Polytope of Type {8,92}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,92}*1472a
Also Known As : {8,92|2}. if this polytope has another name.
Group : SmallGroup(1472,684)
Rank : 3
Schlafli Type : {8,92}
Number of vertices, edges, etc : 8, 368, 92
Order of s0s1s2 : 184
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 : {4,92}*736, {8,46}*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}*64a
46-fold quotients : {4,4}*32, {8,2}*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)( 47,415)( 48,416)
( 49,417)( 50,418)( 51,419)( 52,420)( 53,421)( 54,422)( 55,423)( 56,424)
( 57,425)( 58,426)( 59,427)( 60,428)( 61,429)( 62,430)( 63,431)( 64,432)
( 65,433)( 66,434)( 67,435)( 68,436)( 69,437)( 70,438)( 71,439)( 72,440)
( 73,441)( 74,442)( 75,443)( 76,444)( 77,445)( 78,446)( 79,447)( 80,448)
( 81,449)( 82,450)( 83,451)( 84,452)( 85,453)( 86,454)( 87,455)( 88,456)
( 89,457)( 90,458)( 91,459)( 92,460)( 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)(139,530)(140,531)(141,532)(142,533)(143,534)(144,535)
(145,536)(146,537)(147,538)(148,539)(149,540)(150,541)(151,542)(152,543)
(153,544)(154,545)(155,546)(156,547)(157,548)(158,549)(159,550)(160,551)
(161,552)(162,507)(163,508)(164,509)(165,510)(166,511)(167,512)(168,513)
(169,514)(170,515)(171,516)(172,517)(173,518)(174,519)(175,520)(176,521)
(177,522)(178,523)(179,524)(180,525)(181,526)(182,527)(183,528)(184,529)
(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)(231,599)(232,600)
(233,601)(234,602)(235,603)(236,604)(237,605)(238,606)(239,607)(240,608)
(241,609)(242,610)(243,611)(244,612)(245,613)(246,614)(247,615)(248,616)
(249,617)(250,618)(251,619)(252,620)(253,621)(254,622)(255,623)(256,624)
(257,625)(258,626)(259,627)(260,628)(261,629)(262,630)(263,631)(264,632)
(265,633)(266,634)(267,635)(268,636)(269,637)(270,638)(271,639)(272,640)
(273,641)(274,642)(275,643)(276,644)(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)(323,714)(324,715)(325,716)(326,717)(327,718)(328,719)
(329,720)(330,721)(331,722)(332,723)(333,724)(334,725)(335,726)(336,727)
(337,728)(338,729)(339,730)(340,731)(341,732)(342,733)(343,734)(344,735)
(345,736)(346,691)(347,692)(348,693)(349,694)(350,695)(351,696)(352,697)
(353,698)(354,699)(355,700)(356,701)(357,702)(358,703)(359,704)(360,705)
(361,706)(362,707)(363,708)(364,709)(365,710)(366,711)(367,712)(368,713);;
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)(553,691)(554,713)(555,712)(556,711)(557,710)(558,709)
(559,708)(560,707)(561,706)(562,705)(563,704)(564,703)(565,702)(566,701)
(567,700)(568,699)(569,698)(570,697)(571,696)(572,695)(573,694)(574,693)
(575,692)(576,714)(577,736)(578,735)(579,734)(580,733)(581,732)(582,731)
(583,730)(584,729)(585,728)(586,727)(587,726)(588,725)(589,724)(590,723)
(591,722)(592,721)(593,720)(594,719)(595,718)(596,717)(597,716)(598,715)
(599,645)(600,667)(601,666)(602,665)(603,664)(604,663)(605,662)(606,661)
(607,660)(608,659)(609,658)(610,657)(611,656)(612,655)(613,654)(614,653)
(615,652)(616,651)(617,650)(618,649)(619,648)(620,647)(621,646)(622,668)
(623,690)(624,689)(625,688)(626,687)(627,686)(628,685)(629,684)(630,683)
(631,682)(632,681)(633,680)(634,679)(635,678)(636,677)(637,676)(638,675)
(639,674)(640,673)(641,672)(642,671)(643,670)(644,669);;
