Questions?
See the FAQ
or other info.

Polytope of Type {4,46,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,46,4}*1472
Also Known As : {{4,46|2},{46,4|2}}. if this polytope has another name.
Group : SmallGroup(1472,1181)
Rank : 4
Schlafli Type : {4,46,4}
Number of vertices, edges, etc : 4, 92, 92, 4
Order of s0s1s2s3 : 92
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,46,4}*736, {4,46,2}*736
   4-fold quotients : {2,46,2}*368
   8-fold quotients : {2,23,2}*184
   23-fold quotients : {4,2,4}*64
   46-fold quotients : {2,2,4}*32, {4,2,2}*32
   92-fold quotients : {2,2,2}*16
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)( 93,507)( 94,508)( 95,509)( 96,510)
( 97,511)( 98,512)( 99,513)(100,514)(101,515)(102,516)(103,517)(104,518)
(105,519)(106,520)(107,521)(108,522)(109,523)(110,524)(111,525)(112,526)
(113,527)(114,528)(115,529)(116,530)(117,531)(118,532)(119,533)(120,534)
(121,535)(122,536)(123,537)(124,538)(125,539)(126,540)(127,541)(128,542)
(129,543)(130,544)(131,545)(132,546)(133,547)(134,548)(135,549)(136,550)
(137,551)(138,552)(139,461)(140,462)(141,463)(142,464)(143,465)(144,466)
(145,467)(146,468)(147,469)(148,470)(149,471)(150,472)(151,473)(152,474)
(153,475)(154,476)(155,477)(156,478)(157,479)(158,480)(159,481)(160,482)
(161,483)(162,484)(163,485)(164,486)(165,487)(166,488)(167,489)(168,490)
(169,491)(170,492)(171,493)(172,494)(173,495)(174,496)(175,497)(176,498)
(177,499)(178,500)(179,501)(180,502)(181,503)(182,504)(183,505)(184,506)
(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)(277,691)(278,692)(279,693)(280,694)
(281,695)(282,696)(283,697)(284,698)(285,699)(286,700)(287,701)(288,702)
(289,703)(290,704)(291,705)(292,706)(293,707)(294,708)(295,709)(296,710)
(297,711)(298,712)(299,713)(300,714)(301,715)(302,716)(303,717)(304,718)
(305,719)(306,720)(307,721)(308,722)(309,723)(310,724)(311,725)(312,726)
(313,727)(314,728)(315,729)(316,730)(317,731)(318,732)(319,733)(320,734)
(321,735)(322,736)(323,645)(324,646)(325,647)(326,648)(327,649)(328,650)
(329,651)(330,652)(331,653)(332,654)(333,655)(334,656)(335,657)(336,658)
(337,659)(338,660)(339,661)(340,662)(341,663)(342,664)(343,665)(344,666)
(345,667)(346,668)(347,669)(348,670)(349,671)(350,672)(351,673)(352,674)
(353,675)(354,676)(355,677)(356,678)(357,679)(358,680)(359,681)(360,682)
(361,683)(362,684)(363,685)(364,686)(365,687)(366,688)(367,689)(368,690);;
s1 := (  1, 93)(  2,115)(  3,114)(  4,113)(  5,112)(  6,111)(  7,110)(  8,109)
(  9,108)( 10,107)( 11,106)( 12,105)( 13,104)( 14,103)( 15,102)( 16,101)
( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21, 96)( 22, 95)( 23, 94)( 24,116)
( 25,138)( 26,137)( 27,136)( 28,135)( 29,134)( 30,133)( 31,132)( 32,131)
( 33,130)( 34,129)( 35,128)( 36,127)( 37,126)( 38,125)( 39,124)( 40,123)
( 41,122)( 42,121)( 43,120)( 44,119)( 45,118)( 46,117)( 47,139)( 48,161)
( 49,160)( 50,159)( 51,158)( 52,157)( 53,156)( 54,155)( 55,154)( 56,153)
( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)
( 65,144)( 66,143)( 67,142)( 68,141)( 69,140)( 70,162)( 71,184)( 72,183)
( 73,182)( 74,181)( 75,180)( 76,179)( 77,178)( 78,177)( 79,176)( 80,175)
( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167)
( 89,166)( 90,165)( 91,164)( 92,163)(185,277)(186,299)(187,298)(188,297)
