469,646)(470,645)(471,644)(472,643)(473,642)(474,641)(475,640)(476,639)
(477,638)(478,690)(479,742)(480,741)(481,740)(482,739)(483,738)(484,737)
(485,736)(486,735)(487,734)(488,733)(489,732)(490,731)(491,730)(492,729)
(493,728)(494,727)(495,726)(496,725)(497,724)(498,723)(499,722)(500,721)
(501,720)(502,719)(503,718)(504,717)(505,716)(506,715)(507,714)(508,713)
(509,712)(510,711)(511,710)(512,709)(513,708)(514,707)(515,706)(516,705)
(517,704)(518,703)(519,702)(520,701)(521,700)(522,699)(523,698)(524,697)
(525,696)(526,695)(527,694)(528,693)(529,692)(530,691)(531,743)(532,795)
(533,794)(534,793)(535,792)(536,791)(537,790)(538,789)(539,788)(540,787)
(541,786)(542,785)(543,784)(544,783)(545,782)(546,781)(547,780)(548,779)
(549,778)(550,777)(551,776)(552,775)(553,774)(554,773)(555,772)(556,771)
(557,770)(558,769)(559,768)(560,767)(561,766)(562,765)(563,764)(564,763)
(565,762)(566,761)(567,760)(568,759)(569,758)(570,757)(571,756)(572,755)
(573,754)(574,753)(575,752)(576,751)(577,750)(578,749)(579,748)(580,747)
(581,746)(582,745)(583,744)(584,796)(585,848)(586,847)(587,846)(588,845)
(589,844)(590,843)(591,842)(592,841)(593,840)(594,839)(595,838)(596,837)
(597,836)(598,835)(599,834)(600,833)(601,832)(602,831)(603,830)(604,829)
(605,828)(606,827)(607,826)(608,825)(609,824)(610,823)(611,822)(612,821)
(613,820)(614,819)(615,818)(616,817)(617,816)(618,815)(619,814)(620,813)
(621,812)(622,811)(623,810)(624,809)(625,808)(626,807)(627,806)(628,805)
(629,804)(630,803)(631,802)(632,801)(633,800)(634,799)(635,798)(636,797);;
s1 := ( 1,214)( 2,213)( 3,265)( 4,264)( 5,263)( 6,262)( 7,261)( 8,260)
( 9,259)( 10,258)( 11,257)( 12,256)( 13,255)( 14,254)( 15,253)( 16,252)
( 17,251)( 18,250)( 19,249)( 20,248)( 21,247)( 22,246)( 23,245)( 24,244)
( 25,243)( 26,242)( 27,241)( 28,240)( 29,239)( 30,238)( 31,237)( 32,236)
( 33,235)( 34,234)( 35,233)( 36,232)( 37,231)( 38,230)( 39,229)( 40,228)
( 41,227)( 42,226)( 43,225)( 44,224)( 45,223)( 46,222)( 47,221)( 48,220)
( 49,219)( 50,218)( 51,217)( 52,216)( 53,215)( 54,267)( 55,266)( 56,318)
( 57,317)( 58,316)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)( 64,310)
( 65,309)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,303)( 72,302)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)( 80,294)
( 81,293)( 82,292)( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)( 88,286)
( 89,285)( 90,284)( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)( 96,278)
( 97,277)( 98,276)( 99,275)(100,274)(101,273)(102,272)(103,271)(104,270)
(105,269)(106,268)(107,373)(108,372)(109,424)(110,423)(111,422)(112,421)
(113,420)(114,419)(115,418)(116,417)(117,416)(118,415)(119,414)(120,413)
(121,412)(122,411)(123,410)(124,409)(125,408)(126,407)(127,406)(128,405)
(129,404)(130,403)(131,402)(132,401)(133,400)(134,399)(135,398)(136,397)
(137,396)(138,395)(139,394)(140,393)(141,392)(142,391)(143,390)(144,389)
(145,388)(146,387)(147,386)(148,385)(149,384)(150,383)(151,382)(152,381)
(153,380)(154,379)(155,378)(156,377)(157,376)(158,375)(159,374)(160,320)
