Polytope of Type {44,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,16}*1408b
if this polytope has a name.
Group : SmallGroup(1408,6457)
Rank : 3
Schlafli Type : {44,16}
Number of vertices, edges, etc : 44, 352, 16
Order of s0s1s2 : 176
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 : {44,8}*704a
4-fold quotients : {44,4}*352, {22,8}*352
8-fold quotients : {44,2}*176, {22,4}*176
11-fold quotients : {4,16}*128b
16-fold quotients : {22,2}*88
22-fold quotients : {4,8}*64a
32-fold quotients : {11,2}*44
44-fold quotients : {4,4}*32, {2,8}*32
88-fold quotients : {2,4}*16, {4,2}*16
176-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,177)( 2,187)( 3,186)( 4,185)( 5,184)( 6,183)( 7,182)( 8,181)
( 9,180)( 10,179)( 11,178)( 12,188)( 13,198)( 14,197)( 15,196)( 16,195)
( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,199)( 24,209)
( 25,208)( 26,207)( 27,206)( 28,205)( 29,204)( 30,203)( 31,202)( 32,201)
( 33,200)( 34,210)( 35,220)( 36,219)( 37,218)( 38,217)( 39,216)( 40,215)
( 41,214)( 42,213)( 43,212)( 44,211)( 45,221)( 46,231)( 47,230)( 48,229)
( 49,228)( 50,227)( 51,226)( 52,225)( 53,224)( 54,223)( 55,222)( 56,232)
( 57,242)( 58,241)( 59,240)( 60,239)( 61,238)( 62,237)( 63,236)( 64,235)
( 65,234)( 66,233)( 67,243)( 68,253)( 69,252)( 70,251)( 71,250)( 72,249)
( 73,248)( 74,247)( 75,246)( 76,245)( 77,244)( 78,254)( 79,264)( 80,263)
( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,257)( 87,256)( 88,255)
( 89,276)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)( 96,280)
( 97,279)( 98,278)( 99,277)(100,265)(101,275)(102,274)(103,273)(104,272)
(105,271)(106,270)(107,269)(108,268)(109,267)(110,266)(111,298)(112,308)
(113,307)(114,306)(115,305)(116,304)(117,303)(118,302)(119,301)(120,300)
(121,299)(122,287)(123,297)(124,296)(125,295)(126,294)(127,293)(128,292)
(129,291)(130,290)(131,289)(132,288)(133,320)(134,330)(135,329)(136,328)
(137,327)(138,326)(139,325)(140,324)(141,323)(142,322)(143,321)(144,309)
(145,319)(146,318)(147,317)(148,316)(149,315)(150,314)(151,313)(152,312)
(153,311)(154,310)(155,342)(156,352)(157,351)(158,350)(159,349)(160,348)
(161,347)(162,346)(163,345)(164,344)(165,343)(166,331)(167,341)(168,340)
(169,339)(170,338)(171,337)(172,336)(173,335)(174,334)(175,333)(176,332)
(353,529)(354,539)(355,538)(356,537)(357,536)(358,535)(359,534)(360,533)
(361,532)(362,531)(363,530)(364,540)(365,550)(366,549)(367,548)(368,547)
(369,546)(370,545)(371,544)(372,543)(373,542)(374,541)(375,551)(376,561)
(377,560)(378,559)(379,558)(380,557)(381,556)(382,555)(383,554)(384,553)
(385,552)(386,562)(387,572)(388,571)(389,570)(390,569)(391,568)(392,567)
(393,566)(394,565)(395,564)(396,563)(397,573)(398,583)(399,582)(400,581)
(401,580)(402,579)(403,578)(404,577)(405,576)(406,575)(407,574)(408,584)
(409,594)(410,593)(411,592)(412,591)(413,590)(414,589)(415,588)(416,587)
(417,586)(418,585)(419,595)(420,605)(421,604)(422,603)(423,602)(424,601)
(425,600)(426,599)(427,598)(428,597)(429,596)(430,606)(431,616)(432,615)
(433,614)(434,613)(435,612)(436,611)(437,610)(438,609)(439,608)(440,607)
(441,628)(442,638)(443,637)(444,636)(445,635)(446,634)(447,633)(448,632)
(449,631)(450,630)(451,629)(452,617)(453,627)(454,626)(455,625)(456,624)
(457,623)(458,622)(459,621)(460,620)(461,619)(462,618)(463,650)(464,660)
(465,659)(466,658)(467,657)(468,656)(469,655)(470,654)(471,653)(472,652)
