Polytope of Type {8,92}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,92}*1472b
if this polytope has a name.
Group : SmallGroup(1472,718)
Rank : 3
Schlafli Type : {8,92}
Number of vertices, edges, etc : 8, 368, 92
Order of s0s1s2 : 184
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 : {4,92}*736
4-fold quotients : {2,92}*368, {4,46}*368
8-fold quotients : {2,46}*184
16-fold quotients : {2,23}*92
23-fold quotients : {8,4}*64b
46-fold quotients : {4,4}*32
92-fold quotients : {2,4}*16, {4,2}*16
184-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,369)( 2,370)( 3,371)( 4,372)( 5,373)( 6,374)( 7,375)( 8,376)
( 9,377)( 10,378)( 11,379)( 12,380)( 13,381)( 14,382)( 15,383)( 16,384)
( 17,385)( 18,386)( 19,387)( 20,388)( 21,389)( 22,390)( 23,391)( 24,392)
( 25,393)( 26,394)( 27,395)( 28,396)( 29,397)( 30,398)( 31,399)( 32,400)
( 33,401)( 34,402)( 35,403)( 36,404)( 37,405)( 38,406)( 39,407)( 40,408)
( 41,409)( 42,410)( 43,411)( 44,412)( 45,413)( 46,414)( 47,438)( 48,439)
( 49,440)( 50,441)( 51,442)( 52,443)( 53,444)( 54,445)( 55,446)( 56,447)
( 57,448)( 58,449)( 59,450)( 60,451)( 61,452)( 62,453)( 63,454)( 64,455)
( 65,456)( 66,457)( 67,458)( 68,459)( 69,460)( 70,415)( 71,416)( 72,417)
( 73,418)( 74,419)( 75,420)( 76,421)( 77,422)( 78,423)( 79,424)( 80,425)
( 81,426)( 82,427)( 83,428)( 84,429)( 85,430)( 86,431)( 87,432)( 88,433)
( 89,434)( 90,435)( 91,436)( 92,437)( 93,484)( 94,485)( 95,486)( 96,487)
( 97,488)( 98,489)( 99,490)(100,491)(101,492)(102,493)(103,494)(104,495)
(105,496)(106,497)(107,498)(108,499)(109,500)(110,501)(111,502)(112,503)
(113,504)(114,505)(115,506)(116,461)(117,462)(118,463)(119,464)(120,465)
(121,466)(122,467)(123,468)(124,469)(125,470)(126,471)(127,472)(128,473)
(129,474)(130,475)(131,476)(132,477)(133,478)(134,479)(135,480)(136,481)
(137,482)(138,483)(139,507)(140,508)(141,509)(142,510)(143,511)(144,512)
(145,513)(146,514)(147,515)(148,516)(149,517)(150,518)(151,519)(152,520)
(153,521)(154,522)(155,523)(156,524)(157,525)(158,526)(159,527)(160,528)
(161,529)(162,530)(163,531)(164,532)(165,533)(166,534)(167,535)(168,536)
(169,537)(170,538)(171,539)(172,540)(173,541)(174,542)(175,543)(176,544)
(177,545)(178,546)(179,547)(180,548)(181,549)(182,550)(183,551)(184,552)
(185,553)(186,554)(187,555)(188,556)(189,557)(190,558)(191,559)(192,560)
(193,561)(194,562)(195,563)(196,564)(197,565)(198,566)(199,567)(200,568)
(201,569)(202,570)(203,571)(204,572)(205,573)(206,574)(207,575)(208,576)
(209,577)(210,578)(211,579)(212,580)(213,581)(214,582)(215,583)(216,584)
(217,585)(218,586)(219,587)(220,588)(221,589)(222,590)(223,591)(224,592)
(225,593)(226,594)(227,595)(228,596)(229,597)(230,598)(231,622)(232,623)
(233,624)(234,625)(235,626)(236,627)(237,628)(238,629)(239,630)(240,631)
(241,632)(242,633)(243,634)(244,635)(245,636)(246,637)(247,638)(248,639)
(249,640)(250,641)(251,642)(252,643)(253,644)(254,599)(255,600)(256,601)
(257,602)(258,603)(259,604)(260,605)(261,606)(262,607)(263,608)(264,609)
