Polytope of Type {4,184}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,184}*1472b
if this polytope has a name.
Group : SmallGroup(1472,719)
Rank : 3
Schlafli Type : {4,184}
Number of vertices, edges, etc : 4, 368, 184
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 : {4,8}*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 := ( 1,185)( 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)( 93,300)( 94,301)( 95,302)( 96,303)
( 97,304)( 98,305)( 99,306)(100,307)(101,308)(102,309)(103,310)(104,311)
(105,312)(106,313)(107,314)(108,315)(109,316)(110,317)(111,318)(112,319)
(113,320)(114,321)(115,322)(116,277)(117,278)(118,279)(119,280)(120,281)
(121,282)(122,283)(123,284)(124,285)(125,286)(126,287)(127,288)(128,289)
(129,290)(130,291)(131,292)(132,293)(133,294)(134,295)(135,296)(136,297)
(137,298)(138,299)(139,346)(140,347)(141,348)(142,349)(143,350)(144,351)
(145,352)(146,353)(147,354)(148,355)(149,356)(150,357)(151,358)(152,359)
(153,360)(154,361)(155,362)(156,363)(157,364)(158,365)(159,366)(160,367)
(161,368)(162,323)(163,324)(164,325)(165,326)(166,327)(167,328)(168,329)
(169,330)(170,331)(171,332)(172,333)(173,334)(174,335)(175,336)(176,337)
(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,344)(184,345)
(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)(461,668)(462,669)(463,670)(464,671)
(465,672)(466,673)(467,674)(468,675)(469,676)(470,677)(471,678)(472,679)
(473,680)(474,681)(475,682)(476,683)(477,684)(478,685)(479,686)(480,687)
(481,688)(482,689)(483,690)(484,645)(485,646)(486,647)(487,648)(488,649)
(489,650)(490,651)(491,652)(492,653)(493,654)(494,655)(495,656)(496,657)
(497,658)(498,659)(499,660)(500,661)(501,662)(502,663)(503,664)(504,665)
(505,666)(506,667)(507,714)(508,715)(509,716)(510,717)(511,718)(512,719)
(513,720)(514,721)(515,722)(516,723)(517,724)(518,725)(519,726)(520,727)
(521,728)(522,729)(523,730)(524,731)(525,732)(526,733)(527,734)(528,735)
(529,736)(530,691)(531,692)(532,693)(533,694)(534,695)(535,696)(536,697)
(537,698)(538,699)(539,700)(540,701)(541,702)(542,703)(543,704)(544,705)
(545,706)(546,707)(547,708)(548,709)(549,710)(550,711)(551,712)(552,713);;
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)(553,714)(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 := ( 1,370)( 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)( 47,439)( 48,438)
( 49,460)( 50,459)( 51,458)( 52,457)( 53,456)( 54,455)( 55,454)( 56,453)
( 57,452)( 58,451)( 59,450)( 60,449)( 61,448)( 62,447)( 63,446)( 64,445)
( 65,444)( 66,443)( 67,442)( 68,441)( 69,440)( 70,416)( 71,415)( 72,437)
( 73,436)( 74,435)( 75,434)( 76,433)( 77,432)( 78,431)( 79,430)( 80,429)
( 81,428)( 82,427)( 83,426)( 84,425)( 85,424)( 86,423)( 87,422)( 88,421)
( 89,420)( 90,419)( 91,418)( 92,417)( 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)(139,508)(140,507)(141,529)(142,528)(143,527)(144,526)
(145,525)(146,524)(147,523)(148,522)(149,521)(150,520)(151,519)(152,518)
(153,517)(154,516)(155,515)(156,514)(157,513)(158,512)(159,511)(160,510)
(161,509)(162,531)(163,530)(164,552)(165,551)(166,550)(167,549)(168,548)
(169,547)(170,546)(171,545)(172,544)(173,543)(174,542)(175,541)(176,540)
(177,539)(178,538)(179,537)(180,536)(181,535)(182,534)(183,533)(184,532)
(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)(231,623)(232,622)
(233,644)(234,643)(235,642)(236,641)(237,640)(238,639)(239,638)(240,637)
(241,636)(242,635)(243,634)(244,633)(245,632)(246,631)(247,630)(248,629)
(249,628)(250,627)(251,626)(252,625)(253,624)(254,600)(255,599)(256,621)
(257,620)(258,619)(259,618)(260,617)(261,616)(262,615)(263,614)(264,613)
(265,612)(266,611)(267,610)(268,609)(269,608)(270,607)(271,606)(272,605)
(273,604)(274,603)(275,602)(276,601)(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)(323,692)(324,691)(325,713)(326,712)(327,711)(328,710)
(329,709)(330,708)(331,707)(332,706)(333,705)(334,704)(335,703)(336,702)
(337,701)(338,700)(339,699)(340,698)(341,697)(342,696)(343,695)(344,694)
(345,693)(346,715)(347,714)(348,736)(349,735)(350,734)(351,733)(352,732)