(473,651)(474,639)(475,649)(476,648)(477,647)(478,646)(479,645)(480,644)
(481,643)(482,642)(483,641)(484,640)(485,672)(486,682)(487,681)(488,680)
(489,679)(490,678)(491,677)(492,676)(493,675)(494,674)(495,673)(496,661)
(497,671)(498,670)(499,669)(500,668)(501,667)(502,666)(503,665)(504,664)
(505,663)(506,662)(507,694)(508,704)(509,703)(510,702)(511,701)(512,700)
(513,699)(514,698)(515,697)(516,696)(517,695)(518,683)(519,693)(520,692)
(521,691)(522,690)(523,689)(524,688)(525,687)(526,686)(527,685)(528,684);;
s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)
( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 46)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 79)
( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)
( 76, 81)( 77, 80)( 89,112)( 90,111)( 91,121)( 92,120)( 93,119)( 94,118)
( 95,117)( 96,116)( 97,115)( 98,114)( 99,113)(100,123)(101,122)(102,132)
(103,131)(104,130)(105,129)(106,128)(107,127)(108,126)(109,125)(110,124)
(133,156)(134,155)(135,165)(136,164)(137,163)(138,162)(139,161)(140,160)
(141,159)(142,158)(143,157)(144,167)(145,166)(146,176)(147,175)(148,174)
(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(177,222)(178,221)
(179,231)(180,230)(181,229)(182,228)(183,227)(184,226)(185,225)(186,224)
(187,223)(188,233)(189,232)(190,242)(191,241)(192,240)(193,239)(194,238)
(195,237)(196,236)(197,235)(198,234)(199,255)(200,254)(201,264)(202,263)
(203,262)(204,261)(205,260)(206,259)(207,258)(208,257)(209,256)(210,244)
(211,243)(212,253)(213,252)(214,251)(215,250)(216,249)(217,248)(218,247)
(219,246)(220,245)(265,332)(266,331)(267,341)(268,340)(269,339)(270,338)
(271,337)(272,336)(273,335)(274,334)(275,333)(276,343)(277,342)(278,352)
(279,351)(280,350)(281,349)(282,348)(283,347)(284,346)(285,345)(286,344)
(287,310)(288,309)(289,319)(290,318)(291,317)(292,316)(293,315)(294,314)
(295,313)(296,312)(297,311)(298,321)(299,320)(300,330)(301,329)(302,328)
(303,327)(304,326)(305,325)(306,324)(307,323)(308,322)(353,442)(354,441)
(355,451)(356,450)(357,449)(358,448)(359,447)(360,446)(361,445)(362,444)
(363,443)(364,453)(365,452)(366,462)(367,461)(368,460)(369,459)(370,458)
(371,457)(372,456)(373,455)(374,454)(375,475)(376,474)(377,484)(378,483)
(379,482)(380,481)(381,480)(382,479)(383,478)(384,477)(385,476)(386,464)
(387,463)(388,473)(389,472)(390,471)(391,470)(392,469)(393,468)(394,467)
(395,466)(396,465)(397,486)(398,485)(399,495)(400,494)(401,493)(402,492)
(403,491)(404,490)(405,489)(406,488)(407,487)(408,497)(409,496)(410,506)
(411,505)(412,504)(413,503)(414,502)(415,501)(416,500)(417,499)(418,498)
(419,519)(420,518)(421,528)(422,527)(423,526)(424,525)(425,524)(426,523)
(427,522)(428,521)(429,520)(430,508)(431,507)(432,517)(433,516)(434,515)
(435,514)(436,513)(437,512)(438,511)(439,510)(440,509)(529,673)(530,672)
(531,682)(532,681)(533,680)(534,679)(535,678)(536,677)(537,676)(538,675)
(539,674)(540,662)(541,661)(542,671)(543,670)(544,669)(545,668)(546,667)
(547,666)(548,665)(549,664)(550,663)(551,684)(552,683)(553,693)(554,692)
(555,691)(556,690)(557,689)(558,688)(559,687)(560,686)(561,685)(562,695)
(563,694)(564,704)(565,703)(566,702)(567,701)(568,700)(569,699)(570,698)
(571,697)(572,696)(573,629)(574,628)(575,638)(576,637)(577,636)(578,635)
(579,634)(580,633)(581,632)(582,631)(583,630)(584,618)(585,617)(586,627)
