Polytope of Type {16,46}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,46}*1472
Also Known As : {16,46|2}. if this polytope has another name.
Group : SmallGroup(1472,968)
Rank : 3
Schlafli Type : {16,46}
Number of vertices, edges, etc : 16, 368, 46
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 : {8,46}*736
4-fold quotients : {4,46}*368
8-fold quotients : {2,46}*184
16-fold quotients : {2,23}*92
23-fold quotients : {16,2}*64
46-fold quotients : {8,2}*32
92-fold quotients : {4,2}*16
184-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 47, 70)( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)( 54, 77)
( 55, 78)( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)
( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)( 93,139)
( 94,140)( 95,141)( 96,142)( 97,143)( 98,144)( 99,145)(100,146)(101,147)
(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154)(109,155)
(110,156)(111,157)(112,158)(113,159)(114,160)(115,161)(116,162)(117,163)
(118,164)(119,165)(120,166)(121,167)(122,168)(123,169)(124,170)(125,171)
(126,172)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)
(134,180)(135,181)(136,182)(137,183)(138,184)(231,254)(232,255)(233,256)
(234,257)(235,258)(236,259)(237,260)(238,261)(239,262)(240,263)(241,264)
(242,265)(243,266)(244,267)(245,268)(246,269)(247,270)(248,271)(249,272)
(250,273)(251,274)(252,275)(253,276)(277,323)(278,324)(279,325)(280,326)
(281,327)(282,328)(283,329)(284,330)(285,331)(286,332)(287,333)(288,334)
(289,335)(290,336)(291,337)(292,338)(293,339)(294,340)(295,341)(296,342)
(297,343)(298,344)(299,345)(300,346)(301,347)(302,348)(303,349)(304,350)
(305,351)(306,352)(307,353)(308,354)(309,355)(310,356)(311,357)(312,358)
(313,359)(314,360)(315,361)(316,362)(317,363)(318,364)(319,365)(320,366)
(321,367)(322,368)(369,461)(370,462)(371,463)(372,464)(373,465)(374,466)
(375,467)(376,468)(377,469)(378,470)(379,471)(380,472)(381,473)(382,474)
(383,475)(384,476)(385,477)(386,478)(387,479)(388,480)(389,481)(390,482)
(391,483)(392,484)(393,485)(394,486)(395,487)(396,488)(397,489)(398,490)
(399,491)(400,492)(401,493)(402,494)(403,495)(404,496)(405,497)(406,498)
(407,499)(408,500)(409,501)(410,502)(411,503)(412,504)(413,505)(414,506)
(415,530)(416,531)(417,532)(418,533)(419,534)(420,535)(421,536)(422,537)
(423,538)(424,539)(425,540)(426,541)(427,542)(428,543)(429,544)(430,545)
(431,546)(432,547)(433,548)(434,549)(435,550)(436,551)(437,552)(438,507)
(439,508)(440,509)(441,510)(442,511)(443,512)(444,513)(445,514)(446,515)
(447,516)(448,517)(449,518)(450,519)(451,520)(452,521)(453,522)(454,523)
(455,524)(456,525)(457,526)(458,527)(459,528)(460,529)(553,645)(554,646)
(555,647)(556,648)(557,649)(558,650)(559,651)(560,652)(561,653)(562,654)
(563,655)(564,656)(565,657)(566,658)(567,659)(568,660)(569,661)(570,662)
(571,663)(572,664)(573,665)(574,666)(575,667)(576,668)(577,669)(578,670)
(579,671)(580,672)(581,673)(582,674)(583,675)(584,676)(585,677)(586,678)
(587,679)(588,680)(589,681)(590,682)(591,683)(592,684)(593,685)(594,686)
(595,687)(596,688)(597,689)(598,690)(599,714)(600,715)(601,716)(602,717)
(603,718)(604,719)(605,720)(606,721)(607,722)(608,723)(609,724)(610,725)
(611,726)(612,727)(613,728)(614,729)(615,730)(616,731)(617,732)(618,733)