(265,610)(266,611)(267,612)(268,613)(269,614)(270,615)(271,616)(272,617)
(273,618)(274,619)(275,620)(276,621)(277,668)(278,669)(279,670)(280,671)
(281,672)(282,673)(283,674)(284,675)(285,676)(286,677)(287,678)(288,679)
(289,680)(290,681)(291,682)(292,683)(293,684)(294,685)(295,686)(296,687)
(297,688)(298,689)(299,690)(300,645)(301,646)(302,647)(303,648)(304,649)
(305,650)(306,651)(307,652)(308,653)(309,654)(310,655)(311,656)(312,657)
(313,658)(314,659)(315,660)(316,661)(317,662)(318,663)(319,664)(320,665)
(321,666)(322,667)(323,691)(324,692)(325,693)(326,694)(327,695)(328,696)
(329,697)(330,698)(331,699)(332,700)(333,701)(334,702)(335,703)(336,704)
(337,705)(338,706)(339,707)(340,708)(341,709)(342,710)(343,711)(344,712)
(345,713)(346,714)(347,715)(348,716)(349,717)(350,718)(351,719)(352,720)
(353,721)(354,722)(355,723)(356,724)(357,725)(358,726)(359,727)(360,728)
(361,729)(362,730)(363,731)(364,732)(365,733)(366,734)(367,735)(368,736);;
s1 := ( 2, 23)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)
( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)
( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)( 49, 68)
( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)
( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)
( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 93,116)( 94,138)( 95,137)( 96,136)
( 97,135)( 98,134)( 99,133)(100,132)(101,131)(102,130)(103,129)(104,128)
(105,127)(106,126)(107,125)(108,124)(109,123)(110,122)(111,121)(112,120)
(113,119)(114,118)(115,117)(139,162)(140,184)(141,183)(142,182)(143,181)
(144,180)(145,179)(146,178)(147,177)(148,176)(149,175)(150,174)(151,173)
(152,172)(153,171)(154,170)(155,169)(156,168)(157,167)(158,166)(159,165)
(160,164)(161,163)(185,231)(186,253)(187,252)(188,251)(189,250)(190,249)
(191,248)(192,247)(193,246)(194,245)(195,244)(196,243)(197,242)(198,241)
(199,240)(200,239)(201,238)(202,237)(203,236)(204,235)(205,234)(206,233)
(207,232)(208,254)(209,276)(210,275)(211,274)(212,273)(213,272)(214,271)
(215,270)(216,269)(217,268)(218,267)(219,266)(220,265)(221,264)(222,263)
(223,262)(224,261)(225,260)(226,259)(227,258)(228,257)(229,256)(230,255)
(277,346)(278,368)(279,367)(280,366)(281,365)(282,364)(283,363)(284,362)
(285,361)(286,360)(287,359)(288,358)(289,357)(290,356)(291,355)(292,354)
(293,353)(294,352)(295,351)(296,350)(297,349)(298,348)(299,347)(300,323)
(301,345)(302,344)(303,343)(304,342)(305,341)(306,340)(307,339)(308,338)
(309,337)(310,336)(311,335)(312,334)(313,333)(314,332)(315,331)(316,330)
(317,329)(318,328)(319,327)(320,326)(321,325)(322,324)(369,461)(370,483)
(371,482)(372,481)(373,480)(374,479)(375,478)(376,477)(377,476)(378,475)
(379,474)(380,473)(381,472)(382,471)(383,470)(384,469)(385,468)(386,467)
(387,466)(388,465)(389,464)(390,463)(391,462)(392,484)(393,506)(394,505)
(395,504)(396,503)(397,502)(398,501)(399,500)(400,499)(401,498)(402,497)
(403,496)(404,495)(405,494)(406,493)(407,492)(408,491)(409,490)(410,489)
(411,488)(412,487)(413,486)(414,485)(415,507)(416,529)(417,528)(418,527)
