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Polytope of Type {92,8}

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