(189,296)(190,295)(191,294)(192,293)(193,292)(194,291)(195,290)(196,289)
(197,288)(198,287)(199,286)(200,285)(201,284)(202,283)(203,282)(204,281)
(205,280)(206,279)(207,278)(208,300)(209,322)(210,321)(211,320)(212,319)
(213,318)(214,317)(215,316)(216,315)(217,314)(218,313)(219,312)(220,311)
(221,310)(222,309)(223,308)(224,307)(225,306)(226,305)(227,304)(228,303)
(229,302)(230,301)(231,323)(232,345)(233,344)(234,343)(235,342)(236,341)
(237,340)(238,339)(239,338)(240,337)(241,336)(242,335)(243,334)(244,333)
(245,332)(246,331)(247,330)(248,329)(249,328)(250,327)(251,326)(252,325)
(253,324)(254,346)(255,368)(256,367)(257,366)(258,365)(259,364)(260,363)
(261,362)(262,361)(263,360)(264,359)(265,358)(266,357)(267,356)(268,355)
(269,354)(270,353)(271,352)(272,351)(273,350)(274,349)(275,348)(276,347)
(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)(553,645)(554,667)(555,666)(556,665)
(557,664)(558,663)(559,662)(560,661)(561,660)(562,659)(563,658)(564,657)
(565,656)(566,655)(567,654)(568,653)(569,652)(570,651)(571,650)(572,649)
(573,648)(574,647)(575,646)(576,668)(577,690)(578,689)(579,688)(580,687)
(581,686)(582,685)(583,684)(584,683)(585,682)(586,681)(587,680)(588,679)
(589,678)(590,677)(591,676)(592,675)(593,674)(594,673)(595,672)(596,671)
(597,670)(598,669)(599,691)(600,713)(601,712)(602,711)(603,710)(604,709)
(605,708)(606,707)(607,706)(608,705)(609,704)(610,703)(611,702)(612,701)
(613,700)(614,699)(615,698)(616,697)(617,696)(618,695)(619,694)(620,693)
(621,692)(622,714)(623,736)(624,735)(625,734)(626,733)(627,732)(628,731)
(629,730)(630,729)(631,728)(632,727)(633,726)(634,725)(635,724)(636,723)
(637,722)(638,721)(639,720)(640,719)(641,718)(642,717)(643,716)(644,715);;
s2 := (  1, 94)(  2, 93)(  3,115)(  4,114)(  5,113)(  6,112)(  7,111)(  8,110)
(  9,109)( 10,108)( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)( 16,102)
( 17,101)( 18,100)( 19, 99)( 20, 98)( 21, 97)( 22, 96)( 23, 95)( 24,117)
( 25,116)( 26,138)( 27,137)( 28,136)( 29,135)( 30,134)( 31,133)( 32,132)
( 33,131)( 34,130)( 35,129)( 36,128)( 37,127)( 38,126)( 39,125)( 40,124)
( 41,123)( 42,122)( 43,121)( 44,120)( 45,119)( 46,118)( 47,140)( 48,139)
( 49,161)( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)( 56,154)
( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)( 64,146)
( 65,145)( 66,144)( 67,143)( 68,142)( 69,141)( 70,163)( 71,162)( 72,184)
( 73,183)( 74,182)( 75,181)( 76,180)( 77,179)( 78,178)( 79,177)( 80,176)
( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)( 88,168)
( 89,167)( 90,166)( 91,165)( 92,164)(185,301)(186,300)(187,322)(188,321)
(189,320)(190,319)(191,318)(192,317)(193,316)(194,315)(195,314)(196,313)
(197,312)(198,311)(199,310)(200,309)(201,308)(202,307)(203,306)(204,305)
(205,304)(206,303)(207,302)(208,278)(209,277)(210,299)(211,298)(212,297)
(213,296)(214,295)(215,294)(216,293)(217,292)(218,291)(219,290)(220,289)
(221,288)(222,287)(223,286)(224,285)(225,284)(226,283)(227,282)(228,281)
(229,280)(230,279)(231,347)(232,346)(233,368)(234,367)(235,366)(236,365)
(237,364)(238,363)(239,362)(240,361)(241,360)(242,359)(243,358)(244,357)
(245,356)(246,355)(247,354)(248,353)(249,352)(250,351)(251,350)(252,349)
(253,348)(254,324)(255,323)(256,345)(257,344)(258,343)(259,342)(260,341)