(161,319)(162,371)(163,370)(164,369)(165,368)(166,367)(167,366)(168,365)
(169,364)(170,363)(171,362)(172,361)(173,360)(174,359)(175,358)(176,357)
(177,356)(178,355)(179,354)(180,353)(181,352)(182,351)(183,350)(184,349)
(185,348)(186,347)(187,346)(188,345)(189,344)(190,343)(191,342)(192,341)
(193,340)(194,339)(195,338)(196,337)(197,336)(198,335)(199,334)(200,333)
(201,332)(202,331)(203,330)(204,329)(205,328)(206,327)(207,326)(208,325)
(209,324)(210,323)(211,322)(212,321)(425,744)(426,743)(427,795)(428,794)
(429,793)(430,792)(431,791)(432,790)(433,789)(434,788)(435,787)(436,786)
(437,785)(438,784)(439,783)(440,782)(441,781)(442,780)(443,779)(444,778)
(445,777)(446,776)(447,775)(448,774)(449,773)(450,772)(451,771)(452,770)
(453,769)(454,768)(455,767)(456,766)(457,765)(458,764)(459,763)(460,762)
(461,761)(462,760)(463,759)(464,758)(465,757)(466,756)(467,755)(468,754)
(469,753)(470,752)(471,751)(472,750)(473,749)(474,748)(475,747)(476,746)
(477,745)(478,797)(479,796)(480,848)(481,847)(482,846)(483,845)(484,844)
(485,843)(486,842)(487,841)(488,840)(489,839)(490,838)(491,837)(492,836)
(493,835)(494,834)(495,833)(496,832)(497,831)(498,830)(499,829)(500,828)
(501,827)(502,826)(503,825)(504,824)(505,823)(506,822)(507,821)(508,820)
(509,819)(510,818)(511,817)(512,816)(513,815)(514,814)(515,813)(516,812)
(517,811)(518,810)(519,809)(520,808)(521,807)(522,806)(523,805)(524,804)
(525,803)(526,802)(527,801)(528,800)(529,799)(530,798)(531,638)(532,637)
(533,689)(534,688)(535,687)(536,686)(537,685)(538,684)(539,683)(540,682)
(541,681)(542,680)(543,679)(544,678)(545,677)(546,676)(547,675)(548,674)
(549,673)(550,672)(551,671)(552,670)(553,669)(554,668)(555,667)(556,666)
(557,665)(558,664)(559,663)(560,662)(561,661)(562,660)(563,659)(564,658)
(565,657)(566,656)(567,655)(568,654)(569,653)(570,652)(571,651)(572,650)
(573,649)(574,648)(575,647)(576,646)(577,645)(578,644)(579,643)(580,642)
(581,641)(582,640)(583,639)(584,691)(585,690)(586,742)(587,741)(588,740)
(589,739)(590,738)(591,737)(592,736)(593,735)(594,734)(595,733)(596,732)
(597,731)(598,730)(599,729)(600,728)(601,727)(602,726)(603,725)(604,724)
(605,723)(606,722)(607,721)(608,720)(609,719)(610,718)(611,717)(612,716)
(613,715)(614,714)(615,713)(616,712)(617,711)(618,710)(619,709)(620,708)
(621,707)(622,706)(623,705)(624,704)(625,703)(626,702)(627,701)(628,700)
(629,699)(630,698)(631,697)(632,696)(633,695)(634,694)(635,693)(636,692);;
s2 := ( 1,425)( 2,426)( 3,427)( 4,428)( 5,429)( 6,430)( 7,431)( 8,432)
( 9,433)( 10,434)( 11,435)( 12,436)( 13,437)( 14,438)( 15,439)( 16,440)
( 17,441)( 18,442)( 19,443)( 20,444)( 21,445)( 22,446)( 23,447)( 24,448)
( 25,449)( 26,450)( 27,451)( 28,452)( 29,453)( 30,454)( 31,455)( 32,456)
( 33,457)( 34,458)( 35,459)( 36,460)( 37,461)( 38,462)( 39,463)( 40,464)
( 41,465)( 42,466)( 43,467)( 44,468)( 45,469)( 46,470)( 47,471)( 48,472)
( 49,473)( 50,474)( 51,475)( 52,476)( 53,477)( 54,478)( 55,479)( 56,480)
( 57,481)( 58,482)( 59,483)( 60,484)( 61,485)( 62,486)( 63,487)( 64,488)
( 65,489)( 66,490)( 67,491)( 68,492)( 69,493)( 70,494)( 71,495)( 72,496)