(419,526)(420,525)(421,524)(422,523)(423,522)(424,521)(425,520)(426,519)
(427,518)(428,517)(429,516)(430,515)(431,514)(432,513)(433,512)(434,511)
(435,510)(436,509)(437,508)(438,530)(439,552)(440,551)(441,550)(442,549)
(443,548)(444,547)(445,546)(446,545)(447,544)(448,543)(449,542)(450,541)
(451,540)(452,539)(453,538)(454,537)(455,536)(456,535)(457,534)(458,533)
(459,532)(460,531)(553,714)(554,736)(555,735)(556,734)(557,733)(558,732)
(559,731)(560,730)(561,729)(562,728)(563,727)(564,726)(565,725)(566,724)
(567,723)(568,722)(569,721)(570,720)(571,719)(572,718)(573,717)(574,716)
(575,715)(576,691)(577,713)(578,712)(579,711)(580,710)(581,709)(582,708)
(583,707)(584,706)(585,705)(586,704)(587,703)(588,702)(589,701)(590,700)
(591,699)(592,698)(593,697)(594,696)(595,695)(596,694)(597,693)(598,692)
(599,668)(600,690)(601,689)(602,688)(603,687)(604,686)(605,685)(606,684)
(607,683)(608,682)(609,681)(610,680)(611,679)(612,678)(613,677)(614,676)
(615,675)(616,674)(617,673)(618,672)(619,671)(620,670)(621,669)(622,645)
(623,667)(624,666)(625,665)(626,664)(627,663)(628,662)(629,661)(630,660)
(631,659)(632,658)(633,657)(634,656)(635,655)(636,654)(637,653)(638,652)
(639,651)(640,650)(641,649)(642,648)(643,647)(644,646);;
s2 := ( 1,186)( 2,185)( 3,207)( 4,206)( 5,205)( 6,204)( 7,203)( 8,202)
( 9,201)( 10,200)( 11,199)( 12,198)( 13,197)( 14,196)( 15,195)( 16,194)
( 17,193)( 18,192)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,209)
( 25,208)( 26,230)( 27,229)( 28,228)( 29,227)( 30,226)( 31,225)( 32,224)
( 33,223)( 34,222)( 35,221)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)
( 41,215)( 42,214)( 43,213)( 44,212)( 45,211)( 46,210)( 47,232)( 48,231)
( 49,253)( 50,252)( 51,251)( 52,250)( 53,249)( 54,248)( 55,247)( 56,246)
( 57,245)( 58,244)( 59,243)( 60,242)( 61,241)( 62,240)( 63,239)( 64,238)
( 65,237)( 66,236)( 67,235)( 68,234)( 69,233)( 70,255)( 71,254)( 72,276)
( 73,275)( 74,274)( 75,273)( 76,272)( 77,271)( 78,270)( 79,269)( 80,268)
( 81,267)( 82,266)( 83,265)( 84,264)( 85,263)( 86,262)( 87,261)( 88,260)
( 89,259)( 90,258)( 91,257)( 92,256)( 93,301)( 94,300)( 95,322)( 96,321)
( 97,320)( 98,319)( 99,318)(100,317)(101,316)(102,315)(103,314)(104,313)
(105,312)(106,311)(107,310)(108,309)(109,308)(110,307)(111,306)(112,305)
(113,304)(114,303)(115,302)(116,278)(117,277)(118,299)(119,298)(120,297)
(121,296)(122,295)(123,294)(124,293)(125,292)(126,291)(127,290)(128,289)
(129,288)(130,287)(131,286)(132,285)(133,284)(134,283)(135,282)(136,281)
(137,280)(138,279)(139,347)(140,346)(141,368)(142,367)(143,366)(144,365)
(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)
(153,356)(154,355)(155,354)(156,353)(157,352)(158,351)(159,350)(160,349)
(161,348)(162,324)(163,323)(164,345)(165,344)(166,343)(167,342)(168,341)
(169,340)(170,339)(171,338)(172,337)(173,336)(174,335)(175,334)(176,333)
(177,332)(178,331)(179,330)(180,329)(181,328)(182,327)(183,326)(184,325)
(369,554)(370,553)(371,575)(372,574)(373,573)(374,572)(375,571)(376,570)