(587,626)(588,625)(589,624)(590,623)(591,622)(592,621)(593,620)(594,619)
(595,640)(596,639)(597,649)(598,648)(599,647)(600,646)(601,645)(602,644)
(603,643)(604,642)(605,641)(606,651)(607,650)(608,660)(609,659)(610,658)
(611,657)(612,656)(613,655)(614,654)(615,653)(616,652);;
s2 := ( 1,353)( 2,354)( 3,355)( 4,356)( 5,357)( 6,358)( 7,359)( 8,360)
( 9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)( 16,368)
( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,386)( 24,387)
( 25,388)( 26,389)( 27,390)( 28,391)( 29,392)( 30,393)( 31,394)( 32,395)
( 33,396)( 34,375)( 35,376)( 36,377)( 37,378)( 38,379)( 39,380)( 40,381)
( 41,382)( 42,383)( 43,384)( 44,385)( 45,408)( 46,409)( 47,410)( 48,411)
( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)( 56,397)
( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)( 64,405)
( 65,406)( 66,407)( 67,419)( 68,420)( 69,421)( 70,422)( 71,423)( 72,424)
( 73,425)( 74,426)( 75,427)( 76,428)( 77,429)( 78,430)( 79,431)( 80,432)
( 81,433)( 82,434)( 83,435)( 84,436)( 85,437)( 86,438)( 87,439)( 88,440)
( 89,463)( 90,464)( 91,465)( 92,466)( 93,467)( 94,468)( 95,469)( 96,470)
( 97,471)( 98,472)( 99,473)(100,474)(101,475)(102,476)(103,477)(104,478)
(105,479)(106,480)(107,481)(108,482)(109,483)(110,484)(111,441)(112,442)
(113,443)(114,444)(115,445)(116,446)(117,447)(118,448)(119,449)(120,450)
(121,451)(122,452)(123,453)(124,454)(125,455)(126,456)(127,457)(128,458)
(129,459)(130,460)(131,461)(132,462)(133,518)(134,519)(135,520)(136,521)
(137,522)(138,523)(139,524)(140,525)(141,526)(142,527)(143,528)(144,507)
(145,508)(146,509)(147,510)(148,511)(149,512)(150,513)(151,514)(152,515)
(153,516)(154,517)(155,496)(156,497)(157,498)(158,499)(159,500)(160,501)
(161,502)(162,503)(163,504)(164,505)(165,506)(166,485)(167,486)(168,487)
(169,488)(170,489)(171,490)(172,491)(173,492)(174,493)(175,494)(176,495)
(177,529)(178,530)(179,531)(180,532)(181,533)(182,534)(183,535)(184,536)
(185,537)(186,538)(187,539)(188,540)(189,541)(190,542)(191,543)(192,544)
(193,545)(194,546)(195,547)(196,548)(197,549)(198,550)(199,562)(200,563)
(201,564)(202,565)(203,566)(204,567)(205,568)(206,569)(207,570)(208,571)
(209,572)(210,551)(211,552)(212,553)(213,554)(214,555)(215,556)(216,557)
(217,558)(218,559)(219,560)(220,561)(221,584)(222,585)(223,586)(224,587)
(225,588)(226,589)(227,590)(228,591)(229,592)(230,593)(231,594)(232,573)
(233,574)(234,575)(235,576)(236,577)(237,578)(238,579)(239,580)(240,581)
(241,582)(242,583)(243,595)(244,596)(245,597)(246,598)(247,599)(248,600)
(249,601)(250,602)(251,603)(252,604)(253,605)(254,606)(255,607)(256,608)
(257,609)(258,610)(259,611)(260,612)(261,613)(262,614)(263,615)(264,616)
(265,639)(266,640)(267,641)(268,642)(269,643)(270,644)(271,645)(272,646)
(273,647)(274,648)(275,649)(276,650)(277,651)(278,652)(279,653)(280,654)
(281,655)(282,656)(283,657)(284,658)(285,659)(286,660)(287,617)(288,618)
(289,619)(290,620)(291,621)(292,622)(293,623)(294,624)(295,625)(296,626)
(297,627)(298,628)(299,629)(300,630)(301,631)(302,632)(303,633)(304,634)
(305,635)(306,636)(307,637)(308,638)(309,694)(310,695)(311,696)(312,697)
(313,698)(314,699)(315,700)(316,701)(317,702)(318,703)(319,704)(320,683)
(321,684)(322,685)(323,686)(324,687)(325,688)(326,689)(327,690)(328,691)
(329,692)(330,693)(331,672)(332,673)(333,674)(334,675)(335,676)(336,677)