( 73,497)( 74,498)( 75,499)( 76,500)( 77,501)( 78,502)( 79,503)( 80,504)
( 81,505)( 82,506)( 83,507)( 84,508)( 85,509)( 86,510)( 87,511)( 88,512)
( 89,513)( 90,514)( 91,515)( 92,516)( 93,517)( 94,518)( 95,519)( 96,520)
( 97,521)( 98,522)( 99,523)(100,524)(101,525)(102,526)(103,527)(104,528)
(105,529)(106,530)(107,584)(108,585)(109,586)(110,587)(111,588)(112,589)
(113,590)(114,591)(115,592)(116,593)(117,594)(118,595)(119,596)(120,597)
(121,598)(122,599)(123,600)(124,601)(125,602)(126,603)(127,604)(128,605)
(129,606)(130,607)(131,608)(132,609)(133,610)(134,611)(135,612)(136,613)
(137,614)(138,615)(139,616)(140,617)(141,618)(142,619)(143,620)(144,621)
(145,622)(146,623)(147,624)(148,625)(149,626)(150,627)(151,628)(152,629)
(153,630)(154,631)(155,632)(156,633)(157,634)(158,635)(159,636)(160,531)
(161,532)(162,533)(163,534)(164,535)(165,536)(166,537)(167,538)(168,539)
(169,540)(170,541)(171,542)(172,543)(173,544)(174,545)(175,546)(176,547)
(177,548)(178,549)(179,550)(180,551)(181,552)(182,553)(183,554)(184,555)
(185,556)(186,557)(187,558)(188,559)(189,560)(190,561)(191,562)(192,563)
(193,564)(194,565)(195,566)(196,567)(197,568)(198,569)(199,570)(200,571)
(201,572)(202,573)(203,574)(204,575)(205,576)(206,577)(207,578)(208,579)
(209,580)(210,581)(211,582)(212,583)(213,637)(214,638)(215,639)(216,640)
(217,641)(218,642)(219,643)(220,644)(221,645)(222,646)(223,647)(224,648)
(225,649)(226,650)(227,651)(228,652)(229,653)(230,654)(231,655)(232,656)
(233,657)(234,658)(235,659)(236,660)(237,661)(238,662)(239,663)(240,664)
(241,665)(242,666)(243,667)(244,668)(245,669)(246,670)(247,671)(248,672)
(249,673)(250,674)(251,675)(252,676)(253,677)(254,678)(255,679)(256,680)
(257,681)(258,682)(259,683)(260,684)(261,685)(262,686)(263,687)(264,688)
(265,689)(266,690)(267,691)(268,692)(269,693)(270,694)(271,695)(272,696)
(273,697)(274,698)(275,699)(276,700)(277,701)(278,702)(279,703)(280,704)
(281,705)(282,706)(283,707)(284,708)(285,709)(286,710)(287,711)(288,712)
(289,713)(290,714)(291,715)(292,716)(293,717)(294,718)(295,719)(296,720)
(297,721)(298,722)(299,723)(300,724)(301,725)(302,726)(303,727)(304,728)
(305,729)(306,730)(307,731)(308,732)(309,733)(310,734)(311,735)(312,736)
(313,737)(314,738)(315,739)(316,740)(317,741)(318,742)(319,796)(320,797)
(321,798)(322,799)(323,800)(324,801)(325,802)(326,803)(327,804)(328,805)
(329,806)(330,807)(331,808)(332,809)(333,810)(334,811)(335,812)(336,813)
(337,814)(338,815)(339,816)(340,817)(341,818)(342,819)(343,820)(344,821)
(345,822)(346,823)(347,824)(348,825)(349,826)(350,827)(351,828)(352,829)
(353,830)(354,831)(355,832)(356,833)(357,834)(358,835)(359,836)(360,837)
(361,838)(362,839)(363,840)(364,841)(365,842)(366,843)(367,844)(368,845)
(369,846)(370,847)(371,848)(372,743)(373,744)(374,745)(375,746)(376,747)
(377,748)(378,749)(379,750)(380,751)(381,752)(382,753)(383,754)(384,755)
(385,756)(386,757)(387,758)(388,759)(389,760)(390,761)(391,762)(392,763)
(393,764)(394,765)(395,766)(396,767)(397,768)(398,769)(399,770)(400,771)