(619,734)(620,735)(621,736)(622,691)(623,692)(624,693)(625,694)(626,695)
(627,696)(628,697)(629,698)(630,699)(631,700)(632,701)(633,702)(634,703)
(635,704)(636,705)(637,706)(638,707)(639,708)(640,709)(641,710)(642,711)
(643,712)(644,713);;
s1 := ( 1,553)( 2,575)( 3,574)( 4,573)( 5,572)( 6,571)( 7,570)( 8,569)
( 9,568)( 10,567)( 11,566)( 12,565)( 13,564)( 14,563)( 15,562)( 16,561)
( 17,560)( 18,559)( 19,558)( 20,557)( 21,556)( 22,555)( 23,554)( 24,576)
( 25,598)( 26,597)( 27,596)( 28,595)( 29,594)( 30,593)( 31,592)( 32,591)
( 33,590)( 34,589)( 35,588)( 36,587)( 37,586)( 38,585)( 39,584)( 40,583)
( 41,582)( 42,581)( 43,580)( 44,579)( 45,578)( 46,577)( 47,622)( 48,644)
( 49,643)( 50,642)( 51,641)( 52,640)( 53,639)( 54,638)( 55,637)( 56,636)
( 57,635)( 58,634)( 59,633)( 60,632)( 61,631)( 62,630)( 63,629)( 64,628)
( 65,627)( 66,626)( 67,625)( 68,624)( 69,623)( 70,599)( 71,621)( 72,620)
( 73,619)( 74,618)( 75,617)( 76,616)( 77,615)( 78,614)( 79,613)( 80,612)
( 81,611)( 82,610)( 83,609)( 84,608)( 85,607)( 86,606)( 87,605)( 88,604)
( 89,603)( 90,602)( 91,601)( 92,600)( 93,691)( 94,713)( 95,712)( 96,711)
( 97,710)( 98,709)( 99,708)(100,707)(101,706)(102,705)(103,704)(104,703)
(105,702)(106,701)(107,700)(108,699)(109,698)(110,697)(111,696)(112,695)
(113,694)(114,693)(115,692)(116,714)(117,736)(118,735)(119,734)(120,733)
(121,732)(122,731)(123,730)(124,729)(125,728)(126,727)(127,726)(128,725)
(129,724)(130,723)(131,722)(132,721)(133,720)(134,719)(135,718)(136,717)
(137,716)(138,715)(139,645)(140,667)(141,666)(142,665)(143,664)(144,663)
(145,662)(146,661)(147,660)(148,659)(149,658)(150,657)(151,656)(152,655)
(153,654)(154,653)(155,652)(156,651)(157,650)(158,649)(159,648)(160,647)
(161,646)(162,668)(163,690)(164,689)(165,688)(166,687)(167,686)(168,685)
(169,684)(170,683)(171,682)(172,681)(173,680)(174,679)(175,678)(176,677)
(177,676)(178,675)(179,674)(180,673)(181,672)(182,671)(183,670)(184,669)
(185,369)(186,391)(187,390)(188,389)(189,388)(190,387)(191,386)(192,385)
(193,384)(194,383)(195,382)(196,381)(197,380)(198,379)(199,378)(200,377)
(201,376)(202,375)(203,374)(204,373)(205,372)(206,371)(207,370)(208,392)
(209,414)(210,413)(211,412)(212,411)(213,410)(214,409)(215,408)(216,407)
(217,406)(218,405)(219,404)(220,403)(221,402)(222,401)(223,400)(224,399)
(225,398)(226,397)(227,396)(228,395)(229,394)(230,393)(231,438)(232,460)
(233,459)(234,458)(235,457)(236,456)(237,455)(238,454)(239,453)(240,452)
(241,451)(242,450)(243,449)(244,448)(245,447)(246,446)(247,445)(248,444)
(249,443)(250,442)(251,441)(252,440)(253,439)(254,415)(255,437)(256,436)
(257,435)(258,434)(259,433)(260,432)(261,431)(262,430)(263,429)(264,428)
(265,427)(266,426)(267,425)(268,424)(269,423)(270,422)(271,421)(272,420)
(273,419)(274,418)(275,417)(276,416)(277,507)(278,529)(279,528)(280,527)
(281,526)(282,525)(283,524)(284,523)(285,522)(286,521)(287,520)(288,519)
(289,518)(290,517)(291,516)(292,515)(293,514)(294,513)(295,512)(296,511)
(297,510)(298,509)(299,508)(300,530)(301,552)(302,551)(303,550)(304,549)
(305,548)(306,547)(307,546)(308,545)(309,544)(310,543)(311,542)(312,541)
(313,540)(314,539)(315,538)(316,537)(317,536)(318,535)(319,534)(320,533)
(321,532)(322,531)(323,461)(324,483)(325,482)(326,481)(327,480)(328,479)