(337,678)(338,679)(339,680)(340,681)(341,682)(342,661)(343,662)(344,663)
(345,664)(346,665)(347,666)(348,667)(349,668)(350,669)(351,670)(352,671);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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(704)!( 1,177)( 2,187)( 3,186)( 4,185)( 5,184)( 6,183)( 7,182)
( 8,181)( 9,180)( 10,179)( 11,178)( 12,188)( 13,198)( 14,197)( 15,196)
( 16,195)( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,199)
( 24,209)( 25,208)( 26,207)( 27,206)( 28,205)( 29,204)( 30,203)( 31,202)
( 32,201)( 33,200)( 34,210)( 35,220)( 36,219)( 37,218)( 38,217)( 39,216)
( 40,215)( 41,214)( 42,213)( 43,212)( 44,211)( 45,221)( 46,231)( 47,230)
( 48,229)( 49,228)( 50,227)( 51,226)( 52,225)( 53,224)( 54,223)( 55,222)
( 56,232)( 57,242)( 58,241)( 59,240)( 60,239)( 61,238)( 62,237)( 63,236)
( 64,235)( 65,234)( 66,233)( 67,243)( 68,253)( 69,252)( 70,251)( 71,250)
( 72,249)( 73,248)( 74,247)( 75,246)( 76,245)( 77,244)( 78,254)( 79,264)
( 80,263)( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,257)( 87,256)
( 88,255)( 89,276)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)
( 96,280)( 97,279)( 98,278)( 99,277)(100,265)(101,275)(102,274)(103,273)
(104,272)(105,271)(106,270)(107,269)(108,268)(109,267)(110,266)(111,298)
(112,308)(113,307)(114,306)(115,305)(116,304)(117,303)(118,302)(119,301)
(120,300)(121,299)(122,287)(123,297)(124,296)(125,295)(126,294)(127,293)
(128,292)(129,291)(130,290)(131,289)(132,288)(133,320)(134,330)(135,329)
(136,328)(137,327)(138,326)(139,325)(140,324)(141,323)(142,322)(143,321)
(144,309)(145,319)(146,318)(147,317)(148,316)(149,315)(150,314)(151,313)
(152,312)(153,311)(154,310)(155,342)(156,352)(157,351)(158,350)(159,349)
(160,348)(161,347)(162,346)(163,345)(164,344)(165,343)(166,331)(167,341)
(168,340)(169,339)(170,338)(171,337)(172,336)(173,335)(174,334)(175,333)
(176,332)(353,529)(354,539)(355,538)(356,537)(357,536)(358,535)(359,534)
(360,533)(361,532)(362,531)(363,530)(364,540)(365,550)(366,549)(367,548)
(368,547)(369,546)(370,545)(371,544)(372,543)(373,542)(374,541)(375,551)
(376,561)(377,560)(378,559)(379,558)(380,557)(381,556)(382,555)(383,554)
(384,553)(385,552)(386,562)(387,572)(388,571)(389,570)(390,569)(391,568)
(392,567)(393,566)(394,565)(395,564)(396,563)(397,573)(398,583)(399,582)
(400,581)(401,580)(402,579)(403,578)(404,577)(405,576)(406,575)(407,574)
(408,584)(409,594)(410,593)(411,592)(412,591)(413,590)(414,589)(415,588)
(416,587)(417,586)(418,585)(419,595)(420,605)(421,604)(422,603)(423,602)
(424,601)(425,600)(426,599)(427,598)(428,597)(429,596)(430,606)(431,616)
(432,615)(433,614)(434,613)(435,612)(436,611)(437,610)(438,609)(439,608)
(440,607)(441,628)(442,638)(443,637)(444,636)(445,635)(446,634)(447,633)
(448,632)(449,631)(450,630)(451,629)(452,617)(453,627)(454,626)(455,625)
(456,624)(457,623)(458,622)(459,621)(460,620)(461,619)(462,618)(463,650)
(464,660)(465,659)(466,658)(467,657)(468,656)(469,655)(470,654)(471,653)
(472,652)(473,651)(474,639)(475,649)(476,648)(477,647)(478,646)(479,645)
(480,644)(481,643)(482,642)(483,641)(484,640)(485,672)(486,682)(487,681)
(488,680)(489,679)(490,678)(491,677)(492,676)(493,675)(494,674)(495,673)
(496,661)(497,671)(498,670)(499,669)(500,668)(501,667)(502,666)(503,665)
(504,664)(505,663)(506,662)(507,694)(508,704)(509,703)(510,702)(511,701)
(512,700)(513,699)(514,698)(515,697)(516,696)(517,695)(518,683)(519,693)
