Polytope of Type {178,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {178,4}*1424
Also Known As : {178,4|2}. if this polytope has another name.
Group : SmallGroup(1424,34)
Rank : 3
Schlafli Type : {178,4}
Number of vertices, edges, etc : 178, 356, 4
Order of s0s1s2 : 356
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 : {178,2}*712
4-fold quotients : {89,2}*356
89-fold quotients : {2,4}*16
178-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,179)( 2,267)( 3,266)( 4,265)( 5,264)( 6,263)( 7,262)( 8,261)
( 9,260)( 10,259)( 11,258)( 12,257)( 13,256)( 14,255)( 15,254)( 16,253)
( 17,252)( 18,251)( 19,250)( 20,249)( 21,248)( 22,247)( 23,246)( 24,245)
( 25,244)( 26,243)( 27,242)( 28,241)( 29,240)( 30,239)( 31,238)( 32,237)
( 33,236)( 34,235)( 35,234)( 36,233)( 37,232)( 38,231)( 39,230)( 40,229)
( 41,228)( 42,227)( 43,226)( 44,225)( 45,224)( 46,223)( 47,222)( 48,221)
( 49,220)( 50,219)( 51,218)( 52,217)( 53,216)( 54,215)( 55,214)( 56,213)
( 57,212)( 58,211)( 59,210)( 60,209)( 61,208)( 62,207)( 63,206)( 64,205)
( 65,204)( 66,203)( 67,202)( 68,201)( 69,200)( 70,199)( 71,198)( 72,197)
( 73,196)( 74,195)( 75,194)( 76,193)( 77,192)( 78,191)( 79,190)( 80,189)
( 81,188)( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)( 88,181)
( 89,180)( 90,268)( 91,356)( 92,355)( 93,354)( 94,353)( 95,352)( 96,351)
( 97,350)( 98,349)( 99,348)(100,347)(101,346)(102,345)(103,344)(104,343)
(105,342)(106,341)(107,340)(108,339)(109,338)(110,337)(111,336)(112,335)
(113,334)(114,333)(115,332)(116,331)(117,330)(118,329)(119,328)(120,327)
(121,326)(122,325)(123,324)(124,323)(125,322)(126,321)(127,320)(128,319)
(129,318)(130,317)(131,316)(132,315)(133,314)(134,313)(135,312)(136,311)
(137,310)(138,309)(139,308)(140,307)(141,306)(142,305)(143,304)(144,303)
(145,302)(146,301)(147,300)(148,299)(149,298)(150,297)(151,296)(152,295)
(153,294)(154,293)(155,292)(156,291)(157,290)(158,289)(159,288)(160,287)
(161,286)(162,285)(163,284)(164,283)(165,282)(166,281)(167,280)(168,279)
(169,278)(170,277)(171,276)(172,275)(173,274)(174,273)(175,272)(176,271)
(177,270)(178,269)(357,535)(358,623)(359,622)(360,621)(361,620)(362,619)
(363,618)(364,617)(365,616)(366,615)(367,614)(368,613)(369,612)(370,611)
(371,610)(372,609)(373,608)(374,607)(375,606)(376,605)(377,604)(378,603)
(379,602)(380,601)(381,600)(382,599)(383,598)(384,597)(385,596)(386,595)
(387,594)(388,593)(389,592)(390,591)(391,590)(392,589)(393,588)(394,587)
(395,586)(396,585)(397,584)(398,583)(399,582)(400,581)(401,580)(402,579)
(403,578)(404,577)(405,576)(406,575)(407,574)(408,573)(409,572)(410,571)
(411,570)(412,569)(413,568)(414,567)(415,566)(416,565)(417,564)(418,563)
(419,562)(420,561)(421,560)(422,559)(423,558)(424,557)(425,556)(426,555)
(427,554)(428,553)(429,552)(430,551)(431,550)(432,549)(433,548)(434,547)
(435,546)(436,545)(437,544)(438,543)(439,542)(440,541)(441,540)(442,539)
(443,538)(444,537)(445,536)(446,624)(447,712)(448,711)(449,710)(450,709)
(451,708)(452,707)(453,706)(454,705)(455,704)(456,703)(457,702)(458,701)
