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