(520,692)(521,691)(522,690)(523,689)(524,688)(525,687)(526,686)(527,685)
(528,684);
s1 := Sym(704)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)
( 15, 21)( 16, 20)( 17, 19)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)
( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 46)( 47, 55)
( 48, 54)( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)
( 67, 79)( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)
( 75, 82)( 76, 81)( 77, 80)( 89,112)( 90,111)( 91,121)( 92,120)( 93,119)
( 94,118)( 95,117)( 96,116)( 97,115)( 98,114)( 99,113)(100,123)(101,122)
(102,132)(103,131)(104,130)(105,129)(106,128)(107,127)(108,126)(109,125)
(110,124)(133,156)(134,155)(135,165)(136,164)(137,163)(138,162)(139,161)
(140,160)(141,159)(142,158)(143,157)(144,167)(145,166)(146,176)(147,175)
(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(177,222)
(178,221)(179,231)(180,230)(181,229)(182,228)(183,227)(184,226)(185,225)
(186,224)(187,223)(188,233)(189,232)(190,242)(191,241)(192,240)(193,239)
(194,238)(195,237)(196,236)(197,235)(198,234)(199,255)(200,254)(201,264)
(202,263)(203,262)(204,261)(205,260)(206,259)(207,258)(208,257)(209,256)
(210,244)(211,243)(212,253)(213,252)(214,251)(215,250)(216,249)(217,248)
(218,247)(219,246)(220,245)(265,332)(266,331)(267,341)(268,340)(269,339)
(270,338)(271,337)(272,336)(273,335)(274,334)(275,333)(276,343)(277,342)
(278,352)(279,351)(280,350)(281,349)(282,348)(283,347)(284,346)(285,345)
(286,344)(287,310)(288,309)(289,319)(290,318)(291,317)(292,316)(293,315)
(294,314)(295,313)(296,312)(297,311)(298,321)(299,320)(300,330)(301,329)
(302,328)(303,327)(304,326)(305,325)(306,324)(307,323)(308,322)(353,442)
(354,441)(355,451)(356,450)(357,449)(358,448)(359,447)(360,446)(361,445)
(362,444)(363,443)(364,453)(365,452)(366,462)(367,461)(368,460)(369,459)
(370,458)(371,457)(372,456)(373,455)(374,454)(375,475)(376,474)(377,484)
(378,483)(379,482)(380,481)(381,480)(382,479)(383,478)(384,477)(385,476)
(386,464)(387,463)(388,473)(389,472)(390,471)(391,470)(392,469)(393,468)
(394,467)(395,466)(396,465)(397,486)(398,485)(399,495)(400,494)(401,493)
(402,492)(403,491)(404,490)(405,489)(406,488)(407,487)(408,497)(409,496)
(410,506)(411,505)(412,504)(413,503)(414,502)(415,501)(416,500)(417,499)
(418,498)(419,519)(420,518)(421,528)(422,527)(423,526)(424,525)(425,524)
(426,523)(427,522)(428,521)(429,520)(430,508)(431,507)(432,517)(433,516)
(434,515)(435,514)(436,513)(437,512)(438,511)(439,510)(440,509)(529,673)
(530,672)(531,682)(532,681)(533,680)(534,679)(535,678)(536,677)(537,676)
(538,675)(539,674)(540,662)(541,661)(542,671)(543,670)(544,669)(545,668)
(546,667)(547,666)(548,665)(549,664)(550,663)(551,684)(552,683)(553,693)
(554,692)(555,691)(556,690)(557,689)(558,688)(559,687)(560,686)(561,685)
(562,695)(563,694)(564,704)(565,703)(566,702)(567,701)(568,700)(569,699)
(570,698)(571,697)(572,696)(573,629)(574,628)(575,638)(576,637)(577,636)
(578,635)(579,634)(580,633)(581,632)(582,631)(583,630)(584,618)(585,617)
(586,627)(587,626)(588,625)(589,624)(590,623)(591,622)(592,621)(593,620)
(594,619)(595,640)(596,639)(597,649)(598,648)(599,647)(600,646)(601,645)
(602,644)(603,643)(604,642)(605,641)(606,651)(607,650)(608,660)(609,659)
(610,658)(611,657)(612,656)(613,655)(614,654)(615,653)(616,652);
s2 := Sym(704)!( 1,353)( 2,354)( 3,355)( 4,356)( 5,357)( 6,358)( 7,359)