(261,340)(262,339)(263,338)(264,337)(265,336)(266,335)(267,334)(268,333)
(269,332)(270,331)(271,330)(272,329)(273,328)(274,327)(275,326)(276,325)
(369,508)(370,507)(371,529)(372,528)(373,527)(374,526)(375,525)(376,524)
(377,523)(378,522)(379,521)(380,520)(381,519)(382,518)(383,517)(384,516)
(385,515)(386,514)(387,513)(388,512)(389,511)(390,510)(391,509)(392,531)
(393,530)(394,552)(395,551)(396,550)(397,549)(398,548)(399,547)(400,546)
(401,545)(402,544)(403,543)(404,542)(405,541)(406,540)(407,539)(408,538)
(409,537)(410,536)(411,535)(412,534)(413,533)(414,532)(415,462)(416,461)
(417,483)(418,482)(419,481)(420,480)(421,479)(422,478)(423,477)(424,476)
(425,475)(426,474)(427,473)(428,472)(429,471)(430,470)(431,469)(432,468)
(433,467)(434,466)(435,465)(436,464)(437,463)(438,485)(439,484)(440,506)
(441,505)(442,504)(443,503)(444,502)(445,501)(446,500)(447,499)(448,498)
(449,497)(450,496)(451,495)(452,494)(453,493)(454,492)(455,491)(456,490)
(457,489)(458,488)(459,487)(460,486)(553,715)(554,714)(555,736)(556,735)
(557,734)(558,733)(559,732)(560,731)(561,730)(562,729)(563,728)(564,727)
(565,726)(566,725)(567,724)(568,723)(569,722)(570,721)(571,720)(572,719)
(573,718)(574,717)(575,716)(576,692)(577,691)(578,713)(579,712)(580,711)
(581,710)(582,709)(583,708)(584,707)(585,706)(586,705)(587,704)(588,703)
(589,702)(590,701)(591,700)(592,699)(593,698)(594,697)(595,696)(596,695)
(597,694)(598,693)(599,669)(600,668)(601,690)(602,689)(603,688)(604,687)
(605,686)(606,685)(607,684)(608,683)(609,682)(610,681)(611,680)(612,679)
(613,678)(614,677)(615,676)(616,675)(617,674)(618,673)(619,672)(620,671)
(621,670)(622,646)(623,645)(624,667)(625,666)(626,665)(627,664)(628,663)
(629,662)(630,661)(631,660)(632,659)(633,658)(634,657)(635,656)(636,655)
(637,654)(638,653)(639,652)(640,651)(641,650)(642,649)(643,648)(644,647);;
s3 := (  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);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 93,507)( 94,508)( 95,509)
( 96,510)( 97,511)( 98,512)( 99,513)(100,514)(101,515)(102,516)(103,517)
(104,518)(105,519)(106,520)(107,521)(108,522)(109,523)(110,524)(111,525)
(112,526)(113,527)(114,528)(115,529)(116,530)(117,531)(118,532)(119,533)
(120,534)(121,535)(122,536)(123,537)(124,538)(125,539)(126,540)(127,541)
(128,542)(129,543)(130,544)(131,545)(132,546)(133,547)(134,548)(135,549)
(136,550)(137,551)(138,552)(139,461)(140,462)(141,463)(142,464)(143,465)
(144,466)(145,467)(146,468)(147,469)(148,470)(149,471)(150,472)(151,473)
(152,474)(153,475)(154,476)(155,477)(156,478)(157,479)(158,480)(159,481)
(160,482)(161,483)(162,484)(163,485)(164,486)(165,487)(166,488)(167,489)
(168,490)(169,491)(170,492)(171,493)(172,494)(173,495)(174,496)(175,497)
(176,498)(177,499)(178,500)(179,501)(180,502)(181,503)(182,504)(183,505)
(184,506)(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)(277,691)(278,692)(279,693)
(280,694)(281,695)(282,696)(283,697)(284,698)(285,699)(286,700)(287,701)
(288,702)(289,703)(290,704)(291,705)(292,706)(293,707)(294,708)(295,709)
(296,710)(297,711)(298,712)(299,713)(300,714)(301,715)(302,716)(303,717)
(304,718)(305,719)(306,720)(307,721)(308,722)(309,723)(310,724)(311,725)
(312,726)(313,727)(314,728)(315,729)(316,730)(317,731)(318,732)(319,733)
(320,734)(321,735)(322,736)(323,645)(324,646)(325,647)(326,648)(327,649)