(459,700)(460,699)(461,698)(462,697)(463,696)(464,695)(465,694)(466,693)
(467,692)(468,691)(469,690)(470,689)(471,688)(472,687)(473,686)(474,685)
(475,684)(476,683)(477,682)(478,681)(479,680)(480,679)(481,678)(482,677)
(483,676)(484,675)(485,674)(486,673)(487,672)(488,671)(489,670)(490,669)
(491,668)(492,667)(493,666)(494,665)(495,664)(496,663)(497,662)(498,661)
(499,660)(500,659)(501,658)(502,657)(503,656)(504,655)(505,654)(506,653)
(507,652)(508,651)(509,650)(510,649)(511,648)(512,647)(513,646)(514,645)
(515,644)(516,643)(517,642)(518,641)(519,640)(520,639)(521,638)(522,637)
(523,636)(524,635)(525,634)(526,633)(527,632)(528,631)(529,630)(530,629)
(531,628)(532,627)(533,626)(534,625);;
s1 := ( 1,180)( 2,179)( 3,267)( 4,266)( 5,265)( 6,264)( 7,263)( 8,262)
( 9,261)( 10,260)( 11,259)( 12,258)( 13,257)( 14,256)( 15,255)( 16,254)
( 17,253)( 18,252)( 19,251)( 20,250)( 21,249)( 22,248)( 23,247)( 24,246)
( 25,245)( 26,244)( 27,243)( 28,242)( 29,241)( 30,240)( 31,239)( 32,238)
( 33,237)( 34,236)( 35,235)( 36,234)( 37,233)( 38,232)( 39,231)( 40,230)
( 41,229)( 42,228)( 43,227)( 44,226)( 45,225)( 46,224)( 47,223)( 48,222)
( 49,221)( 50,220)( 51,219)( 52,218)( 53,217)( 54,216)( 55,215)( 56,214)
( 57,213)( 58,212)( 59,211)( 60,210)( 61,209)( 62,208)( 63,207)( 64,206)
( 65,205)( 66,204)( 67,203)( 68,202)( 69,201)( 70,200)( 71,199)( 72,198)
( 73,197)( 74,196)( 75,195)( 76,194)( 77,193)( 78,192)( 79,191)( 80,190)
( 81,189)( 82,188)( 83,187)( 84,186)( 85,185)( 86,184)( 87,183)( 88,182)
( 89,181)( 90,269)( 91,268)( 92,356)( 93,355)( 94,354)( 95,353)( 96,352)
( 97,351)( 98,350)( 99,349)(100,348)(101,347)(102,346)(103,345)(104,344)
(105,343)(106,342)(107,341)(108,340)(109,339)(110,338)(111,337)(112,336)
(113,335)(114,334)(115,333)(116,332)(117,331)(118,330)(119,329)(120,328)
(121,327)(122,326)(123,325)(124,324)(125,323)(126,322)(127,321)(128,320)
(129,319)(130,318)(131,317)(132,316)(133,315)(134,314)(135,313)(136,312)
(137,311)(138,310)(139,309)(140,308)(141,307)(142,306)(143,305)(144,304)
(145,303)(146,302)(147,301)(148,300)(149,299)(150,298)(151,297)(152,296)
(153,295)(154,294)(155,293)(156,292)(157,291)(158,290)(159,289)(160,288)
(161,287)(162,286)(163,285)(164,284)(165,283)(166,282)(167,281)(168,280)
(169,279)(170,278)(171,277)(172,276)(173,275)(174,274)(175,273)(176,272)
(177,271)(178,270)(357,625)(358,624)(359,712)(360,711)(361,710)(362,709)
(363,708)(364,707)(365,706)(366,705)(367,704)(368,703)(369,702)(370,701)
(371,700)(372,699)(373,698)(374,697)(375,696)(376,695)(377,694)(378,693)
(379,692)(380,691)(381,690)(382,689)(383,688)(384,687)(385,686)(386,685)
(387,684)(388,683)(389,682)(390,681)(391,680)(392,679)(393,678)(394,677)
(395,676)(396,675)(397,674)(398,673)(399,672)(400,671)(401,670)(402,669)
(403,668)(404,667)(405,666)(406,665)(407,664)(408,663)(409,662)(410,661)
(411,660)(412,659)(413,658)(414,657)(415,656)(416,655)(417,654)(418,653)
(419,652)(420,651)(421,650)(422,649)(423,648)(424,647)(425,646)(426,645)