( 8,360)( 9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)
( 16,368)( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,386)
( 24,387)( 25,388)( 26,389)( 27,390)( 28,391)( 29,392)( 30,393)( 31,394)
( 32,395)( 33,396)( 34,375)( 35,376)( 36,377)( 37,378)( 38,379)( 39,380)
( 40,381)( 41,382)( 42,383)( 43,384)( 44,385)( 45,408)( 46,409)( 47,410)
( 48,411)( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)
( 56,397)( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)
( 64,405)( 65,406)( 66,407)( 67,419)( 68,420)( 69,421)( 70,422)( 71,423)
( 72,424)( 73,425)( 74,426)( 75,427)( 76,428)( 77,429)( 78,430)( 79,431)
( 80,432)( 81,433)( 82,434)( 83,435)( 84,436)( 85,437)( 86,438)( 87,439)
( 88,440)( 89,463)( 90,464)( 91,465)( 92,466)( 93,467)( 94,468)( 95,469)
( 96,470)( 97,471)( 98,472)( 99,473)(100,474)(101,475)(102,476)(103,477)
(104,478)(105,479)(106,480)(107,481)(108,482)(109,483)(110,484)(111,441)
(112,442)(113,443)(114,444)(115,445)(116,446)(117,447)(118,448)(119,449)
(120,450)(121,451)(122,452)(123,453)(124,454)(125,455)(126,456)(127,457)
(128,458)(129,459)(130,460)(131,461)(132,462)(133,518)(134,519)(135,520)
(136,521)(137,522)(138,523)(139,524)(140,525)(141,526)(142,527)(143,528)
(144,507)(145,508)(146,509)(147,510)(148,511)(149,512)(150,513)(151,514)
(152,515)(153,516)(154,517)(155,496)(156,497)(157,498)(158,499)(159,500)
(160,501)(161,502)(162,503)(163,504)(164,505)(165,506)(166,485)(167,486)
(168,487)(169,488)(170,489)(171,490)(172,491)(173,492)(174,493)(175,494)
(176,495)(177,529)(178,530)(179,531)(180,532)(181,533)(182,534)(183,535)
(184,536)(185,537)(186,538)(187,539)(188,540)(189,541)(190,542)(191,543)
(192,544)(193,545)(194,546)(195,547)(196,548)(197,549)(198,550)(199,562)
(200,563)(201,564)(202,565)(203,566)(204,567)(205,568)(206,569)(207,570)
(208,571)(209,572)(210,551)(211,552)(212,553)(213,554)(214,555)(215,556)
(216,557)(217,558)(218,559)(219,560)(220,561)(221,584)(222,585)(223,586)
(224,587)(225,588)(226,589)(227,590)(228,591)(229,592)(230,593)(231,594)
(232,573)(233,574)(234,575)(235,576)(236,577)(237,578)(238,579)(239,580)
(240,581)(241,582)(242,583)(243,595)(244,596)(245,597)(246,598)(247,599)
(248,600)(249,601)(250,602)(251,603)(252,604)(253,605)(254,606)(255,607)
(256,608)(257,609)(258,610)(259,611)(260,612)(261,613)(262,614)(263,615)
(264,616)(265,639)(266,640)(267,641)(268,642)(269,643)(270,644)(271,645)
(272,646)(273,647)(274,648)(275,649)(276,650)(277,651)(278,652)(279,653)
(280,654)(281,655)(282,656)(283,657)(284,658)(285,659)(286,660)(287,617)
(288,618)(289,619)(290,620)(291,621)(292,622)(293,623)(294,624)(295,625)
(296,626)(297,627)(298,628)(299,629)(300,630)(301,631)(302,632)(303,633)
(304,634)(305,635)(306,636)(307,637)(308,638)(309,694)(310,695)(311,696)
(312,697)(313,698)(314,699)(315,700)(316,701)(317,702)(318,703)(319,704)
(320,683)(321,684)(322,685)(323,686)(324,687)(325,688)(326,689)(327,690)
(328,691)(329,692)(330,693)(331,672)(332,673)(333,674)(334,675)(335,676)
(336,677)(337,678)(338,679)(339,680)(340,681)(341,682)(342,661)(343,662)
(344,663)(345,664)(346,665)(347,666)(348,667)(349,668)(350,669)(351,670)
(352,671);
poly := sub<Sym(704)|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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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