(401,772)(402,773)(403,774)(404,775)(405,776)(406,777)(407,778)(408,779)
(409,780)(410,781)(411,782)(412,783)(413,784)(414,785)(415,786)(416,787)
(417,788)(418,789)(419,790)(420,791)(421,792)(422,793)(423,794)(424,795);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(848)!( 1,213)( 2,265)( 3,264)( 4,263)( 5,262)( 6,261)( 7,260)
( 8,259)( 9,258)( 10,257)( 11,256)( 12,255)( 13,254)( 14,253)( 15,252)
( 16,251)( 17,250)( 18,249)( 19,248)( 20,247)( 21,246)( 22,245)( 23,244)
( 24,243)( 25,242)( 26,241)( 27,240)( 28,239)( 29,238)( 30,237)( 31,236)
( 32,235)( 33,234)( 34,233)( 35,232)( 36,231)( 37,230)( 38,229)( 39,228)
( 40,227)( 41,226)( 42,225)( 43,224)( 44,223)( 45,222)( 46,221)( 47,220)
( 48,219)( 49,218)( 50,217)( 51,216)( 52,215)( 53,214)( 54,266)( 55,318)
( 56,317)( 57,316)( 58,315)( 59,314)( 60,313)( 61,312)( 62,311)( 63,310)
( 64,309)( 65,308)( 66,307)( 67,306)( 68,305)( 69,304)( 70,303)( 71,302)
( 72,301)( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,295)( 79,294)
( 80,293)( 81,292)( 82,291)( 83,290)( 84,289)( 85,288)( 86,287)( 87,286)
( 88,285)( 89,284)( 90,283)( 91,282)( 92,281)( 93,280)( 94,279)( 95,278)
( 96,277)( 97,276)( 98,275)( 99,274)(100,273)(101,272)(102,271)(103,270)
(104,269)(105,268)(106,267)(107,319)(108,371)(109,370)(110,369)(111,368)
(112,367)(113,366)(114,365)(115,364)(116,363)(117,362)(118,361)(119,360)
(120,359)(121,358)(122,357)(123,356)(124,355)(125,354)(126,353)(127,352)
(128,351)(129,350)(130,349)(131,348)(132,347)(133,346)(134,345)(135,344)
(136,343)(137,342)(138,341)(139,340)(140,339)(141,338)(142,337)(143,336)
(144,335)(145,334)(146,333)(147,332)(148,331)(149,330)(150,329)(151,328)
(152,327)(153,326)(154,325)(155,324)(156,323)(157,322)(158,321)(159,320)
(160,372)(161,424)(162,423)(163,422)(164,421)(165,420)(166,419)(167,418)
(168,417)(169,416)(170,415)(171,414)(172,413)(173,412)(174,411)(175,410)
(176,409)(177,408)(178,407)(179,406)(180,405)(181,404)(182,403)(183,402)
(184,401)(185,400)(186,399)(187,398)(188,397)(189,396)(190,395)(191,394)
(192,393)(193,392)(194,391)(195,390)(196,389)(197,388)(198,387)(199,386)
(200,385)(201,384)(202,383)(203,382)(204,381)(205,380)(206,379)(207,378)
(208,377)(209,376)(210,375)(211,374)(212,373)(425,637)(426,689)(427,688)
(428,687)(429,686)(430,685)(431,684)(432,683)(433,682)(434,681)(435,680)
(436,679)(437,678)(438,677)(439,676)(440,675)(441,674)(442,673)(443,672)
(444,671)(445,670)(446,669)(447,668)(448,667)(449,666)(450,665)(451,664)
(452,663)(453,662)(454,661)(455,660)(456,659)(457,658)(458,657)(459,656)
(460,655)(461,654)(462,653)(463,652)(464,651)(465,650)(466,649)(467,648)
(468,647)(469,646)(470,645)(471,644)(472,643)(473,642)(474,641)(475,640)
(476,639)(477,638)(478,690)(479,742)(480,741)(481,740)(482,739)(483,738)
(484,737)(485,736)(486,735)(487,734)(488,733)(489,732)(490,731)(491,730)
(492,729)(493,728)(494,727)(495,726)(496,725)(497,724)(498,723)(499,722)
(500,721)(501,720)(502,719)(503,718)(504,717)(505,716)(506,715)(507,714)
(508,713)(509,712)(510,711)(511,710)(512,709)(513,708)(514,707)(515,706)