(377,569)(378,568)(379,567)(380,566)(381,565)(382,564)(383,563)(384,562)
(385,561)(386,560)(387,559)(388,558)(389,557)(390,556)(391,555)(392,577)
(393,576)(394,598)(395,597)(396,596)(397,595)(398,594)(399,593)(400,592)
(401,591)(402,590)(403,589)(404,588)(405,587)(406,586)(407,585)(408,584)
(409,583)(410,582)(411,581)(412,580)(413,579)(414,578)(415,600)(416,599)
(417,621)(418,620)(419,619)(420,618)(421,617)(422,616)(423,615)(424,614)
(425,613)(426,612)(427,611)(428,610)(429,609)(430,608)(431,607)(432,606)
(433,605)(434,604)(435,603)(436,602)(437,601)(438,623)(439,622)(440,644)
(441,643)(442,642)(443,641)(444,640)(445,639)(446,638)(447,637)(448,636)
(449,635)(450,634)(451,633)(452,632)(453,631)(454,630)(455,629)(456,628)
(457,627)(458,626)(459,625)(460,624)(461,669)(462,668)(463,690)(464,689)
(465,688)(466,687)(467,686)(468,685)(469,684)(470,683)(471,682)(472,681)
(473,680)(474,679)(475,678)(476,677)(477,676)(478,675)(479,674)(480,673)
(481,672)(482,671)(483,670)(484,646)(485,645)(486,667)(487,666)(488,665)
(489,664)(490,663)(491,662)(492,661)(493,660)(494,659)(495,658)(496,657)
(497,656)(498,655)(499,654)(500,653)(501,652)(502,651)(503,650)(504,649)
(505,648)(506,647)(507,715)(508,714)(509,736)(510,735)(511,734)(512,733)
(513,732)(514,731)(515,730)(516,729)(517,728)(518,727)(519,726)(520,725)
(521,724)(522,723)(523,722)(524,721)(525,720)(526,719)(527,718)(528,717)
(529,716)(530,692)(531,691)(532,713)(533,712)(534,711)(535,710)(536,709)
(537,708)(538,707)(539,706)(540,705)(541,704)(542,703)(543,702)(544,701)
(545,700)(546,699)(547,698)(548,697)(549,696)(550,695)(551,694)(552,693);;
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*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(736)!( 1,369)( 2,370)( 3,371)( 4,372)( 5,373)( 6,374)( 7,375)
( 8,376)( 9,377)( 10,378)( 11,379)( 12,380)( 13,381)( 14,382)( 15,383)
( 16,384)( 17,385)( 18,386)( 19,387)( 20,388)( 21,389)( 22,390)( 23,391)
( 24,392)( 25,393)( 26,394)( 27,395)( 28,396)( 29,397)( 30,398)( 31,399)
( 32,400)( 33,401)( 34,402)( 35,403)( 36,404)( 37,405)( 38,406)( 39,407)
( 40,408)( 41,409)( 42,410)( 43,411)( 44,412)( 45,413)( 46,414)( 47,438)
( 48,439)( 49,440)( 50,441)( 51,442)( 52,443)( 53,444)( 54,445)( 55,446)
( 56,447)( 57,448)( 58,449)( 59,450)( 60,451)( 61,452)( 62,453)( 63,454)
( 64,455)( 65,456)( 66,457)( 67,458)( 68,459)( 69,460)( 70,415)( 71,416)
( 72,417)( 73,418)( 74,419)( 75,420)( 76,421)( 77,422)( 78,423)( 79,424)
( 80,425)( 81,426)( 82,427)( 83,428)( 84,429)( 85,430)( 86,431)( 87,432)
( 88,433)( 89,434)( 90,435)( 91,436)( 92,437)( 93,484)( 94,485)( 95,486)
( 96,487)( 97,488)( 98,489)( 99,490)(100,491)(101,492)(102,493)(103,494)
(104,495)(105,496)(106,497)(107,498)(108,499)(109,500)(110,501)(111,502)
(112,503)(113,504)(114,505)(115,506)(116,461)(117,462)(118,463)(119,464)
(120,465)(121,466)(122,467)(123,468)(124,469)(125,470)(126,471)(127,472)
(128,473)(129,474)(130,475)(131,476)(132,477)(133,478)(134,479)(135,480)
(136,481)(137,482)(138,483)(139,507)(140,508)(141,509)(142,510)(143,511)