(329,478)(330,477)(331,476)(332,475)(333,474)(334,473)(335,472)(336,471)
(337,470)(338,469)(339,468)(340,467)(341,466)(342,465)(343,464)(344,463)
(345,462)(346,484)(347,506)(348,505)(349,504)(350,503)(351,502)(352,501)
(353,500)(354,499)(355,498)(356,497)(357,496)(358,495)(359,494)(360,493)
(361,492)(362,491)(363,490)(364,489)(365,488)(366,487)(367,486)(368,485);;
s2 := ( 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)( 47,232)( 48,231)
( 49,253)( 50,252)( 51,251)( 52,250)( 53,249)( 54,248)( 55,247)( 56,246)
( 57,245)( 58,244)( 59,243)( 60,242)( 61,241)( 62,240)( 63,239)( 64,238)
( 65,237)( 66,236)( 67,235)( 68,234)( 69,233)( 70,255)( 71,254)( 72,276)
( 73,275)( 74,274)( 75,273)( 76,272)( 77,271)( 78,270)( 79,269)( 80,268)
( 81,267)( 82,266)( 83,265)( 84,264)( 85,263)( 86,262)( 87,261)( 88,260)
( 89,259)( 90,258)( 91,257)( 92,256)( 93,278)( 94,277)( 95,299)( 96,298)
( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,291)(104,290)
(105,289)(106,288)(107,287)(108,286)(109,285)(110,284)(111,283)(112,282)
(113,281)(114,280)(115,279)(116,301)(117,300)(118,322)(119,321)(120,320)
(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)(128,312)
(129,311)(130,310)(131,309)(132,308)(133,307)(134,306)(135,305)(136,304)
(137,303)(138,302)(139,324)(140,323)(141,345)(142,344)(143,343)(144,342)
(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,335)(152,334)
(153,333)(154,332)(155,331)(156,330)(157,329)(158,328)(159,327)(160,326)
(161,325)(162,347)(163,346)(164,368)(165,367)(166,366)(167,365)(168,364)
(169,363)(170,362)(171,361)(172,360)(173,359)(174,358)(175,357)(176,356)
(177,355)(178,354)(179,353)(180,352)(181,351)(182,350)(183,349)(184,348)
(369,554)(370,553)(371,575)(372,574)(373,573)(374,572)(375,571)(376,570)
(377,569)(378,568)(379,567)(380,566)(381,565)(382,564)(383,563)(384,562)
(385,561)(386,560)(387,559)(388,558)(389,557)(390,556)(391,555)(392,577)
(393,576)(394,598)(395,597)(396,596)(397,595)(398,594)(399,593)(400,592)
(401,591)(402,590)(403,589)(404,588)(405,587)(406,586)(407,585)(408,584)
(409,583)(410,582)(411,581)(412,580)(413,579)(414,578)(415,600)(416,599)
(417,621)(418,620)(419,619)(420,618)(421,617)(422,616)(423,615)(424,614)
(425,613)(426,612)(427,611)(428,610)(429,609)(430,608)(431,607)(432,606)
(433,605)(434,604)(435,603)(436,602)(437,601)(438,623)(439,622)(440,644)
(441,643)(442,642)(443,641)(444,640)(445,639)(446,638)(447,637)(448,636)
(449,635)(450,634)(451,633)(452,632)(453,631)(454,630)(455,629)(456,628)
(457,627)(458,626)(459,625)(460,624)(461,646)(462,645)(463,667)(464,666)
(465,665)(466,664)(467,663)(468,662)(469,661)(470,660)(471,659)(472,658)
(473,657)(474,656)(475,655)(476,654)(477,653)(478,652)(479,651)(480,650)
(481,649)(482,648)(483,647)(484,669)(485,668)(486,690)(487,689)(488,688)
(489,687)(490,686)(491,685)(492,684)(493,683)(494,682)(495,681)(496,680)
(497,679)(498,678)(499,677)(500,676)(501,675)(502,674)(503,673)(504,672)
(505,671)(506,670)(507,692)(508,691)(509,713)(510,712)(511,711)(512,710)
(513,709)(514,708)(515,707)(516,706)(517,705)(518,704)(519,703)(520,702)
(521,701)(522,700)(523,699)(524,698)(525,697)(526,696)(527,695)(528,694)
(529,693)(530,715)(531,714)(532,736)(533,735)(534,734)(535,733)(536,732)