(516,705)(517,704)(518,703)(519,702)(520,701)(521,700)(522,699)(523,698)
(524,697)(525,696)(526,695)(527,694)(528,693)(529,692)(530,691)(531,743)
(532,795)(533,794)(534,793)(535,792)(536,791)(537,790)(538,789)(539,788)
(540,787)(541,786)(542,785)(543,784)(544,783)(545,782)(546,781)(547,780)
(548,779)(549,778)(550,777)(551,776)(552,775)(553,774)(554,773)(555,772)
(556,771)(557,770)(558,769)(559,768)(560,767)(561,766)(562,765)(563,764)
(564,763)(565,762)(566,761)(567,760)(568,759)(569,758)(570,757)(571,756)
(572,755)(573,754)(574,753)(575,752)(576,751)(577,750)(578,749)(579,748)
(580,747)(581,746)(582,745)(583,744)(584,796)(585,848)(586,847)(587,846)
(588,845)(589,844)(590,843)(591,842)(592,841)(593,840)(594,839)(595,838)
(596,837)(597,836)(598,835)(599,834)(600,833)(601,832)(602,831)(603,830)
(604,829)(605,828)(606,827)(607,826)(608,825)(609,824)(610,823)(611,822)
(612,821)(613,820)(614,819)(615,818)(616,817)(617,816)(618,815)(619,814)
(620,813)(621,812)(622,811)(623,810)(624,809)(625,808)(626,807)(627,806)
(628,805)(629,804)(630,803)(631,802)(632,801)(633,800)(634,799)(635,798)
(636,797);
s1 := Sym(848)!( 1,214)( 2,213)( 3,265)( 4,264)( 5,263)( 6,262)( 7,261)
( 8,260)( 9,259)( 10,258)( 11,257)( 12,256)( 13,255)( 14,254)( 15,253)
( 16,252)( 17,251)( 18,250)( 19,249)( 20,248)( 21,247)( 22,246)( 23,245)
( 24,244)( 25,243)( 26,242)( 27,241)( 28,240)( 29,239)( 30,238)( 31,237)
( 32,236)( 33,235)( 34,234)( 35,233)( 36,232)( 37,231)( 38,230)( 39,229)
( 40,228)( 41,227)( 42,226)( 43,225)( 44,224)( 45,223)( 46,222)( 47,221)
( 48,220)( 49,219)( 50,218)( 51,217)( 52,216)( 53,215)( 54,267)( 55,266)
( 56,318)( 57,317)( 58,316)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)
( 64,310)( 65,309)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,303)
( 72,302)( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)
( 80,294)( 81,293)( 82,292)( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)
( 88,286)( 89,285)( 90,284)( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)
( 96,278)( 97,277)( 98,276)( 99,275)(100,274)(101,273)(102,272)(103,271)
(104,270)(105,269)(106,268)(107,373)(108,372)(109,424)(110,423)(111,422)
(112,421)(113,420)(114,419)(115,418)(116,417)(117,416)(118,415)(119,414)
(120,413)(121,412)(122,411)(123,410)(124,409)(125,408)(126,407)(127,406)
(128,405)(129,404)(130,403)(131,402)(132,401)(133,400)(134,399)(135,398)
(136,397)(137,396)(138,395)(139,394)(140,393)(141,392)(142,391)(143,390)
(144,389)(145,388)(146,387)(147,386)(148,385)(149,384)(150,383)(151,382)
(152,381)(153,380)(154,379)(155,378)(156,377)(157,376)(158,375)(159,374)
(160,320)(161,319)(162,371)(163,370)(164,369)(165,368)(166,367)(167,366)
(168,365)(169,364)(170,363)(171,362)(172,361)(173,360)(174,359)(175,358)
(176,357)(177,356)(178,355)(179,354)(180,353)(181,352)(182,351)(183,350)
(184,349)(185,348)(186,347)(187,346)(188,345)(189,344)(190,343)(191,342)
(192,341)(193,340)(194,339)(195,338)(196,337)(197,336)(198,335)(199,334)
(200,333)(201,332)(202,331)(203,330)(204,329)(205,328)(206,327)(207,326)
