Polytope of Type {16,44}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,44}*1408a
Also Known As : {16,44|2}. if this polytope has another name.
Group : SmallGroup(1408,6423)
Rank : 3
Schlafli Type : {16,44}
Number of vertices, edges, etc : 16, 352, 44
Order of s0s1s2 : 176
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 : {8,44}*704a, {16,22}*704
4-fold quotients : {4,44}*352, {8,22}*352
8-fold quotients : {2,44}*176, {4,22}*176
11-fold quotients : {16,4}*128a
16-fold quotients : {2,22}*88
22-fold quotients : {8,4}*64a, {16,2}*64
32-fold quotients : {2,11}*44
44-fold quotients : {4,4}*32, {8,2}*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 := ( 1,353)( 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)( 45,397)( 46,398)( 47,399)( 48,400)
( 49,401)( 50,402)( 51,403)( 52,404)( 53,405)( 54,406)( 55,407)( 56,408)
( 57,409)( 58,410)( 59,411)( 60,412)( 61,413)( 62,414)( 63,415)( 64,416)
( 65,417)( 66,418)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)( 72,435)
( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)( 80,421)
( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)( 88,429)
( 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)(133,507)(134,508)(135,509)(136,510)
(137,511)(138,512)(139,513)(140,514)(141,515)(142,516)(143,517)(144,518)
(145,519)(146,520)(147,521)(148,522)(149,523)(150,524)(151,525)(152,526)
(153,527)(154,528)(155,485)(156,486)(157,487)(158,488)(159,489)(160,490)
(161,491)(162,492)(163,493)(164,494)(165,495)(166,496)(167,497)(168,498)
(169,499)(170,500)(171,501)(172,502)(173,503)(174,504)(175,505)(176,506)
(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)(221,573)(222,574)(223,575)(224,576)
(225,577)(226,578)(227,579)(228,580)(229,581)(230,582)(231,583)(232,584)
(233,585)(234,586)(235,587)(236,588)(237,589)(238,590)(239,591)(240,592)
(241,593)(242,594)(243,606)(244,607)(245,608)(246,609)(247,610)(248,611)
(249,612)(250,613)(251,614)(252,615)(253,616)(254,595)(255,596)(256,597)
(257,598)(258,599)(259,600)(260,601)(261,602)(262,603)(263,604)(264,605)
(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)(309,683)(310,684)(311,685)(312,686)
(313,687)(314,688)(315,689)(316,690)(317,691)(318,692)(319,693)(320,694)
(321,695)(322,696)(323,697)(324,698)(325,699)(326,700)(327,701)(328,702)
(329,703)(330,704)(331,661)(332,662)(333,663)(334,664)(335,665)(336,666)
(337,667)(338,668)(339,669)(340,670)(341,671)(342,672)(343,673)(344,674)
(345,675)(346,676)(347,677)(348,678)(349,679)(350,680)(351,681)(352,682);;
s1 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)
( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 67, 78)
( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)
( 76, 80)( 77, 79)( 89,111)( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)
( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,122)(101,132)(102,131)
(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)
(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)(140,159)
(141,158)(142,157)(143,156)(144,166)(145,176)(146,175)(147,174)(148,173)
(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(177,221)(178,231)
(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)
(187,222)(188,232)(189,242)(190,241)(191,240)(192,239)(193,238)(194,237)
(195,236)(196,235)(197,234)(198,233)(199,254)(200,264)(201,263)(202,262)
(203,261)(204,260)(205,259)(206,258)(207,257)(208,256)(209,255)(210,243)