(144,512)(145,513)(146,514)(147,515)(148,516)(149,517)(150,518)(151,519)
(152,520)(153,521)(154,522)(155,523)(156,524)(157,525)(158,526)(159,527)
(160,528)(161,529)(162,530)(163,531)(164,532)(165,533)(166,534)(167,535)
(168,536)(169,537)(170,538)(171,539)(172,540)(173,541)(174,542)(175,543)
(176,544)(177,545)(178,546)(179,547)(180,548)(181,549)(182,550)(183,551)
(184,552)(185,553)(186,554)(187,555)(188,556)(189,557)(190,558)(191,559)
(192,560)(193,561)(194,562)(195,563)(196,564)(197,565)(198,566)(199,567)
(200,568)(201,569)(202,570)(203,571)(204,572)(205,573)(206,574)(207,575)
(208,576)(209,577)(210,578)(211,579)(212,580)(213,581)(214,582)(215,583)
(216,584)(217,585)(218,586)(219,587)(220,588)(221,589)(222,590)(223,591)
(224,592)(225,593)(226,594)(227,595)(228,596)(229,597)(230,598)(231,622)
(232,623)(233,624)(234,625)(235,626)(236,627)(237,628)(238,629)(239,630)
(240,631)(241,632)(242,633)(243,634)(244,635)(245,636)(246,637)(247,638)
(248,639)(249,640)(250,641)(251,642)(252,643)(253,644)(254,599)(255,600)
(256,601)(257,602)(258,603)(259,604)(260,605)(261,606)(262,607)(263,608)
(264,609)(265,610)(266,611)(267,612)(268,613)(269,614)(270,615)(271,616)
(272,617)(273,618)(274,619)(275,620)(276,621)(277,668)(278,669)(279,670)
(280,671)(281,672)(282,673)(283,674)(284,675)(285,676)(286,677)(287,678)
(288,679)(289,680)(290,681)(291,682)(292,683)(293,684)(294,685)(295,686)
(296,687)(297,688)(298,689)(299,690)(300,645)(301,646)(302,647)(303,648)
(304,649)(305,650)(306,651)(307,652)(308,653)(309,654)(310,655)(311,656)
(312,657)(313,658)(314,659)(315,660)(316,661)(317,662)(318,663)(319,664)
(320,665)(321,666)(322,667)(323,691)(324,692)(325,693)(326,694)(327,695)
(328,696)(329,697)(330,698)(331,699)(332,700)(333,701)(334,702)(335,703)
(336,704)(337,705)(338,706)(339,707)(340,708)(341,709)(342,710)(343,711)
(344,712)(345,713)(346,714)(347,715)(348,716)(349,717)(350,718)(351,719)
(352,720)(353,721)(354,722)(355,723)(356,724)(357,725)(358,726)(359,727)
(360,728)(361,729)(362,730)(363,731)(364,732)(365,733)(366,734)(367,735)
(368,736);
s1 := Sym(736)!( 2, 23)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)
( 9, 16)( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)
( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)
( 49, 68)( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)
( 57, 60)( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)
( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 93,116)( 94,138)( 95,137)
( 96,136)( 97,135)( 98,134)( 99,133)(100,132)(101,131)(102,130)(103,129)
(104,128)(105,127)(106,126)(107,125)(108,124)(109,123)(110,122)(111,121)
(112,120)(113,119)(114,118)(115,117)(139,162)(140,184)(141,183)(142,182)
(143,181)(144,180)(145,179)(146,178)(147,177)(148,176)(149,175)(150,174)
(151,173)(152,172)(153,171)(154,170)(155,169)(156,168)(157,167)(158,166)
(159,165)(160,164)(161,163)(185,231)(186,253)(187,252)(188,251)(189,250)
(190,249)(191,248)(192,247)(193,246)(194,245)(195,244)(196,243)(197,242)