(537,731)(538,730)(539,729)(540,728)(541,727)(542,726)(543,725)(544,724)
(545,723)(546,722)(547,721)(548,720)(549,719)(550,718)(551,717)(552,716);;
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*s2*s1*s0*s1*s2*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!( 47, 70)( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)
( 54, 77)( 55, 78)( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)
( 62, 85)( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)
( 93,139)( 94,140)( 95,141)( 96,142)( 97,143)( 98,144)( 99,145)(100,146)
(101,147)(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154)
(109,155)(110,156)(111,157)(112,158)(113,159)(114,160)(115,161)(116,162)
(117,163)(118,164)(119,165)(120,166)(121,167)(122,168)(123,169)(124,170)
(125,171)(126,172)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)
(133,179)(134,180)(135,181)(136,182)(137,183)(138,184)(231,254)(232,255)
(233,256)(234,257)(235,258)(236,259)(237,260)(238,261)(239,262)(240,263)
(241,264)(242,265)(243,266)(244,267)(245,268)(246,269)(247,270)(248,271)
(249,272)(250,273)(251,274)(252,275)(253,276)(277,323)(278,324)(279,325)
(280,326)(281,327)(282,328)(283,329)(284,330)(285,331)(286,332)(287,333)
(288,334)(289,335)(290,336)(291,337)(292,338)(293,339)(294,340)(295,341)
(296,342)(297,343)(298,344)(299,345)(300,346)(301,347)(302,348)(303,349)
(304,350)(305,351)(306,352)(307,353)(308,354)(309,355)(310,356)(311,357)
(312,358)(313,359)(314,360)(315,361)(316,362)(317,363)(318,364)(319,365)
(320,366)(321,367)(322,368)(369,461)(370,462)(371,463)(372,464)(373,465)
(374,466)(375,467)(376,468)(377,469)(378,470)(379,471)(380,472)(381,473)
(382,474)(383,475)(384,476)(385,477)(386,478)(387,479)(388,480)(389,481)
(390,482)(391,483)(392,484)(393,485)(394,486)(395,487)(396,488)(397,489)
(398,490)(399,491)(400,492)(401,493)(402,494)(403,495)(404,496)(405,497)
(406,498)(407,499)(408,500)(409,501)(410,502)(411,503)(412,504)(413,505)
(414,506)(415,530)(416,531)(417,532)(418,533)(419,534)(420,535)(421,536)
(422,537)(423,538)(424,539)(425,540)(426,541)(427,542)(428,543)(429,544)
(430,545)(431,546)(432,547)(433,548)(434,549)(435,550)(436,551)(437,552)
(438,507)(439,508)(440,509)(441,510)(442,511)(443,512)(444,513)(445,514)
(446,515)(447,516)(448,517)(449,518)(450,519)(451,520)(452,521)(453,522)
(454,523)(455,524)(456,525)(457,526)(458,527)(459,528)(460,529)(553,645)
(554,646)(555,647)(556,648)(557,649)(558,650)(559,651)(560,652)(561,653)
(562,654)(563,655)(564,656)(565,657)(566,658)(567,659)(568,660)(569,661)
(570,662)(571,663)(572,664)(573,665)(574,666)(575,667)(576,668)(577,669)
(578,670)(579,671)(580,672)(581,673)(582,674)(583,675)(584,676)(585,677)
(586,678)(587,679)(588,680)(589,681)(590,682)(591,683)(592,684)(593,685)
(594,686)(595,687)(596,688)(597,689)(598,690)(599,714)(600,715)(601,716)
(602,717)(603,718)(604,719)(605,720)(606,721)(607,722)(608,723)(609,724)
(610,725)(611,726)(612,727)(613,728)(614,729)(615,730)(616,731)(617,732)
(618,733)(619,734)(620,735)(621,736)(622,691)(623,692)(624,693)(625,694)
(626,695)(627,696)(628,697)(629,698)(630,699)(631,700)(632,701)(633,702)
(634,703)(635,704)(636,705)(637,706)(638,707)(639,708)(640,709)(641,710)
(642,711)(643,712)(644,713);
s1 := Sym(736)!( 1,553)( 2,575)( 3,574)( 4,573)( 5,572)( 6,571)( 7,570)