(211,253)(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)(218,246)
(219,245)(220,244)(265,331)(266,341)(267,340)(268,339)(269,338)(270,337)
(271,336)(272,335)(273,334)(274,333)(275,332)(276,342)(277,352)(278,351)
(279,350)(280,349)(281,348)(282,347)(283,346)(284,345)(285,344)(286,343)
(287,309)(288,319)(289,318)(290,317)(291,316)(292,315)(293,314)(294,313)
(295,312)(296,311)(297,310)(298,320)(299,330)(300,329)(301,328)(302,327)
(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)(353,441)(354,451)
(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)
(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)
(371,456)(372,455)(373,454)(374,453)(375,474)(376,484)(377,483)(378,482)
(379,481)(380,480)(381,479)(382,478)(383,477)(384,476)(385,475)(386,463)
(387,473)(388,472)(389,471)(390,470)(391,469)(392,468)(393,467)(394,466)
(395,465)(396,464)(397,485)(398,495)(399,494)(400,493)(401,492)(402,491)
(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)(410,505)
(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)
(419,518)(420,528)(421,527)(422,526)(423,525)(424,524)(425,523)(426,522)
(427,521)(428,520)(429,519)(430,507)(431,517)(432,516)(433,515)(434,514)
(435,513)(436,512)(437,511)(438,510)(439,509)(440,508)(529,661)(530,671)
(531,670)(532,669)(533,668)(534,667)(535,666)(536,665)(537,664)(538,663)
(539,662)(540,672)(541,682)(542,681)(543,680)(544,679)(545,678)(546,677)
(547,676)(548,675)(549,674)(550,673)(551,694)(552,704)(553,703)(554,702)
(555,701)(556,700)(557,699)(558,698)(559,697)(560,696)(561,695)(562,683)
(563,693)(564,692)(565,691)(566,690)(567,689)(568,688)(569,687)(570,686)
(571,685)(572,684)(573,617)(574,627)(575,626)(576,625)(577,624)(578,623)
(579,622)(580,621)(581,620)(582,619)(583,618)(584,628)(585,638)(586,637)
(587,636)(588,635)(589,634)(590,633)(591,632)(592,631)(593,630)(594,629)
(595,650)(596,660)(597,659)(598,658)(599,657)(600,656)(601,655)(602,654)
(603,653)(604,652)(605,651)(606,639)(607,649)(608,648)(609,647)(610,646)
(611,645)(612,644)(613,643)(614,642)(615,641)(616,640);;
s2 := ( 1,178)( 2,177)( 3,187)( 4,186)( 5,185)( 6,184)( 7,183)( 8,182)
( 9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)( 16,196)
( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,200)( 24,199)
( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,204)( 31,203)( 32,202)
( 33,201)( 34,211)( 35,210)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)
( 41,215)( 42,214)( 43,213)( 44,212)( 45,222)( 46,221)( 47,231)( 48,230)
( 49,229)( 50,228)( 51,227)( 52,226)( 53,225)( 54,224)( 55,223)( 56,233)
( 57,232)( 58,242)( 59,241)( 60,240)( 61,239)( 62,238)( 63,237)( 64,236)
( 65,235)( 66,234)( 67,244)( 68,243)( 69,253)( 70,252)( 71,251)( 72,250)
( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,255)( 79,254)( 80,264)
( 81,263)( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)( 88,256)
( 89,266)( 90,265)( 91,275)( 92,274)( 93,273)( 94,272)( 95,271)( 96,270)
( 97,269)( 98,268)( 99,267)(100,277)(101,276)(102,286)(103,285)(104,284)
(105,283)(106,282)(107,281)(108,280)(109,279)(110,278)(111,288)(112,287)
(113,297)(114,296)(115,295)(116,294)(117,293)(118,292)(119,291)(120,290)
(121,289)(122,299)(123,298)(124,308)(125,307)(126,306)(127,305)(128,304)
(129,303)(130,302)(131,301)(132,300)(133,310)(134,309)(135,319)(136,318)
(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)(144,321)
