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Polytope of Type {46,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,16}*1472
Also Known As : {46,16|2}. if this polytope has another name.
Group : SmallGroup(1472,968)
Rank : 3
Schlafli Type : {46,16}
Number of vertices, edges, etc : 46, 368, 16
Order of s0s1s2 : 368
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 : {46,8}*736
   4-fold quotients : {46,4}*368
   8-fold quotients : {46,2}*184
   16-fold quotients : {23,2}*92
   23-fold quotients : {2,16}*64
   46-fold quotients : {2,8}*32
   92-fold quotients : {2,4}*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 := (  1,186)(  2,185)(  3,207)(  4,206)(  5,205)(  6,204)(  7,203)(  8,202)
(  9,201)( 10,200)( 11,199)( 12,198)( 13,197)( 14,196)( 15,195)( 16,194)
( 17,193)( 18,192)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,209)
( 25,208)( 26,230)( 27,229)( 28,228)( 29,227)( 30,226)( 31,225)( 32,224)
( 33,223)( 34,222)( 35,221)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)
( 41,215)( 42,214)( 43,213)( 44,212)( 45,211)( 46,210)( 47,255)( 48,254)
( 49,276)( 50,275)( 51,274)( 52,273)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)( 64,261)
( 65,260)( 66,259)( 67,258)( 68,257)( 69,256)( 70,232)( 71,231)( 72,253)
( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)( 80,245)
( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)( 88,237)
( 89,236)( 90,235)( 91,234)( 92,233)( 93,324)( 94,323)( 95,345)( 96,344)
( 97,343)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)(104,336)
(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)(112,328)
(113,327)(114,326)(115,325)(116,347)(117,346)(118,368)(119,367)(120,366)
(121,365)(122,364)(123,363)(124,362)(125,361)(126,360)(127,359)(128,358)
(129,357)(130,356)(131,355)(132,354)(133,353)(134,352)(135,351)(136,350)
(137,349)(138,348)(139,278)(140,277)(141,299)(142,298)(143,297)(144,296)
(145,295)(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)(152,288)
(153,287)(154,286)(155,285)(156,284)(157,283)(158,282)(159,281)(160,280)
(161,279)(162,301)(163,300)(164,322)(165,321)(166,320)(167,319)(168,318)
(169,317)(170,316)(171,315)(172,314)(173,313)(174,312)(175,311)(176,310)
(177,309)(178,308)(179,307)(180,306)(181,305)(182,304)(183,303)(184,302)
(369,646)(370,645)(371,667)(372,666)(373,665)(374,664)(375,663)(376,662)
(377,661)(378,660)(379,659)(380,658)(381,657)(382,656)(383,655)(384,654)
(385,653)(386,652)(387,651)(388,650)(389,649)(390,648)(391,647)(392,669)
(393,668)(394,690)(395,689)(396,688)(397,687)(398,686)(399,685)(400,684)
(401,683)(402,682)(403,681)(404,680)(405,679)(406,678)(407,677)(408,676)
(409,675)(410,674)(411,673)(412,672)(413,671)(414,670)(415,715)(416,714)
(417,736)(418,735)(419,734)(420,733)(421,732)(422,731)(423,730)(424,729)
(425,728)(426,727)(427,726)(428,725)(429,724)(430,723)(431,722)(432,721)
(433,720)(434,719)(435,718)(436,717)(437,716)(438,692)(439,691)(440,713)
(441,712)(442,711)(443,710)(444,709)(445,708)(446,707)(447,706)(448,705)
(449,704)(450,703)(451,702)(452,701)(453,700)(454,699)(455,698)(456,697)
(457,696)(458,695)(459,694)(460,693)(461,554)(462,553)(463,575)(464,574)
(465,573)(466,572)(467,571)(468,570)(469,569)(470,568)(471,567)(472,566)