( 8,569)( 9,568)( 10,567)( 11,566)( 12,565)( 13,564)( 14,563)( 15,562)
( 16,561)( 17,560)( 18,559)( 19,558)( 20,557)( 21,556)( 22,555)( 23,554)
( 24,576)( 25,598)( 26,597)( 27,596)( 28,595)( 29,594)( 30,593)( 31,592)
( 32,591)( 33,590)( 34,589)( 35,588)( 36,587)( 37,586)( 38,585)( 39,584)
( 40,583)( 41,582)( 42,581)( 43,580)( 44,579)( 45,578)( 46,577)( 47,622)
( 48,644)( 49,643)( 50,642)( 51,641)( 52,640)( 53,639)( 54,638)( 55,637)
( 56,636)( 57,635)( 58,634)( 59,633)( 60,632)( 61,631)( 62,630)( 63,629)
( 64,628)( 65,627)( 66,626)( 67,625)( 68,624)( 69,623)( 70,599)( 71,621)
( 72,620)( 73,619)( 74,618)( 75,617)( 76,616)( 77,615)( 78,614)( 79,613)
( 80,612)( 81,611)( 82,610)( 83,609)( 84,608)( 85,607)( 86,606)( 87,605)
( 88,604)( 89,603)( 90,602)( 91,601)( 92,600)( 93,691)( 94,713)( 95,712)
( 96,711)( 97,710)( 98,709)( 99,708)(100,707)(101,706)(102,705)(103,704)
(104,703)(105,702)(106,701)(107,700)(108,699)(109,698)(110,697)(111,696)
(112,695)(113,694)(114,693)(115,692)(116,714)(117,736)(118,735)(119,734)
(120,733)(121,732)(122,731)(123,730)(124,729)(125,728)(126,727)(127,726)
(128,725)(129,724)(130,723)(131,722)(132,721)(133,720)(134,719)(135,718)
(136,717)(137,716)(138,715)(139,645)(140,667)(141,666)(142,665)(143,664)
(144,663)(145,662)(146,661)(147,660)(148,659)(149,658)(150,657)(151,656)
(152,655)(153,654)(154,653)(155,652)(156,651)(157,650)(158,649)(159,648)
(160,647)(161,646)(162,668)(163,690)(164,689)(165,688)(166,687)(167,686)
(168,685)(169,684)(170,683)(171,682)(172,681)(173,680)(174,679)(175,678)
(176,677)(177,676)(178,675)(179,674)(180,673)(181,672)(182,671)(183,670)
(184,669)(185,369)(186,391)(187,390)(188,389)(189,388)(190,387)(191,386)
(192,385)(193,384)(194,383)(195,382)(196,381)(197,380)(198,379)(199,378)
(200,377)(201,376)(202,375)(203,374)(204,373)(205,372)(206,371)(207,370)
(208,392)(209,414)(210,413)(211,412)(212,411)(213,410)(214,409)(215,408)
(216,407)(217,406)(218,405)(219,404)(220,403)(221,402)(222,401)(223,400)
(224,399)(225,398)(226,397)(227,396)(228,395)(229,394)(230,393)(231,438)
(232,460)(233,459)(234,458)(235,457)(236,456)(237,455)(238,454)(239,453)
(240,452)(241,451)(242,450)(243,449)(244,448)(245,447)(246,446)(247,445)
(248,444)(249,443)(250,442)(251,441)(252,440)(253,439)(254,415)(255,437)
(256,436)(257,435)(258,434)(259,433)(260,432)(261,431)(262,430)(263,429)
(264,428)(265,427)(266,426)(267,425)(268,424)(269,423)(270,422)(271,421)
(272,420)(273,419)(274,418)(275,417)(276,416)(277,507)(278,529)(279,528)
(280,527)(281,526)(282,525)(283,524)(284,523)(285,522)(286,521)(287,520)
(288,519)(289,518)(290,517)(291,516)(292,515)(293,514)(294,513)(295,512)
(296,511)(297,510)(298,509)(299,508)(300,530)(301,552)(302,551)(303,550)
(304,549)(305,548)(306,547)(307,546)(308,545)(309,544)(310,543)(311,542)
(312,541)(313,540)(314,539)(315,538)(316,537)(317,536)(318,535)(319,534)
(320,533)(321,532)(322,531)(323,461)(324,483)(325,482)(326,481)(327,480)
(328,479)(329,478)(330,477)(331,476)(332,475)(333,474)(334,473)(335,472)
(336,471)(337,470)(338,469)(339,468)(340,467)(341,466)(342,465)(343,464)
(344,463)(345,462)(346,484)(347,506)(348,505)(349,504)(350,503)(351,502)
(352,501)(353,500)(354,499)(355,498)(356,497)(357,496)(358,495)(359,494)