(427,644)(428,643)(429,642)(430,641)(431,640)(432,639)(433,638)(434,637)
(435,636)(436,635)(437,634)(438,633)(439,632)(440,631)(441,630)(442,629)
(443,628)(444,627)(445,626)(446,536)(447,535)(448,623)(449,622)(450,621)
(451,620)(452,619)(453,618)(454,617)(455,616)(456,615)(457,614)(458,613)
(459,612)(460,611)(461,610)(462,609)(463,608)(464,607)(465,606)(466,605)
(467,604)(468,603)(469,602)(470,601)(471,600)(472,599)(473,598)(474,597)
(475,596)(476,595)(477,594)(478,593)(479,592)(480,591)(481,590)(482,589)
(483,588)(484,587)(485,586)(486,585)(487,584)(488,583)(489,582)(490,581)
(491,580)(492,579)(493,578)(494,577)(495,576)(496,575)(497,574)(498,573)
(499,572)(500,571)(501,570)(502,569)(503,568)(504,567)(505,566)(506,565)
(507,564)(508,563)(509,562)(510,561)(511,560)(512,559)(513,558)(514,557)
(515,556)(516,555)(517,554)(518,553)(519,552)(520,551)(521,550)(522,549)
(523,548)(524,547)(525,546)(526,545)(527,544)(528,543)(529,542)(530,541)
(531,540)(532,539)(533,538)(534,537);;
s2 := ( 1,357)( 2,358)( 3,359)( 4,360)( 5,361)( 6,362)( 7,363)( 8,364)
( 9,365)( 10,366)( 11,367)( 12,368)( 13,369)( 14,370)( 15,371)( 16,372)
( 17,373)( 18,374)( 19,375)( 20,376)( 21,377)( 22,378)( 23,379)( 24,380)
( 25,381)( 26,382)( 27,383)( 28,384)( 29,385)( 30,386)( 31,387)( 32,388)
( 33,389)( 34,390)( 35,391)( 36,392)( 37,393)( 38,394)( 39,395)( 40,396)
( 41,397)( 42,398)( 43,399)( 44,400)( 45,401)( 46,402)( 47,403)( 48,404)
( 49,405)( 50,406)( 51,407)( 52,408)( 53,409)( 54,410)( 55,411)( 56,412)
( 57,413)( 58,414)( 59,415)( 60,416)( 61,417)( 62,418)( 63,419)( 64,420)
( 65,421)( 66,422)( 67,423)( 68,424)( 69,425)( 70,426)( 71,427)( 72,428)
( 73,429)( 74,430)( 75,431)( 76,432)( 77,433)( 78,434)( 79,435)( 80,436)
( 81,437)( 82,438)( 83,439)( 84,440)( 85,441)( 86,442)( 87,443)( 88,444)
( 89,445)( 90,446)( 91,447)( 92,448)( 93,449)( 94,450)( 95,451)( 96,452)
( 97,453)( 98,454)( 99,455)(100,456)(101,457)(102,458)(103,459)(104,460)
(105,461)(106,462)(107,463)(108,464)(109,465)(110,466)(111,467)(112,468)
(113,469)(114,470)(115,471)(116,472)(117,473)(118,474)(119,475)(120,476)
(121,477)(122,478)(123,479)(124,480)(125,481)(126,482)(127,483)(128,484)
(129,485)(130,486)(131,487)(132,488)(133,489)(134,490)(135,491)(136,492)
(137,493)(138,494)(139,495)(140,496)(141,497)(142,498)(143,499)(144,500)
(145,501)(146,502)(147,503)(148,504)(149,505)(150,506)(151,507)(152,508)
(153,509)(154,510)(155,511)(156,512)(157,513)(158,514)(159,515)(160,516)
(161,517)(162,518)(163,519)(164,520)(165,521)(166,522)(167,523)(168,524)
(169,525)(170,526)(171,527)(172,528)(173,529)(174,530)(175,531)(176,532)
(177,533)(178,534)(179,535)(180,536)(181,537)(182,538)(183,539)(184,540)
(185,541)(186,542)(187,543)(188,544)(189,545)(190,546)(191,547)(192,548)
(193,549)(194,550)(195,551)(196,552)(197,553)(198,554)(199,555)(200,556)
(201,557)(202,558)(203,559)(204,560)(205,561)(206,562)(207,563)(208,564)
(209,565)(210,566)(211,567)(212,568)(213,569)(214,570)(215,571)(216,572)
(217,573)(218,574)(219,575)(220,576)(221,577)(222,578)(223,579)(224,580)