(208,325)(209,324)(210,323)(211,322)(212,321)(425,744)(426,743)(427,795)
(428,794)(429,793)(430,792)(431,791)(432,790)(433,789)(434,788)(435,787)
(436,786)(437,785)(438,784)(439,783)(440,782)(441,781)(442,780)(443,779)
(444,778)(445,777)(446,776)(447,775)(448,774)(449,773)(450,772)(451,771)
(452,770)(453,769)(454,768)(455,767)(456,766)(457,765)(458,764)(459,763)
(460,762)(461,761)(462,760)(463,759)(464,758)(465,757)(466,756)(467,755)
(468,754)(469,753)(470,752)(471,751)(472,750)(473,749)(474,748)(475,747)
(476,746)(477,745)(478,797)(479,796)(480,848)(481,847)(482,846)(483,845)
(484,844)(485,843)(486,842)(487,841)(488,840)(489,839)(490,838)(491,837)
(492,836)(493,835)(494,834)(495,833)(496,832)(497,831)(498,830)(499,829)
(500,828)(501,827)(502,826)(503,825)(504,824)(505,823)(506,822)(507,821)
(508,820)(509,819)(510,818)(511,817)(512,816)(513,815)(514,814)(515,813)
(516,812)(517,811)(518,810)(519,809)(520,808)(521,807)(522,806)(523,805)
(524,804)(525,803)(526,802)(527,801)(528,800)(529,799)(530,798)(531,638)
(532,637)(533,689)(534,688)(535,687)(536,686)(537,685)(538,684)(539,683)
(540,682)(541,681)(542,680)(543,679)(544,678)(545,677)(546,676)(547,675)
(548,674)(549,673)(550,672)(551,671)(552,670)(553,669)(554,668)(555,667)
(556,666)(557,665)(558,664)(559,663)(560,662)(561,661)(562,660)(563,659)
(564,658)(565,657)(566,656)(567,655)(568,654)(569,653)(570,652)(571,651)
(572,650)(573,649)(574,648)(575,647)(576,646)(577,645)(578,644)(579,643)
(580,642)(581,641)(582,640)(583,639)(584,691)(585,690)(586,742)(587,741)
(588,740)(589,739)(590,738)(591,737)(592,736)(593,735)(594,734)(595,733)
(596,732)(597,731)(598,730)(599,729)(600,728)(601,727)(602,726)(603,725)
(604,724)(605,723)(606,722)(607,721)(608,720)(609,719)(610,718)(611,717)
(612,716)(613,715)(614,714)(615,713)(616,712)(617,711)(618,710)(619,709)
(620,708)(621,707)(622,706)(623,705)(624,704)(625,703)(626,702)(627,701)
(628,700)(629,699)(630,698)(631,697)(632,696)(633,695)(634,694)(635,693)
(636,692);
s2 := Sym(848)!( 1,425)( 2,426)( 3,427)( 4,428)( 5,429)( 6,430)( 7,431)
( 8,432)( 9,433)( 10,434)( 11,435)( 12,436)( 13,437)( 14,438)( 15,439)
( 16,440)( 17,441)( 18,442)( 19,443)( 20,444)( 21,445)( 22,446)( 23,447)
( 24,448)( 25,449)( 26,450)( 27,451)( 28,452)( 29,453)( 30,454)( 31,455)
( 32,456)( 33,457)( 34,458)( 35,459)( 36,460)( 37,461)( 38,462)( 39,463)
( 40,464)( 41,465)( 42,466)( 43,467)( 44,468)( 45,469)( 46,470)( 47,471)
( 48,472)( 49,473)( 50,474)( 51,475)( 52,476)( 53,477)( 54,478)( 55,479)
( 56,480)( 57,481)( 58,482)( 59,483)( 60,484)( 61,485)( 62,486)( 63,487)
( 64,488)( 65,489)( 66,490)( 67,491)( 68,492)( 69,493)( 70,494)( 71,495)
( 72,496)( 73,497)( 74,498)( 75,499)( 76,500)( 77,501)( 78,502)( 79,503)
( 80,504)( 81,505)( 82,506)( 83,507)( 84,508)( 85,509)( 86,510)( 87,511)
( 88,512)( 89,513)( 90,514)( 91,515)( 92,516)( 93,517)( 94,518)( 95,519)
( 96,520)( 97,521)( 98,522)( 99,523)(100,524)(101,525)(102,526)(103,527)
(104,528)(105,529)(106,530)(107,584)(108,585)(109,586)(110,587)(111,588)