(145,320)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)(152,324)
(153,323)(154,322)(155,332)(156,331)(157,341)(158,340)(159,339)(160,338)
(161,337)(162,336)(163,335)(164,334)(165,333)(166,343)(167,342)(168,352)
(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,344)
(353,530)(354,529)(355,539)(356,538)(357,537)(358,536)(359,535)(360,534)
(361,533)(362,532)(363,531)(364,541)(365,540)(366,550)(367,549)(368,548)
(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)(375,552)(376,551)
(377,561)(378,560)(379,559)(380,558)(381,557)(382,556)(383,555)(384,554)
(385,553)(386,563)(387,562)(388,572)(389,571)(390,570)(391,569)(392,568)
(393,567)(394,566)(395,565)(396,564)(397,574)(398,573)(399,583)(400,582)
(401,581)(402,580)(403,579)(404,578)(405,577)(406,576)(407,575)(408,585)
(409,584)(410,594)(411,593)(412,592)(413,591)(414,590)(415,589)(416,588)
(417,587)(418,586)(419,596)(420,595)(421,605)(422,604)(423,603)(424,602)
(425,601)(426,600)(427,599)(428,598)(429,597)(430,607)(431,606)(432,616)
(433,615)(434,614)(435,613)(436,612)(437,611)(438,610)(439,609)(440,608)
(441,618)(442,617)(443,627)(444,626)(445,625)(446,624)(447,623)(448,622)
(449,621)(450,620)(451,619)(452,629)(453,628)(454,638)(455,637)(456,636)
(457,635)(458,634)(459,633)(460,632)(461,631)(462,630)(463,640)(464,639)
(465,649)(466,648)(467,647)(468,646)(469,645)(470,644)(471,643)(472,642)
(473,641)(474,651)(475,650)(476,660)(477,659)(478,658)(479,657)(480,656)
(481,655)(482,654)(483,653)(484,652)(485,662)(486,661)(487,671)(488,670)
(489,669)(490,668)(491,667)(492,666)(493,665)(494,664)(495,663)(496,673)
(497,672)(498,682)(499,681)(500,680)(501,679)(502,678)(503,677)(504,676)
(505,675)(506,674)(507,684)(508,683)(509,693)(510,692)(511,691)(512,690)
(513,689)(514,688)(515,687)(516,686)(517,685)(518,695)(519,694)(520,704)
(521,703)(522,702)(523,701)(524,700)(525,699)(526,698)(527,697)(528,696);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 45,397)( 46,398)( 47,399)
( 48,400)( 49,401)( 50,402)( 51,403)( 52,404)( 53,405)( 54,406)( 55,407)
( 56,408)( 57,409)( 58,410)( 59,411)( 60,412)( 61,413)( 62,414)( 63,415)
( 64,416)( 65,417)( 66,418)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)
( 72,435)( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)
( 80,421)( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)
( 88,429)( 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)(133,507)(134,508)(135,509)
(136,510)(137,511)(138,512)(139,513)(140,514)(141,515)(142,516)(143,517)
(144,518)(145,519)(146,520)(147,521)(148,522)(149,523)(150,524)(151,525)
(152,526)(153,527)(154,528)(155,485)(156,486)(157,487)(158,488)(159,489)
(160,490)(161,491)(162,492)(163,493)(164,494)(165,495)(166,496)(167,497)
(168,498)(169,499)(170,500)(171,501)(172,502)(173,503)(174,504)(175,505)
(176,506)(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)(221,573)(222,574)(223,575)
(224,576)(225,577)(226,578)(227,579)(228,580)(229,581)(230,582)(231,583)
(232,584)(233,585)(234,586)(235,587)(236,588)(237,589)(238,590)(239,591)
(240,592)(241,593)(242,594)(243,606)(244,607)(245,608)(246,609)(247,610)
(248,611)(249,612)(250,613)(251,614)(252,615)(253,616)(254,595)(255,596)
(256,597)(257,598)(258,599)(259,600)(260,601)(261,602)(262,603)(263,604)
(264,605)(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)(309,683)(310,684)(311,685)