(225,581)(226,582)(227,583)(228,584)(229,585)(230,586)(231,587)(232,588)
(233,589)(234,590)(235,591)(236,592)(237,593)(238,594)(239,595)(240,596)
(241,597)(242,598)(243,599)(244,600)(245,601)(246,602)(247,603)(248,604)
(249,605)(250,606)(251,607)(252,608)(253,609)(254,610)(255,611)(256,612)
(257,613)(258,614)(259,615)(260,616)(261,617)(262,618)(263,619)(264,620)
(265,621)(266,622)(267,623)(268,624)(269,625)(270,626)(271,627)(272,628)
(273,629)(274,630)(275,631)(276,632)(277,633)(278,634)(279,635)(280,636)
(281,637)(282,638)(283,639)(284,640)(285,641)(286,642)(287,643)(288,644)
(289,645)(290,646)(291,647)(292,648)(293,649)(294,650)(295,651)(296,652)
(297,653)(298,654)(299,655)(300,656)(301,657)(302,658)(303,659)(304,660)
(305,661)(306,662)(307,663)(308,664)(309,665)(310,666)(311,667)(312,668)
(313,669)(314,670)(315,671)(316,672)(317,673)(318,674)(319,675)(320,676)
(321,677)(322,678)(323,679)(324,680)(325,681)(326,682)(327,683)(328,684)
(329,685)(330,686)(331,687)(332,688)(333,689)(334,690)(335,691)(336,692)
(337,693)(338,694)(339,695)(340,696)(341,697)(342,698)(343,699)(344,700)
(345,701)(346,702)(347,703)(348,704)(349,705)(350,706)(351,707)(352,708)
(353,709)(354,710)(355,711)(356,712);;
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, 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*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*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*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(712)!( 1,179)( 2,267)( 3,266)( 4,265)( 5,264)( 6,263)( 7,262)
( 8,261)( 9,260)( 10,259)( 11,258)( 12,257)( 13,256)( 14,255)( 15,254)
( 16,253)( 17,252)( 18,251)( 19,250)( 20,249)( 21,248)( 22,247)( 23,246)
( 24,245)( 25,244)( 26,243)( 27,242)( 28,241)( 29,240)( 30,239)( 31,238)
( 32,237)( 33,236)( 34,235)( 35,234)( 36,233)( 37,232)( 38,231)( 39,230)
( 40,229)( 41,228)( 42,227)( 43,226)( 44,225)( 45,224)( 46,223)( 47,222)
( 48,221)( 49,220)( 50,219)( 51,218)( 52,217)( 53,216)( 54,215)( 55,214)
( 56,213)( 57,212)( 58,211)( 59,210)( 60,209)( 61,208)( 62,207)( 63,206)
( 64,205)( 65,204)( 66,203)( 67,202)( 68,201)( 69,200)( 70,199)( 71,198)
( 72,197)( 73,196)( 74,195)( 75,194)( 76,193)( 77,192)( 78,191)( 79,190)
( 80,189)( 81,188)( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)
( 88,181)( 89,180)( 90,268)( 91,356)( 92,355)( 93,354)( 94,353)( 95,352)
( 96,351)( 97,350)( 98,349)( 99,348)(100,347)(101,346)(102,345)(103,344)
(104,343)(105,342)(106,341)(107,340)(108,339)(109,338)(110,337)(111,336)
(112,335)(113,334)(114,333)(115,332)(116,331)(117,330)(118,329)(119,328)
(120,327)(121,326)(122,325)(123,324)(124,323)(125,322)(126,321)(127,320)
(128,319)(129,318)(130,317)(131,316)(132,315)(133,314)(134,313)(135,312)
(136,311)(137,310)(138,309)(139,308)(140,307)(141,306)(142,305)(143,304)
(144,303)(145,302)(146,301)(147,300)(148,299)(149,298)(150,297)(151,296)
(152,295)(153,294)(154,293)(155,292)(156,291)(157,290)(158,289)(159,288)