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)( 93,278)( 94,277)( 95,299)( 96,298)
( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,291)(104,290)
(105,289)(106,288)(107,287)(108,286)(109,285)(110,284)(111,283)(112,282)
(113,281)(114,280)(115,279)(116,301)(117,300)(118,322)(119,321)(120,320)
(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)(128,312)
(129,311)(130,310)(131,309)(132,308)(133,307)(134,306)(135,305)(136,304)
(137,303)(138,302)(139,324)(140,323)(141,345)(142,344)(143,343)(144,342)
(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,335)(152,334)
(153,333)(154,332)(155,331)(156,330)(157,329)(158,328)(159,327)(160,326)
(161,325)(162,347)(163,346)(164,368)(165,367)(166,366)(167,365)(168,364)
(169,363)(170,362)(171,361)(172,360)(173,359)(174,358)(175,357)(176,356)
(177,355)(178,354)(179,353)(180,352)(181,351)(182,350)(183,349)(184,348)
(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)(461,646)(462,645)(463,667)(464,666)
(465,665)(466,664)(467,663)(468,662)(469,661)(470,660)(471,659)(472,658)
(473,657)(474,656)(475,655)(476,654)(477,653)(478,652)(479,651)(480,650)
(481,649)(482,648)(483,647)(484,669)(485,668)(486,690)(487,689)(488,688)
(489,687)(490,686)(491,685)(492,684)(493,683)(494,682)(495,681)(496,680)
(497,679)(498,678)(499,677)(500,676)(501,675)(502,674)(503,673)(504,672)
(505,671)(506,670)(507,692)(508,691)(509,713)(510,712)(511,711)(512,710)
(513,709)(514,708)(515,707)(516,706)(517,705)(518,704)(519,703)(520,702)
(521,701)(522,700)(523,699)(524,698)(525,697)(526,696)(527,695)(528,694)
(529,693)(530,715)(531,714)(532,736)(533,735)(534,734)(535,733)(536,732)
(537,731)(538,730)(539,729)(540,728)(541,727)(542,726)(543,725)(544,724)
(545,723)(546,722)(547,721)(548,720)(549,719)(550,718)(551,717)(552,716);;
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,
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)( 47,415)
( 48,416)( 49,417)( 50,418)( 51,419)( 52,420)( 53,421)( 54,422)( 55,423)
( 56,424)( 57,425)( 58,426)( 59,427)( 60,428)( 61,429)( 62,430)( 63,431)
( 64,432)( 65,433)( 66,434)( 67,435)( 68,436)( 69,437)( 70,438)( 71,439)
( 72,440)( 73,441)( 74,442)( 75,443)( 76,444)( 77,445)( 78,446)( 79,447)
( 80,448)( 81,449)( 82,450)( 83,451)( 84,452)( 85,453)( 86,454)( 87,455)
( 88,456)( 89,457)( 90,458)( 91,459)( 92,460)( 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)(139,530)(140,531)(141,532)(142,533)(143,534)
(144,535)(145,536)(146,537)(147,538)(148,539)(149,540)(150,541)(151,542)
(152,543)(153,544)(154,545)(155,546)(156,547)(157,548)(158,549)(159,550)
(160,551)(161,552)(162,507)(163,508)(164,509)(165,510)(166,511)(167,512)
(168,513)(169,514)(170,515)(171,516)(172,517)(173,518)(174,519)(175,520)
(176,521)(177,522)(178,523)(179,524)(180,525)(181,526)(182,527)(183,528)
(184,529)(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)(231,599)
(232,600)(233,601)(234,602)(235,603)(236,604)(237,605)(238,606)(239,607)
(240,608)(241,609)(242,610)(243,611)(244,612)(245,613)(246,614)(247,615)
(248,616)(249,617)(250,618)(251,619)(252,620)(253,621)(254,622)(255,623)
(256,624)(257,625)(258,626)(259,627)(260,628)(261,629)(262,630)(263,631)
(264,632)(265,633)(266,634)(267,635)(268,636)(269,637)(270,638)(271,639)