(112,589)(113,590)(114,591)(115,592)(116,593)(117,594)(118,595)(119,596)
(120,597)(121,598)(122,599)(123,600)(124,601)(125,602)(126,603)(127,604)
(128,605)(129,606)(130,607)(131,608)(132,609)(133,610)(134,611)(135,612)
(136,613)(137,614)(138,615)(139,616)(140,617)(141,618)(142,619)(143,620)
(144,621)(145,622)(146,623)(147,624)(148,625)(149,626)(150,627)(151,628)
(152,629)(153,630)(154,631)(155,632)(156,633)(157,634)(158,635)(159,636)
(160,531)(161,532)(162,533)(163,534)(164,535)(165,536)(166,537)(167,538)
(168,539)(169,540)(170,541)(171,542)(172,543)(173,544)(174,545)(175,546)
(176,547)(177,548)(178,549)(179,550)(180,551)(181,552)(182,553)(183,554)
(184,555)(185,556)(186,557)(187,558)(188,559)(189,560)(190,561)(191,562)
(192,563)(193,564)(194,565)(195,566)(196,567)(197,568)(198,569)(199,570)
(200,571)(201,572)(202,573)(203,574)(204,575)(205,576)(206,577)(207,578)
(208,579)(209,580)(210,581)(211,582)(212,583)(213,637)(214,638)(215,639)
(216,640)(217,641)(218,642)(219,643)(220,644)(221,645)(222,646)(223,647)
(224,648)(225,649)(226,650)(227,651)(228,652)(229,653)(230,654)(231,655)
(232,656)(233,657)(234,658)(235,659)(236,660)(237,661)(238,662)(239,663)
(240,664)(241,665)(242,666)(243,667)(244,668)(245,669)(246,670)(247,671)
(248,672)(249,673)(250,674)(251,675)(252,676)(253,677)(254,678)(255,679)
(256,680)(257,681)(258,682)(259,683)(260,684)(261,685)(262,686)(263,687)
(264,688)(265,689)(266,690)(267,691)(268,692)(269,693)(270,694)(271,695)
(272,696)(273,697)(274,698)(275,699)(276,700)(277,701)(278,702)(279,703)
(280,704)(281,705)(282,706)(283,707)(284,708)(285,709)(286,710)(287,711)
(288,712)(289,713)(290,714)(291,715)(292,716)(293,717)(294,718)(295,719)
(296,720)(297,721)(298,722)(299,723)(300,724)(301,725)(302,726)(303,727)
(304,728)(305,729)(306,730)(307,731)(308,732)(309,733)(310,734)(311,735)
(312,736)(313,737)(314,738)(315,739)(316,740)(317,741)(318,742)(319,796)
(320,797)(321,798)(322,799)(323,800)(324,801)(325,802)(326,803)(327,804)
(328,805)(329,806)(330,807)(331,808)(332,809)(333,810)(334,811)(335,812)
(336,813)(337,814)(338,815)(339,816)(340,817)(341,818)(342,819)(343,820)
(344,821)(345,822)(346,823)(347,824)(348,825)(349,826)(350,827)(351,828)
(352,829)(353,830)(354,831)(355,832)(356,833)(357,834)(358,835)(359,836)
(360,837)(361,838)(362,839)(363,840)(364,841)(365,842)(366,843)(367,844)
(368,845)(369,846)(370,847)(371,848)(372,743)(373,744)(374,745)(375,746)
(376,747)(377,748)(378,749)(379,750)(380,751)(381,752)(382,753)(383,754)
(384,755)(385,756)(386,757)(387,758)(388,759)(389,760)(390,761)(391,762)
(392,763)(393,764)(394,765)(395,766)(396,767)(397,768)(398,769)(399,770)
(400,771)(401,772)(402,773)(403,774)(404,775)(405,776)(406,777)(407,778)
(408,779)(409,780)(410,781)(411,782)(412,783)(413,784)(414,785)(415,786)
(416,787)(417,788)(418,789)(419,790)(420,791)(421,792)(422,793)(423,794)
(424,795);
poly := sub<Sym(848)|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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*s0*s1*s0*s1 >;
References : None.
to this polytope