(160,287)(161,286)(162,285)(163,284)(164,283)(165,282)(166,281)(167,280)
(168,279)(169,278)(170,277)(171,276)(172,275)(173,274)(174,273)(175,272)
(176,271)(177,270)(178,269)(357,535)(358,623)(359,622)(360,621)(361,620)
(362,619)(363,618)(364,617)(365,616)(366,615)(367,614)(368,613)(369,612)
(370,611)(371,610)(372,609)(373,608)(374,607)(375,606)(376,605)(377,604)
(378,603)(379,602)(380,601)(381,600)(382,599)(383,598)(384,597)(385,596)
(386,595)(387,594)(388,593)(389,592)(390,591)(391,590)(392,589)(393,588)
(394,587)(395,586)(396,585)(397,584)(398,583)(399,582)(400,581)(401,580)
(402,579)(403,578)(404,577)(405,576)(406,575)(407,574)(408,573)(409,572)
(410,571)(411,570)(412,569)(413,568)(414,567)(415,566)(416,565)(417,564)
(418,563)(419,562)(420,561)(421,560)(422,559)(423,558)(424,557)(425,556)
(426,555)(427,554)(428,553)(429,552)(430,551)(431,550)(432,549)(433,548)
(434,547)(435,546)(436,545)(437,544)(438,543)(439,542)(440,541)(441,540)
(442,539)(443,538)(444,537)(445,536)(446,624)(447,712)(448,711)(449,710)
(450,709)(451,708)(452,707)(453,706)(454,705)(455,704)(456,703)(457,702)
(458,701)(459,700)(460,699)(461,698)(462,697)(463,696)(464,695)(465,694)
(466,693)(467,692)(468,691)(469,690)(470,689)(471,688)(472,687)(473,686)
(474,685)(475,684)(476,683)(477,682)(478,681)(479,680)(480,679)(481,678)
(482,677)(483,676)(484,675)(485,674)(486,673)(487,672)(488,671)(489,670)
(490,669)(491,668)(492,667)(493,666)(494,665)(495,664)(496,663)(497,662)
(498,661)(499,660)(500,659)(501,658)(502,657)(503,656)(504,655)(505,654)
(506,653)(507,652)(508,651)(509,650)(510,649)(511,648)(512,647)(513,646)
(514,645)(515,644)(516,643)(517,642)(518,641)(519,640)(520,639)(521,638)
(522,637)(523,636)(524,635)(525,634)(526,633)(527,632)(528,631)(529,630)
(530,629)(531,628)(532,627)(533,626)(534,625);
s1 := Sym(712)!( 1,180)( 2,179)( 3,267)( 4,266)( 5,265)( 6,264)( 7,263)
( 8,262)( 9,261)( 10,260)( 11,259)( 12,258)( 13,257)( 14,256)( 15,255)
( 16,254)( 17,253)( 18,252)( 19,251)( 20,250)( 21,249)( 22,248)( 23,247)
( 24,246)( 25,245)( 26,244)( 27,243)( 28,242)( 29,241)( 30,240)( 31,239)
( 32,238)( 33,237)( 34,236)( 35,235)( 36,234)( 37,233)( 38,232)( 39,231)
( 40,230)( 41,229)( 42,228)( 43,227)( 44,226)( 45,225)( 46,224)( 47,223)
( 48,222)( 49,221)( 50,220)( 51,219)( 52,218)( 53,217)( 54,216)( 55,215)
( 56,214)( 57,213)( 58,212)( 59,211)( 60,210)( 61,209)( 62,208)( 63,207)
( 64,206)( 65,205)( 66,204)( 67,203)( 68,202)( 69,201)( 70,200)( 71,199)
( 72,198)( 73,197)( 74,196)( 75,195)( 76,194)( 77,193)( 78,192)( 79,191)
( 80,190)( 81,189)( 82,188)( 83,187)( 84,186)( 85,185)( 86,184)( 87,183)
( 88,182)( 89,181)( 90,269)( 91,268)( 92,356)( 93,355)( 94,354)( 95,353)
( 96,352)( 97,351)( 98,350)( 99,349)(100,348)(101,347)(102,346)(103,345)
(104,344)(105,343)(106,342)(107,341)(108,340)(109,339)(110,338)(111,337)
(112,336)(113,335)(114,334)(115,333)(116,332)(117,331)(118,330)(119,329)
(120,328)(121,327)(122,326)(123,325)(124,324)(125,323)(126,322)(127,321)
(128,320)(129,319)(130,318)(131,317)(132,316)(133,315)(134,314)(135,313)