(328,650)(329,651)(330,652)(331,653)(332,654)(333,655)(334,656)(335,657)
(336,658)(337,659)(338,660)(339,661)(340,662)(341,663)(342,664)(343,665)
(344,666)(345,667)(346,668)(347,669)(348,670)(349,671)(350,672)(351,673)
(352,674)(353,675)(354,676)(355,677)(356,678)(357,679)(358,680)(359,681)
(360,682)(361,683)(362,684)(363,685)(364,686)(365,687)(366,688)(367,689)
(368,690);
s1 := Sym(736)!(  1, 93)(  2,115)(  3,114)(  4,113)(  5,112)(  6,111)(  7,110)
(  8,109)(  9,108)( 10,107)( 11,106)( 12,105)( 13,104)( 14,103)( 15,102)
( 16,101)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21, 96)( 22, 95)( 23, 94)
( 24,116)( 25,138)( 26,137)( 27,136)( 28,135)( 29,134)( 30,133)( 31,132)
( 32,131)( 33,130)( 34,129)( 35,128)( 36,127)( 37,126)( 38,125)( 39,124)
( 40,123)( 41,122)( 42,121)( 43,120)( 44,119)( 45,118)( 46,117)( 47,139)
( 48,161)( 49,160)( 50,159)( 51,158)( 52,157)( 53,156)( 54,155)( 55,154)
( 56,153)( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)
( 64,145)( 65,144)( 66,143)( 67,142)( 68,141)( 69,140)( 70,162)( 71,184)
( 72,183)( 73,182)( 74,181)( 75,180)( 76,179)( 77,178)( 78,177)( 79,176)
( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)
( 88,167)( 89,166)( 90,165)( 91,164)( 92,163)(185,277)(186,299)(187,298)
(188,297)(189,296)(190,295)(191,294)(192,293)(193,292)(194,291)(195,290)
(196,289)(197,288)(198,287)(199,286)(200,285)(201,284)(202,283)(203,282)
(204,281)(205,280)(206,279)(207,278)(208,300)(209,322)(210,321)(211,320)
(212,319)(213,318)(214,317)(215,316)(216,315)(217,314)(218,313)(219,312)
(220,311)(221,310)(222,309)(223,308)(224,307)(225,306)(226,305)(227,304)
(228,303)(229,302)(230,301)(231,323)(232,345)(233,344)(234,343)(235,342)
(236,341)(237,340)(238,339)(239,338)(240,337)(241,336)(242,335)(243,334)
(244,333)(245,332)(246,331)(247,330)(248,329)(249,328)(250,327)(251,326)
(252,325)(253,324)(254,346)(255,368)(256,367)(257,366)(258,365)(259,364)
(260,363)(261,362)(262,361)(263,360)(264,359)(265,358)(266,357)(267,356)
(268,355)(269,354)(270,353)(271,352)(272,351)(273,350)(274,349)(275,348)
(276,347)(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)(553,645)(554,667)(555,666)
(556,665)(557,664)(558,663)(559,662)(560,661)(561,660)(562,659)(563,658)
(564,657)(565,656)(566,655)(567,654)(568,653)(569,652)(570,651)(571,650)
(572,649)(573,648)(574,647)(575,646)(576,668)(577,690)(578,689)(579,688)
(580,687)(581,686)(582,685)(583,684)(584,683)(585,682)(586,681)(587,680)
(588,679)(589,678)(590,677)(591,676)(592,675)(593,674)(594,673)(595,672)
(596,671)(597,670)(598,669)(599,691)(600,713)(601,712)(602,711)(603,710)
(604,709)(605,708)(606,707)(607,706)(608,705)(609,704)(610,703)(611,702)
(612,701)(613,700)(614,699)(615,698)(616,697)(617,696)(618,695)(619,694)
(620,693)(621,692)(622,714)(623,736)(624,735)(625,734)(626,733)(627,732)
(628,731)(629,730)(630,729)(631,728)(632,727)(633,726)(634,725)(635,724)
(636,723)(637,722)(638,721)(639,720)(640,719)(641,718)(642,717)(643,716)
(644,715);
s2 := Sym(736)!(  1, 94)(  2, 93)(  3,115)(  4,114)(  5,113)(  6,112)(  7,111)
(  8,110)(  9,109)( 10,108)( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)
( 16,102)( 17,101)( 18,100)( 19, 99)( 20, 98)( 21, 97)( 22, 96)( 23, 95)
( 24,117)( 25,116)( 26,138)( 27,137)( 28,136)( 29,135)( 30,134)( 31,133)