(198,241)(199,240)(200,239)(201,238)(202,237)(203,236)(204,235)(205,234)
(206,233)(207,232)(208,254)(209,276)(210,275)(211,274)(212,273)(213,272)
(214,271)(215,270)(216,269)(217,268)(218,267)(219,266)(220,265)(221,264)
(222,263)(223,262)(224,261)(225,260)(226,259)(227,258)(228,257)(229,256)
(230,255)(277,346)(278,368)(279,367)(280,366)(281,365)(282,364)(283,363)
(284,362)(285,361)(286,360)(287,359)(288,358)(289,357)(290,356)(291,355)
(292,354)(293,353)(294,352)(295,351)(296,350)(297,349)(298,348)(299,347)
(300,323)(301,345)(302,344)(303,343)(304,342)(305,341)(306,340)(307,339)
(308,338)(309,337)(310,336)(311,335)(312,334)(313,333)(314,332)(315,331)
(316,330)(317,329)(318,328)(319,327)(320,326)(321,325)(322,324)(369,461)
(370,483)(371,482)(372,481)(373,480)(374,479)(375,478)(376,477)(377,476)
(378,475)(379,474)(380,473)(381,472)(382,471)(383,470)(384,469)(385,468)
(386,467)(387,466)(388,465)(389,464)(390,463)(391,462)(392,484)(393,506)
(394,505)(395,504)(396,503)(397,502)(398,501)(399,500)(400,499)(401,498)
(402,497)(403,496)(404,495)(405,494)(406,493)(407,492)(408,491)(409,490)
(410,489)(411,488)(412,487)(413,486)(414,485)(415,507)(416,529)(417,528)
(418,527)(419,526)(420,525)(421,524)(422,523)(423,522)(424,521)(425,520)
(426,519)(427,518)(428,517)(429,516)(430,515)(431,514)(432,513)(433,512)
(434,511)(435,510)(436,509)(437,508)(438,530)(439,552)(440,551)(441,550)
(442,549)(443,548)(444,547)(445,546)(446,545)(447,544)(448,543)(449,542)
(450,541)(451,540)(452,539)(453,538)(454,537)(455,536)(456,535)(457,534)
(458,533)(459,532)(460,531)(553,714)(554,736)(555,735)(556,734)(557,733)
(558,732)(559,731)(560,730)(561,729)(562,728)(563,727)(564,726)(565,725)
(566,724)(567,723)(568,722)(569,721)(570,720)(571,719)(572,718)(573,717)
(574,716)(575,715)(576,691)(577,713)(578,712)(579,711)(580,710)(581,709)
(582,708)(583,707)(584,706)(585,705)(586,704)(587,703)(588,702)(589,701)
(590,700)(591,699)(592,698)(593,697)(594,696)(595,695)(596,694)(597,693)
(598,692)(599,668)(600,690)(601,689)(602,688)(603,687)(604,686)(605,685)
(606,684)(607,683)(608,682)(609,681)(610,680)(611,679)(612,678)(613,677)
(614,676)(615,675)(616,674)(617,673)(618,672)(619,671)(620,670)(621,669)
(622,645)(623,667)(624,666)(625,665)(626,664)(627,663)(628,662)(629,661)
(630,660)(631,659)(632,658)(633,657)(634,656)(635,655)(636,654)(637,653)
(638,652)(639,651)(640,650)(641,649)(642,648)(643,647)(644,646);
s2 := Sym(736)!( 1,186)( 2,185)( 3,207)( 4,206)( 5,205)( 6,204)( 7,203)
( 8,202)( 9,201)( 10,200)( 11,199)( 12,198)( 13,197)( 14,196)( 15,195)
( 16,194)( 17,193)( 18,192)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)
( 24,209)( 25,208)( 26,230)( 27,229)( 28,228)( 29,227)( 30,226)( 31,225)
( 32,224)( 33,223)( 34,222)( 35,221)( 36,220)( 37,219)( 38,218)( 39,217)
( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,211)( 46,210)( 47,232)
( 48,231)( 49,253)( 50,252)( 51,251)( 52,250)( 53,249)( 54,248)( 55,247)
( 56,246)( 57,245)( 58,244)( 59,243)( 60,242)( 61,241)( 62,240)( 63,239)
( 64,238)( 65,237)( 66,236)( 67,235)( 68,234)( 69,233)( 70,255)( 71,254)
( 72,276)( 73,275)( 74,274)( 75,273)( 76,272)( 77,271)( 78,270)( 79,269)
( 80,268)( 81,267)( 82,266)( 83,265)( 84,264)( 85,263)( 86,262)( 87,261)
( 88,260)( 89,259)( 90,258)( 91,257)( 92,256)( 93,301)( 94,300)( 95,322)
( 96,321)( 97,320)( 98,319)( 99,318)(100,317)(101,316)(102,315)(103,314)
(104,313)(105,312)(106,311)(107,310)(108,309)(109,308)(110,307)(111,306)
(112,305)(113,304)(114,303)(115,302)(116,278)(117,277)(118,299)(119,298)
(120,297)(121,296)(122,295)(123,294)(124,293)(125,292)(126,291)(127,290)
(128,289)(129,288)(130,287)(131,286)(132,285)(133,284)(134,283)(135,282)
(136,281)(137,280)(138,279)(139,347)(140,346)(141,368)(142,367)(143,366)
(144,365)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)
(152,357)(153,356)(154,355)(155,354)(156,353)(157,352)(158,351)(159,350)
(160,349)(161,348)(162,324)(163,323)(164,345)(165,344)(166,343)(167,342)
(168,341)(169,340)(170,339)(171,338)(172,337)(173,336)(174,335)(175,334)
(176,333)(177,332)(178,331)(179,330)(180,329)(181,328)(182,327)(183,326)
(184,325)(369,554)(370,553)(371,575)(372,574)(373,573)(374,572)(375,571)
(376,570)(377,569)(378,568)(379,567)(380,566)(381,565)(382,564)(383,563)
(384,562)(385,561)(386,560)(387,559)(388,558)(389,557)(390,556)(391,555)
(392,577)(393,576)(394,598)(395,597)(396,596)(397,595)(398,594)(399,593)
(400,592)(401,591)(402,590)(403,589)(404,588)(405,587)(406,586)(407,585)
(408,584)(409,583)(410,582)(411,581)(412,580)(413,579)(414,578)(415,600)
(416,599)(417,621)(418,620)(419,619)(420,618)(421,617)(422,616)(423,615)
(424,614)(425,613)(426,612)(427,611)(428,610)(429,609)(430,608)(431,607)
(432,606)(433,605)(434,604)(435,603)(436,602)(437,601)(438,623)(439,622)
(440,644)(441,643)(442,642)(443,641)(444,640)(445,639)(446,638)(447,637)
(448,636)(449,635)(450,634)(451,633)(452,632)(453,631)(454,630)(455,629)
(456,628)(457,627)(458,626)(459,625)(460,624)(461,669)(462,668)(463,690)
(464,689)(465,688)(466,687)(467,686)(468,685)(469,684)(470,683)(471,682)
(472,681)(473,680)(474,679)(475,678)(476,677)(477,676)(478,675)(479,674)
(480,673)(481,672)(482,671)(483,670)(484,646)(485,645)(486,667)(487,666)
(488,665)(489,664)(490,663)(491,662)(492,661)(493,660)(494,659)(495,658)
(496,657)(497,656)(498,655)(499,654)(500,653)(501,652)(502,651)(503,650)
(504,649)(505,648)(506,647)(507,715)(508,714)(509,736)(510,735)(511,734)
(512,733)(513,732)(514,731)(515,730)(516,729)(517,728)(518,727)(519,726)
(520,725)(521,724)(522,723)(523,722)(524,721)(525,720)(526,719)(527,718)
(528,717)(529,716)(530,692)(531,691)(532,713)(533,712)(534,711)(535,710)
(536,709)(537,708)(538,707)(539,706)(540,705)(541,704)(542,703)(543,702)
(544,701)(545,700)(546,699)(547,698)(548,697)(549,696)(550,695)(551,694)
(552,693);
poly := sub<Sym(736)|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*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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