(312,686)(313,687)(314,688)(315,689)(316,690)(317,691)(318,692)(319,693)
(320,694)(321,695)(322,696)(323,697)(324,698)(325,699)(326,700)(327,701)
(328,702)(329,703)(330,704)(331,661)(332,662)(333,663)(334,664)(335,665)
(336,666)(337,667)(338,668)(339,669)(340,670)(341,671)(342,672)(343,673)
(344,674)(345,675)(346,676)(347,677)(348,678)(349,679)(350,680)(351,681)
(352,682);
s1 := Sym(704)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)
( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 46, 55)( 47, 54)
( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)
( 67, 78)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)
( 75, 81)( 76, 80)( 77, 79)( 89,111)( 90,121)( 91,120)( 92,119)( 93,118)
( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,122)(101,132)
(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)
(110,123)(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)
(140,159)(141,158)(142,157)(143,156)(144,166)(145,176)(146,175)(147,174)
(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(177,221)
(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)
(186,223)(187,222)(188,232)(189,242)(190,241)(191,240)(192,239)(193,238)
(194,237)(195,236)(196,235)(197,234)(198,233)(199,254)(200,264)(201,263)
(202,262)(203,261)(204,260)(205,259)(206,258)(207,257)(208,256)(209,255)
(210,243)(211,253)(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)
(218,246)(219,245)(220,244)(265,331)(266,341)(267,340)(268,339)(269,338)
(270,337)(271,336)(272,335)(273,334)(274,333)(275,332)(276,342)(277,352)
(278,351)(279,350)(280,349)(281,348)(282,347)(283,346)(284,345)(285,344)
(286,343)(287,309)(288,319)(289,318)(290,317)(291,316)(292,315)(293,314)
(294,313)(295,312)(296,311)(297,310)(298,320)(299,330)(300,329)(301,328)
(302,327)(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)(353,441)
(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)
(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)
(370,457)(371,456)(372,455)(373,454)(374,453)(375,474)(376,484)(377,483)
(378,482)(379,481)(380,480)(381,479)(382,478)(383,477)(384,476)(385,475)
(386,463)(387,473)(388,472)(389,471)(390,470)(391,469)(392,468)(393,467)
(394,466)(395,465)(396,464)(397,485)(398,495)(399,494)(400,493)(401,492)
(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)
(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)
(418,497)(419,518)(420,528)(421,527)(422,526)(423,525)(424,524)(425,523)
(426,522)(427,521)(428,520)(429,519)(430,507)(431,517)(432,516)(433,515)
(434,514)(435,513)(436,512)(437,511)(438,510)(439,509)(440,508)(529,661)
(530,671)(531,670)(532,669)(533,668)(534,667)(535,666)(536,665)(537,664)
(538,663)(539,662)(540,672)(541,682)(542,681)(543,680)(544,679)(545,678)
(546,677)(547,676)(548,675)(549,674)(550,673)(551,694)(552,704)(553,703)
(554,702)(555,701)(556,700)(557,699)(558,698)(559,697)(560,696)(561,695)
(562,683)(563,693)(564,692)(565,691)(566,690)(567,689)(568,688)(569,687)
(570,686)(571,685)(572,684)(573,617)(574,627)(575,626)(576,625)(577,624)
(578,623)(579,622)(580,621)(581,620)(582,619)(583,618)(584,628)(585,638)
(586,637)(587,636)(588,635)(589,634)(590,633)(591,632)(592,631)(593,630)
(594,629)(595,650)(596,660)(597,659)(598,658)(599,657)(600,656)(601,655)
(602,654)(603,653)(604,652)(605,651)(606,639)(607,649)(608,648)(609,647)
(610,646)(611,645)(612,644)(613,643)(614,642)(615,641)(616,640);
s2 := Sym(704)!( 1,178)( 2,177)( 3,187)( 4,186)( 5,185)( 6,184)( 7,183)
( 8,182)( 9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)
( 16,196)( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,200)
( 24,199)( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,204)( 31,203)
( 32,202)( 33,201)( 34,211)( 35,210)( 36,220)( 37,219)( 38,218)( 39,217)
( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,222)( 46,221)( 47,231)
( 48,230)( 49,229)( 50,228)( 51,227)( 52,226)( 53,225)( 54,224)( 55,223)
( 56,233)( 57,232)( 58,242)( 59,241)( 60,240)( 61,239)( 62,238)( 63,237)
( 64,236)( 65,235)( 66,234)( 67,244)( 68,243)( 69,253)( 70,252)( 71,251)
( 72,250)( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,255)( 79,254)
( 80,264)( 81,263)( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)
( 88,256)( 89,266)( 90,265)( 91,275)( 92,274)( 93,273)( 94,272)( 95,271)
( 96,270)( 97,269)( 98,268)( 99,267)(100,277)(101,276)(102,286)(103,285)
(104,284)(105,283)(106,282)(107,281)(108,280)(109,279)(110,278)(111,288)
(112,287)(113,297)(114,296)(115,295)(116,294)(117,293)(118,292)(119,291)
(120,290)(121,289)(122,299)(123,298)(124,308)(125,307)(126,306)(127,305)
(128,304)(129,303)(130,302)(131,301)(132,300)(133,310)(134,309)(135,319)
(136,318)(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)
(144,321)(145,320)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)
(152,324)(153,323)(154,322)(155,332)(156,331)(157,341)(158,340)(159,339)
(160,338)(161,337)(162,336)(163,335)(164,334)(165,333)(166,343)(167,342)
(168,352)(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)
(176,344)(353,530)(354,529)(355,539)(356,538)(357,537)(358,536)(359,535)
(360,534)(361,533)(362,532)(363,531)(364,541)(365,540)(366,550)(367,549)
(368,548)(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)(375,552)
(376,551)(377,561)(378,560)(379,559)(380,558)(381,557)(382,556)(383,555)
(384,554)(385,553)(386,563)(387,562)(388,572)(389,571)(390,570)(391,569)
(392,568)(393,567)(394,566)(395,565)(396,564)(397,574)(398,573)(399,583)
(400,582)(401,581)(402,580)(403,579)(404,578)(405,577)(406,576)(407,575)
(408,585)(409,584)(410,594)(411,593)(412,592)(413,591)(414,590)(415,589)
(416,588)(417,587)(418,586)(419,596)(420,595)(421,605)(422,604)(423,603)
(424,602)(425,601)(426,600)(427,599)(428,598)(429,597)(430,607)(431,606)
(432,616)(433,615)(434,614)(435,613)(436,612)(437,611)(438,610)(439,609)
(440,608)(441,618)(442,617)(443,627)(444,626)(445,625)(446,624)(447,623)
(448,622)(449,621)(450,620)(451,619)(452,629)(453,628)(454,638)(455,637)
(456,636)(457,635)(458,634)(459,633)(460,632)(461,631)(462,630)(463,640)
(464,639)(465,649)(466,648)(467,647)(468,646)(469,645)(470,644)(471,643)
(472,642)(473,641)(474,651)(475,650)(476,660)(477,659)(478,658)(479,657)
(480,656)(481,655)(482,654)(483,653)(484,652)(485,662)(486,661)(487,671)
(488,670)(489,669)(490,668)(491,667)(492,666)(493,665)(494,664)(495,663)
(496,673)(497,672)(498,682)(499,681)(500,680)(501,679)(502,678)(503,677)
(504,676)(505,675)(506,674)(507,684)(508,683)(509,693)(510,692)(511,691)
(512,690)(513,689)(514,688)(515,687)(516,686)(517,685)(518,695)(519,694)
(520,704)(521,703)(522,702)(523,701)(524,700)(525,699)(526,698)(527,697)
(528,696);
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, 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 >;
References : None.
to this polytope