(473,565)(474,564)(475,563)(476,562)(477,561)(478,560)(479,559)(480,558)
(481,557)(482,556)(483,555)(484,577)(485,576)(486,598)(487,597)(488,596)
(489,595)(490,594)(491,593)(492,592)(493,591)(494,590)(495,589)(496,588)
(497,587)(498,586)(499,585)(500,584)(501,583)(502,582)(503,581)(504,580)
(505,579)(506,578)(507,623)(508,622)(509,644)(510,643)(511,642)(512,641)
(513,640)(514,639)(515,638)(516,637)(517,636)(518,635)(519,634)(520,633)
(521,632)(522,631)(523,630)(524,629)(525,628)(526,627)(527,626)(528,625)
(529,624)(530,600)(531,599)(532,621)(533,620)(534,619)(535,618)(536,617)
(537,616)(538,615)(539,614)(540,613)(541,612)(542,611)(543,610)(544,609)
(545,608)(546,607)(547,606)(548,605)(549,604)(550,603)(551,602)(552,601);;
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)( 47,438)( 48,439)
( 49,440)( 50,441)( 51,442)( 52,443)( 53,444)( 54,445)( 55,446)( 56,447)
( 57,448)( 58,449)( 59,450)( 60,451)( 61,452)( 62,453)( 63,454)( 64,455)
( 65,456)( 66,457)( 67,458)( 68,459)( 69,460)( 70,415)( 71,416)( 72,417)
( 73,418)( 74,419)( 75,420)( 76,421)( 77,422)( 78,423)( 79,424)( 80,425)
( 81,426)( 82,427)( 83,428)( 84,429)( 85,430)( 86,431)( 87,432)( 88,433)
( 89,434)( 90,435)( 91,436)( 92,437)( 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)(231,622)(232,623)
(233,624)(234,625)(235,626)(236,627)(237,628)(238,629)(239,630)(240,631)
(241,632)(242,633)(243,634)(244,635)(245,636)(246,637)(247,638)(248,639)
(249,640)(250,641)(251,642)(252,643)(253,644)(254,599)(255,600)(256,601)
(257,602)(258,603)(259,604)(260,605)(261,606)(262,607)(263,608)(264,609)
(265,610)(266,611)(267,612)(268,613)(269,614)(270,615)(271,616)(272,617)
(273,618)(274,619)(275,620)(276,621)(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);;
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*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 ];;
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)!(  1,186)(  2,185)(  3,207)(  4,206)(  5,205)(  6,204)(  7,203)
(  8,202)(  9,201)( 10,200)( 11,199)( 12,198)( 13,197)( 14,196)( 15,195)
( 16,194)( 17,193)( 18,192)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)
( 24,209)( 25,208)( 26,230)( 27,229)( 28,228)( 29,227)( 30,226)( 31,225)
( 32,224)( 33,223)( 34,222)( 35,221)( 36,220)( 37,219)( 38,218)( 39,217)
( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,211)( 46,210)( 47,255)
( 48,254)( 49,276)( 50,275)( 51,274)( 52,273)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)
( 64,261)( 65,260)( 66,259)( 67,258)( 68,257)( 69,256)( 70,232)( 71,231)
( 72,253)( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)
( 80,245)( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)
( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,324)( 94,323)( 95,345)
( 96,344)( 97,343)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)
(104,336)(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)
(112,328)(113,327)(114,326)(115,325)(116,347)(117,346)(118,368)(119,367)
(120,366)(121,365)(122,364)(123,363)(124,362)(125,361)(126,360)(127,359)
(128,358)(129,357)(130,356)(131,355)(132,354)(133,353)(134,352)(135,351)
(136,350)(137,349)(138,348)(139,278)(140,277)(141,299)(142,298)(143,297)
(144,296)(145,295)(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)
(152,288)(153,287)(154,286)(155,285)(156,284)(157,283)(158,282)(159,281)
(160,280)(161,279)(162,301)(163,300)(164,322)(165,321)(166,320)(167,319)
(168,318)(169,317)(170,316)(171,315)(172,314)(173,313)(174,312)(175,311)
(176,310)(177,309)(178,308)(179,307)(180,306)(181,305)(182,304)(183,303)
(184,302)(369,646)(370,645)(371,667)(372,666)(373,665)(374,664)(375,663)
(376,662)(377,661)(378,660)(379,659)(380,658)(381,657)(382,656)(383,655)
(384,654)(385,653)(386,652)(387,651)(388,650)(389,649)(390,648)(391,647)
(392,669)(393,668)(394,690)(395,689)(396,688)(397,687)(398,686)(399,685)
(400,684)(401,683)(402,682)(403,681)(404,680)(405,679)(406,678)(407,677)
(408,676)(409,675)(410,674)(411,673)(412,672)(413,671)(414,670)(415,715)
(416,714)(417,736)(418,735)(419,734)(420,733)(421,732)(422,731)(423,730)
(424,729)(425,728)(426,727)(427,726)(428,725)(429,724)(430,723)(431,722)
(432,721)(433,720)(434,719)(435,718)(436,717)(437,716)(438,692)(439,691)
(440,713)(441,712)(442,711)(443,710)(444,709)(445,708)(446,707)(447,706)
(448,705)(449,704)(450,703)(451,702)(452,701)(453,700)(454,699)(455,698)
(456,697)(457,696)(458,695)(459,694)(460,693)(461,554)(462,553)(463,575)
(464,574)(465,573)(466,572)(467,571)(468,570)(469,569)(470,568)(471,567)
(472,566)(473,565)(474,564)(475,563)(476,562)(477,561)(478,560)(479,559)
(480,558)(481,557)(482,556)(483,555)(484,577)(485,576)(486,598)(487,597)
(488,596)(489,595)(490,594)(491,593)(492,592)(493,591)(494,590)(495,589)
(496,588)(497,587)(498,586)(499,585)(500,584)(501,583)(502,582)(503,581)
(504,580)(505,579)(506,578)(507,623)(508,622)(509,644)(510,643)(511,642)
(512,641)(513,640)(514,639)(515,638)(516,637)(517,636)(518,635)(519,634)
(520,633)(521,632)(522,631)(523,630)(524,629)(525,628)(526,627)(527,626)
(528,625)(529,624)(530,600)(531,599)(532,621)(533,620)(534,619)(535,618)
(536,617)(537,616)(538,615)(539,614)(540,613)(541,612)(542,611)(543,610)
(544,609)(545,608)(546,607)(547,606)(548,605)(549,604)(550,603)(551,602)
(552,601);
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)( 47,438)
( 48,439)( 49,440)( 50,441)( 51,442)( 52,443)( 53,444)( 54,445)( 55,446)
( 56,447)( 57,448)( 58,449)( 59,450)( 60,451)( 61,452)( 62,453)( 63,454)
( 64,455)( 65,456)( 66,457)( 67,458)( 68,459)( 69,460)( 70,415)( 71,416)
( 72,417)( 73,418)( 74,419)( 75,420)( 76,421)( 77,422)( 78,423)( 79,424)
( 80,425)( 81,426)( 82,427)( 83,428)( 84,429)( 85,430)( 86,431)( 87,432)
( 88,433)( 89,434)( 90,435)( 91,436)( 92,437)( 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)(231,622)
(232,623)(233,624)(234,625)(235,626)(236,627)(237,628)(238,629)(239,630)
(240,631)(241,632)(242,633)(243,634)(244,635)(245,636)(246,637)(247,638)
(248,639)(249,640)(250,641)(251,642)(252,643)(253,644)(254,599)(255,600)
(256,601)(257,602)(258,603)(259,604)(260,605)(261,606)(262,607)(263,608)
(264,609)(265,610)(266,611)(267,612)(268,613)(269,614)(270,615)(271,616)
(272,617)(273,618)(274,619)(275,620)(276,621)(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);
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*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 >; 
 
References : None.
to this polytope