( 32,132)( 33,131)( 34,130)( 35,129)( 36,128)( 37,127)( 38,126)( 39,125)
( 40,124)( 41,123)( 42,122)( 43,121)( 44,120)( 45,119)( 46,118)( 47,140)
( 48,139)( 49,161)( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)
( 56,154)( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)
( 64,146)( 65,145)( 66,144)( 67,143)( 68,142)( 69,141)( 70,163)( 71,162)
( 72,184)( 73,183)( 74,182)( 75,181)( 76,180)( 77,179)( 78,178)( 79,177)
( 80,176)( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)
( 88,168)( 89,167)( 90,166)( 91,165)( 92,164)(185,301)(186,300)(187,322)
(188,321)(189,320)(190,319)(191,318)(192,317)(193,316)(194,315)(195,314)
(196,313)(197,312)(198,311)(199,310)(200,309)(201,308)(202,307)(203,306)
(204,305)(205,304)(206,303)(207,302)(208,278)(209,277)(210,299)(211,298)
(212,297)(213,296)(214,295)(215,294)(216,293)(217,292)(218,291)(219,290)
(220,289)(221,288)(222,287)(223,286)(224,285)(225,284)(226,283)(227,282)
(228,281)(229,280)(230,279)(231,347)(232,346)(233,368)(234,367)(235,366)
(236,365)(237,364)(238,363)(239,362)(240,361)(241,360)(242,359)(243,358)
(244,357)(245,356)(246,355)(247,354)(248,353)(249,352)(250,351)(251,350)
(252,349)(253,348)(254,324)(255,323)(256,345)(257,344)(258,343)(259,342)
(260,341)(261,340)(262,339)(263,338)(264,337)(265,336)(266,335)(267,334)
(268,333)(269,332)(270,331)(271,330)(272,329)(273,328)(274,327)(275,326)
(276,325)(369,508)(370,507)(371,529)(372,528)(373,527)(374,526)(375,525)
(376,524)(377,523)(378,522)(379,521)(380,520)(381,519)(382,518)(383,517)
(384,516)(385,515)(386,514)(387,513)(388,512)(389,511)(390,510)(391,509)
(392,531)(393,530)(394,552)(395,551)(396,550)(397,549)(398,548)(399,547)
(400,546)(401,545)(402,544)(403,543)(404,542)(405,541)(406,540)(407,539)
(408,538)(409,537)(410,536)(411,535)(412,534)(413,533)(414,532)(415,462)
(416,461)(417,483)(418,482)(419,481)(420,480)(421,479)(422,478)(423,477)
(424,476)(425,475)(426,474)(427,473)(428,472)(429,471)(430,470)(431,469)
(432,468)(433,467)(434,466)(435,465)(436,464)(437,463)(438,485)(439,484)
(440,506)(441,505)(442,504)(443,503)(444,502)(445,501)(446,500)(447,499)
(448,498)(449,497)(450,496)(451,495)(452,494)(453,493)(454,492)(455,491)
(456,490)(457,489)(458,488)(459,487)(460,486)(553,715)(554,714)(555,736)
(556,735)(557,734)(558,733)(559,732)(560,731)(561,730)(562,729)(563,728)
(564,727)(565,726)(566,725)(567,724)(568,723)(569,722)(570,721)(571,720)
(572,719)(573,718)(574,717)(575,716)(576,692)(577,691)(578,713)(579,712)
(580,711)(581,710)(582,709)(583,708)(584,707)(585,706)(586,705)(587,704)
(588,703)(589,702)(590,701)(591,700)(592,699)(593,698)(594,697)(595,696)
(596,695)(597,694)(598,693)(599,669)(600,668)(601,690)(602,689)(603,688)
(604,687)(605,686)(606,685)(607,684)(608,683)(609,682)(610,681)(611,680)
(612,679)(613,678)(614,677)(615,676)(616,675)(617,674)(618,673)(619,672)
(620,671)(621,670)(622,646)(623,645)(624,667)(625,666)(626,665)(627,664)
(628,663)(629,662)(630,661)(631,660)(632,659)(633,658)(634,657)(635,656)
(636,655)(637,654)(638,653)(639,652)(640,651)(641,650)(642,649)(643,648)
(644,647);
s3 := 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);
poly := sub<Sym(736)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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