(360,493)(361,492)(362,491)(363,490)(364,489)(365,488)(366,487)(367,486)
(368,485);
s2 := 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)( 47,232)
( 48,231)( 49,253)( 50,252)( 51,251)( 52,250)( 53,249)( 54,248)( 55,247)
( 56,246)( 57,245)( 58,244)( 59,243)( 60,242)( 61,241)( 62,240)( 63,239)
( 64,238)( 65,237)( 66,236)( 67,235)( 68,234)( 69,233)( 70,255)( 71,254)
( 72,276)( 73,275)( 74,274)( 75,273)( 76,272)( 77,271)( 78,270)( 79,269)
( 80,268)( 81,267)( 82,266)( 83,265)( 84,264)( 85,263)( 86,262)( 87,261)
( 88,260)( 89,259)( 90,258)( 91,257)( 92,256)( 93,278)( 94,277)( 95,299)
( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,291)
(104,290)(105,289)(106,288)(107,287)(108,286)(109,285)(110,284)(111,283)
(112,282)(113,281)(114,280)(115,279)(116,301)(117,300)(118,322)(119,321)
(120,320)(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)
(128,312)(129,311)(130,310)(131,309)(132,308)(133,307)(134,306)(135,305)
(136,304)(137,303)(138,302)(139,324)(140,323)(141,345)(142,344)(143,343)
(144,342)(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,335)
(152,334)(153,333)(154,332)(155,331)(156,330)(157,329)(158,328)(159,327)
(160,326)(161,325)(162,347)(163,346)(164,368)(165,367)(166,366)(167,365)
(168,364)(169,363)(170,362)(171,361)(172,360)(173,359)(174,358)(175,357)
(176,356)(177,355)(178,354)(179,353)(180,352)(181,351)(182,350)(183,349)
(184,348)(369,554)(370,553)(371,575)(372,574)(373,573)(374,572)(375,571)
(376,570)(377,569)(378,568)(379,567)(380,566)(381,565)(382,564)(383,563)
(384,562)(385,561)(386,560)(387,559)(388,558)(389,557)(390,556)(391,555)
(392,577)(393,576)(394,598)(395,597)(396,596)(397,595)(398,594)(399,593)
(400,592)(401,591)(402,590)(403,589)(404,588)(405,587)(406,586)(407,585)
(408,584)(409,583)(410,582)(411,581)(412,580)(413,579)(414,578)(415,600)
(416,599)(417,621)(418,620)(419,619)(420,618)(421,617)(422,616)(423,615)
(424,614)(425,613)(426,612)(427,611)(428,610)(429,609)(430,608)(431,607)
(432,606)(433,605)(434,604)(435,603)(436,602)(437,601)(438,623)(439,622)
(440,644)(441,643)(442,642)(443,641)(444,640)(445,639)(446,638)(447,637)
(448,636)(449,635)(450,634)(451,633)(452,632)(453,631)(454,630)(455,629)
(456,628)(457,627)(458,626)(459,625)(460,624)(461,646)(462,645)(463,667)
(464,666)(465,665)(466,664)(467,663)(468,662)(469,661)(470,660)(471,659)
(472,658)(473,657)(474,656)(475,655)(476,654)(477,653)(478,652)(479,651)
(480,650)(481,649)(482,648)(483,647)(484,669)(485,668)(486,690)(487,689)
(488,688)(489,687)(490,686)(491,685)(492,684)(493,683)(494,682)(495,681)
(496,680)(497,679)(498,678)(499,677)(500,676)(501,675)(502,674)(503,673)
(504,672)(505,671)(506,670)(507,692)(508,691)(509,713)(510,712)(511,711)
(512,710)(513,709)(514,708)(515,707)(516,706)(517,705)(518,704)(519,703)
(520,702)(521,701)(522,700)(523,699)(524,698)(525,697)(526,696)(527,695)
(528,694)(529,693)(530,715)(531,714)(532,736)(533,735)(534,734)(535,733)
(536,732)(537,731)(538,730)(539,729)(540,728)(541,727)(542,726)(543,725)
(544,724)(545,723)(546,722)(547,721)(548,720)(549,719)(550,718)(551,717)
(552,716);
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*s2*s1*s0*s1*s2*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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