(353,731)(354,730)(355,729)(356,728)(357,727)(358,726)(359,725)(360,724)
(361,723)(362,722)(363,721)(364,720)(365,719)(366,718)(367,717)(368,716);;
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
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)( 93,300)( 94,301)( 95,302)
( 96,303)( 97,304)( 98,305)( 99,306)(100,307)(101,308)(102,309)(103,310)
(104,311)(105,312)(106,313)(107,314)(108,315)(109,316)(110,317)(111,318)
(112,319)(113,320)(114,321)(115,322)(116,277)(117,278)(118,279)(119,280)
(120,281)(121,282)(122,283)(123,284)(124,285)(125,286)(126,287)(127,288)
(128,289)(129,290)(130,291)(131,292)(132,293)(133,294)(134,295)(135,296)
(136,297)(137,298)(138,299)(139,346)(140,347)(141,348)(142,349)(143,350)
(144,351)(145,352)(146,353)(147,354)(148,355)(149,356)(150,357)(151,358)
(152,359)(153,360)(154,361)(155,362)(156,363)(157,364)(158,365)(159,366)
(160,367)(161,368)(162,323)(163,324)(164,325)(165,326)(166,327)(167,328)
(168,329)(169,330)(170,331)(171,332)(172,333)(173,334)(174,335)(175,336)
(176,337)(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,344)
(184,345)(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)(461,668)(462,669)(463,670)
(464,671)(465,672)(466,673)(467,674)(468,675)(469,676)(470,677)(471,678)
(472,679)(473,680)(474,681)(475,682)(476,683)(477,684)(478,685)(479,686)
(480,687)(481,688)(482,689)(483,690)(484,645)(485,646)(486,647)(487,648)
(488,649)(489,650)(490,651)(491,652)(492,653)(493,654)(494,655)(495,656)
(496,657)(497,658)(498,659)(499,660)(500,661)(501,662)(502,663)(503,664)
(504,665)(505,666)(506,667)(507,714)(508,715)(509,716)(510,717)(511,718)
(512,719)(513,720)(514,721)(515,722)(516,723)(517,724)(518,725)(519,726)
(520,727)(521,728)(522,729)(523,730)(524,731)(525,732)(526,733)(527,734)
(528,735)(529,736)(530,691)(531,692)(532,693)(533,694)(534,695)(535,696)
(536,697)(537,698)(538,699)(539,700)(540,701)(541,702)(542,703)(543,704)
(544,705)(545,706)(546,707)(547,708)(548,709)(549,710)(550,711)(551,712)
(552,713);
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)(553,714)(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)!( 1,370)( 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)( 47,439)
( 48,438)( 49,460)( 50,459)( 51,458)( 52,457)( 53,456)( 54,455)( 55,454)
( 56,453)( 57,452)( 58,451)( 59,450)( 60,449)( 61,448)( 62,447)( 63,446)
( 64,445)( 65,444)( 66,443)( 67,442)( 68,441)( 69,440)( 70,416)( 71,415)
( 72,437)( 73,436)( 74,435)( 75,434)( 76,433)( 77,432)( 78,431)( 79,430)
( 80,429)( 81,428)( 82,427)( 83,426)( 84,425)( 85,424)( 86,423)( 87,422)
( 88,421)( 89,420)( 90,419)( 91,418)( 92,417)( 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)(139,508)(140,507)(141,529)(142,528)(143,527)
(144,526)(145,525)(146,524)(147,523)(148,522)(149,521)(150,520)(151,519)
(152,518)(153,517)(154,516)(155,515)(156,514)(157,513)(158,512)(159,511)
(160,510)(161,509)(162,531)(163,530)(164,552)(165,551)(166,550)(167,549)
(168,548)(169,547)(170,546)(171,545)(172,544)(173,543)(174,542)(175,541)
(176,540)(177,539)(178,538)(179,537)(180,536)(181,535)(182,534)(183,533)
(184,532)(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)(231,623)
(232,622)(233,644)(234,643)(235,642)(236,641)(237,640)(238,639)(239,638)
(240,637)(241,636)(242,635)(243,634)(244,633)(245,632)(246,631)(247,630)
(248,629)(249,628)(250,627)(251,626)(252,625)(253,624)(254,600)(255,599)
(256,621)(257,620)(258,619)(259,618)(260,617)(261,616)(262,615)(263,614)
(264,613)(265,612)(266,611)(267,610)(268,609)(269,608)(270,607)(271,606)
(272,605)(273,604)(274,603)(275,602)(276,601)(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)(323,692)(324,691)(325,713)(326,712)(327,711)
(328,710)(329,709)(330,708)(331,707)(332,706)(333,705)(334,704)(335,703)
(336,702)(337,701)(338,700)(339,699)(340,698)(341,697)(342,696)(343,695)
(344,694)(345,693)(346,715)(347,714)(348,736)(349,735)(350,734)(351,733)
(352,732)(353,731)(354,730)(355,729)(356,728)(357,727)(358,726)(359,725)
(360,724)(361,723)(362,722)(363,721)(364,720)(365,719)(366,718)(367,717)
(368,716);
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope