Polytope of Type {44,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,16}*1408a
Also Known As : {44,16|2}. if this polytope has another name.
Group : SmallGroup(1408,6423)
Rank : 3
Schlafli Type : {44,16}
Number of vertices, edges, etc : 44, 352, 16
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 : {44,8}*704a, {22,16}*704
4-fold quotients : {44,4}*352, {22,8}*352
8-fold quotients : {44,2}*176, {22,4}*176
11-fold quotients : {4,16}*128a
16-fold quotients : {22,2}*88
22-fold quotients : {4,8}*64a, {2,16}*64
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)
( 89,265)( 90,275)( 91,274)( 92,273)( 93,272)( 94,271)( 95,270)( 96,269)
( 97,268)( 98,267)( 99,266)(100,276)(101,286)(102,285)(103,284)(104,283)
(105,282)(106,281)(107,280)(108,279)(109,278)(110,277)(111,287)(112,297)
(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)(120,289)
(121,288)(122,298)(123,308)(124,307)(125,306)(126,305)(127,304)(128,303)
(129,302)(130,301)(131,300)(132,299)(133,309)(134,319)(135,318)(136,317)
(137,316)(138,315)(139,314)(140,313)(141,312)(142,311)(143,310)(144,320)
(145,330)(146,329)(147,328)(148,327)(149,326)(150,325)(151,324)(152,323)
(153,322)(154,321)(155,331)(156,341)(157,340)(158,339)(159,338)(160,337)
(161,336)(162,335)(163,334)(164,333)(165,332)(166,342)(167,352)(168,351)
(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)(176,343)
(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)
(441,617)(442,627)(443,626)(444,625)(445,624)(446,623)(447,622)(448,621)
(449,620)(450,619)(451,618)(452,628)(453,638)(454,637)(455,636)(456,635)
(457,634)(458,633)(459,632)(460,631)(461,630)(462,629)(463,639)(464,649)
(465,648)(466,647)(467,646)(468,645)(469,644)(470,643)(471,642)(472,641)
(473,640)(474,650)(475,660)(476,659)(477,658)(478,657)(479,656)(480,655)
(481,654)(482,653)(483,652)(484,651)(485,661)(486,671)(487,670)(488,669)
(489,668)(490,667)(491,666)(492,665)(493,664)(494,663)(495,662)(496,672)
(497,682)(498,681)(499,680)(500,679)(501,678)(502,677)(503,676)(504,675)
(505,674)(506,673)(507,683)(508,693)(509,692)(510,691)(511,690)(512,689)
(513,688)(514,687)(515,686)(516,685)(517,684)(518,694)(519,704)(520,703)
(521,702)(522,701)(523,700)(524,699)(525,698)(526,697)(527,696)(528,695);;
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)(529,662)(530,661)
(531,671)(532,670)(533,669)(534,668)(535,667)(536,666)(537,665)(538,664)
(539,663)(540,673)(541,672)(542,682)(543,681)(544,680)(545,679)(546,678)
(547,677)(548,676)(549,675)(550,674)(551,695)(552,694)(553,704)(554,703)
(555,702)(556,701)(557,700)(558,699)(559,698)(560,697)(561,696)(562,684)
(563,683)(564,693)(565,692)(566,691)(567,690)(568,689)(569,688)(570,687)
(571,686)(572,685)(573,618)(574,617)(575,627)(576,626)(577,625)(578,624)
(579,623)(580,622)(581,621)(582,620)(583,619)(584,629)(585,628)(586,638)
(587,637)(588,636)(589,635)(590,634)(591,633)(592,632)(593,631)(594,630)
(595,651)(596,650)(597,660)(598,659)(599,658)(600,657)(601,656)(602,655)
(603,654)(604,653)(605,652)(606,640)(607,639)(608,649)(609,648)(610,647)
(611,646)(612,645)(613,644)(614,643)(615,642)(616,641);;
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)( 45,397)( 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);;
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 ];;
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)( 89,265)( 90,275)( 91,274)( 92,273)( 93,272)( 94,271)( 95,270)
( 96,269)( 97,268)( 98,267)( 99,266)(100,276)(101,286)(102,285)(103,284)
(104,283)(105,282)(106,281)(107,280)(108,279)(109,278)(110,277)(111,287)
(112,297)(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)
(120,289)(121,288)(122,298)(123,308)(124,307)(125,306)(126,305)(127,304)
(128,303)(129,302)(130,301)(131,300)(132,299)(133,309)(134,319)(135,318)
(136,317)(137,316)(138,315)(139,314)(140,313)(141,312)(142,311)(143,310)
(144,320)(145,330)(146,329)(147,328)(148,327)(149,326)(150,325)(151,324)
(152,323)(153,322)(154,321)(155,331)(156,341)(157,340)(158,339)(159,338)
(160,337)(161,336)(162,335)(163,334)(164,333)(165,332)(166,342)(167,352)
(168,351)(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)
(176,343)(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)(441,617)(442,627)(443,626)(444,625)(445,624)(446,623)(447,622)
(448,621)(449,620)(450,619)(451,618)(452,628)(453,638)(454,637)(455,636)
(456,635)(457,634)(458,633)(459,632)(460,631)(461,630)(462,629)(463,639)
(464,649)(465,648)(466,647)(467,646)(468,645)(469,644)(470,643)(471,642)
(472,641)(473,640)(474,650)(475,660)(476,659)(477,658)(478,657)(479,656)
(480,655)(481,654)(482,653)(483,652)(484,651)(485,661)(486,671)(487,670)
(488,669)(489,668)(490,667)(491,666)(492,665)(493,664)(494,663)(495,662)
(496,672)(497,682)(498,681)(499,680)(500,679)(501,678)(502,677)(503,676)
(504,675)(505,674)(506,673)(507,683)(508,693)(509,692)(510,691)(511,690)
(512,689)(513,688)(514,687)(515,686)(516,685)(517,684)(518,694)(519,704)
(520,703)(521,702)(522,701)(523,700)(524,699)(525,698)(526,697)(527,696)
(528,695);
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)(529,662)
(530,661)(531,671)(532,670)(533,669)(534,668)(535,667)(536,666)(537,665)
(538,664)(539,663)(540,673)(541,672)(542,682)(543,681)(544,680)(545,679)
(546,678)(547,677)(548,676)(549,675)(550,674)(551,695)(552,694)(553,704)
(554,703)(555,702)(556,701)(557,700)(558,699)(559,698)(560,697)(561,696)
(562,684)(563,683)(564,693)(565,692)(566,691)(567,690)(568,689)(569,688)
(570,687)(571,686)(572,685)(573,618)(574,617)(575,627)(576,626)(577,625)
(578,624)(579,623)(580,622)(581,621)(582,620)(583,619)(584,629)(585,628)
(586,638)(587,637)(588,636)(589,635)(590,634)(591,633)(592,632)(593,631)
(594,630)(595,651)(596,650)(597,660)(598,659)(599,658)(600,657)(601,656)
(602,655)(603,654)(604,653)(605,652)(606,640)(607,639)(608,649)(609,648)
(610,647)(611,646)(612,645)(613,644)(614,643)(615,642)(616,641);
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)( 45,397)( 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);
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,
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 >;
References : None.
to this polytope