(272,640)(273,641)(274,642)(275,643)(276,644)(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)(323,714)(324,715)(325,716)(326,717)(327,718)
(328,719)(329,720)(330,721)(331,722)(332,723)(333,724)(334,725)(335,726)
(336,727)(337,728)(338,729)(339,730)(340,731)(341,732)(342,733)(343,734)
(344,735)(345,736)(346,691)(347,692)(348,693)(349,694)(350,695)(351,696)
(352,697)(353,698)(354,699)(355,700)(356,701)(357,702)(358,703)(359,704)
(360,705)(361,706)(362,707)(363,708)(364,709)(365,710)(366,711)(367,712)
(368,713);
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)(553,691)(554,713)(555,712)(556,711)(557,710)
(558,709)(559,708)(560,707)(561,706)(562,705)(563,704)(564,703)(565,702)
(566,701)(567,700)(568,699)(569,698)(570,697)(571,696)(572,695)(573,694)
(574,693)(575,692)(576,714)(577,736)(578,735)(579,734)(580,733)(581,732)
(582,731)(583,730)(584,729)(585,728)(586,727)(587,726)(588,725)(589,724)
(590,723)(591,722)(592,721)(593,720)(594,719)(595,718)(596,717)(597,716)
(598,715)(599,645)(600,667)(601,666)(602,665)(603,664)(604,663)(605,662)
(606,661)(607,660)(608,659)(609,658)(610,657)(611,656)(612,655)(613,654)
(614,653)(615,652)(616,651)(617,650)(618,649)(619,648)(620,647)(621,646)
(622,668)(623,690)(624,689)(625,688)(626,687)(627,686)(628,685)(629,684)
(630,683)(631,682)(632,681)(633,680)(634,679)(635,678)(636,677)(637,676)
(638,675)(639,674)(640,673)(641,672)(642,671)(643,670)(644,669);
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)( 93,278)( 94,277)( 95,299)
( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,291)
(104,290)(105,289)(106,288)(107,287)(108,286)(109,285)(110,284)(111,283)
(112,282)(113,281)(114,280)(115,279)(116,301)(117,300)(118,322)(119,321)
(120,320)(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)
(128,312)(129,311)(130,310)(131,309)(132,308)(133,307)(134,306)(135,305)
(136,304)(137,303)(138,302)(139,324)(140,323)(141,345)(142,344)(143,343)
(144,342)(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,335)
(152,334)(153,333)(154,332)(155,331)(156,330)(157,329)(158,328)(159,327)
(160,326)(161,325)(162,347)(163,346)(164,368)(165,367)(166,366)(167,365)
(168,364)(169,363)(170,362)(171,361)(172,360)(173,359)(174,358)(175,357)
(176,356)(177,355)(178,354)(179,353)(180,352)(181,351)(182,350)(183,349)
(184,348)(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)(461,646)(462,645)(463,667)
(464,666)(465,665)(466,664)(467,663)(468,662)(469,661)(470,660)(471,659)
(472,658)(473,657)(474,656)(475,655)(476,654)(477,653)(478,652)(479,651)
(480,650)(481,649)(482,648)(483,647)(484,669)(485,668)(486,690)(487,689)
(488,688)(489,687)(490,686)(491,685)(492,684)(493,683)(494,682)(495,681)
(496,680)(497,679)(498,678)(499,677)(500,676)(501,675)(502,674)(503,673)
(504,672)(505,671)(506,670)(507,692)(508,691)(509,713)(510,712)(511,711)
(512,710)(513,709)(514,708)(515,707)(516,706)(517,705)(518,704)(519,703)
(520,702)(521,701)(522,700)(523,699)(524,698)(525,697)(526,696)(527,695)
(528,694)(529,693)(530,715)(531,714)(532,736)(533,735)(534,734)(535,733)
(536,732)(537,731)(538,730)(539,729)(540,728)(541,727)(542,726)(543,725)
(544,724)(545,723)(546,722)(547,721)(548,720)(549,719)(550,718)(551,717)
(552,716);
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, s0*s1*s2*s1*s0*s1*s2*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