(136,312)(137,311)(138,310)(139,309)(140,308)(141,307)(142,306)(143,305)
(144,304)(145,303)(146,302)(147,301)(148,300)(149,299)(150,298)(151,297)
(152,296)(153,295)(154,294)(155,293)(156,292)(157,291)(158,290)(159,289)
(160,288)(161,287)(162,286)(163,285)(164,284)(165,283)(166,282)(167,281)
(168,280)(169,279)(170,278)(171,277)(172,276)(173,275)(174,274)(175,273)
(176,272)(177,271)(178,270)(357,625)(358,624)(359,712)(360,711)(361,710)
(362,709)(363,708)(364,707)(365,706)(366,705)(367,704)(368,703)(369,702)
(370,701)(371,700)(372,699)(373,698)(374,697)(375,696)(376,695)(377,694)
(378,693)(379,692)(380,691)(381,690)(382,689)(383,688)(384,687)(385,686)
(386,685)(387,684)(388,683)(389,682)(390,681)(391,680)(392,679)(393,678)
(394,677)(395,676)(396,675)(397,674)(398,673)(399,672)(400,671)(401,670)
(402,669)(403,668)(404,667)(405,666)(406,665)(407,664)(408,663)(409,662)
(410,661)(411,660)(412,659)(413,658)(414,657)(415,656)(416,655)(417,654)
(418,653)(419,652)(420,651)(421,650)(422,649)(423,648)(424,647)(425,646)
(426,645)(427,644)(428,643)(429,642)(430,641)(431,640)(432,639)(433,638)
(434,637)(435,636)(436,635)(437,634)(438,633)(439,632)(440,631)(441,630)
(442,629)(443,628)(444,627)(445,626)(446,536)(447,535)(448,623)(449,622)
(450,621)(451,620)(452,619)(453,618)(454,617)(455,616)(456,615)(457,614)
(458,613)(459,612)(460,611)(461,610)(462,609)(463,608)(464,607)(465,606)
(466,605)(467,604)(468,603)(469,602)(470,601)(471,600)(472,599)(473,598)
(474,597)(475,596)(476,595)(477,594)(478,593)(479,592)(480,591)(481,590)
(482,589)(483,588)(484,587)(485,586)(486,585)(487,584)(488,583)(489,582)
(490,581)(491,580)(492,579)(493,578)(494,577)(495,576)(496,575)(497,574)
(498,573)(499,572)(500,571)(501,570)(502,569)(503,568)(504,567)(505,566)
(506,565)(507,564)(508,563)(509,562)(510,561)(511,560)(512,559)(513,558)
(514,557)(515,556)(516,555)(517,554)(518,553)(519,552)(520,551)(521,550)
(522,549)(523,548)(524,547)(525,546)(526,545)(527,544)(528,543)(529,542)
(530,541)(531,540)(532,539)(533,538)(534,537);
s2 := Sym(712)!( 1,357)( 2,358)( 3,359)( 4,360)( 5,361)( 6,362)( 7,363)
( 8,364)( 9,365)( 10,366)( 11,367)( 12,368)( 13,369)( 14,370)( 15,371)
( 16,372)( 17,373)( 18,374)( 19,375)( 20,376)( 21,377)( 22,378)( 23,379)
( 24,380)( 25,381)( 26,382)( 27,383)( 28,384)( 29,385)( 30,386)( 31,387)
( 32,388)( 33,389)( 34,390)( 35,391)( 36,392)( 37,393)( 38,394)( 39,395)
( 40,396)( 41,397)( 42,398)( 43,399)( 44,400)( 45,401)( 46,402)( 47,403)
( 48,404)( 49,405)( 50,406)( 51,407)( 52,408)( 53,409)( 54,410)( 55,411)
( 56,412)( 57,413)( 58,414)( 59,415)( 60,416)( 61,417)( 62,418)( 63,419)
( 64,420)( 65,421)( 66,422)( 67,423)( 68,424)( 69,425)( 70,426)( 71,427)
( 72,428)( 73,429)( 74,430)( 75,431)( 76,432)( 77,433)( 78,434)( 79,435)
( 80,436)( 81,437)( 82,438)( 83,439)( 84,440)( 85,441)( 86,442)( 87,443)
( 88,444)( 89,445)( 90,446)( 91,447)( 92,448)( 93,449)( 94,450)( 95,451)
( 96,452)( 97,453)( 98,454)( 99,455)(100,456)(101,457)(102,458)(103,459)
(104,460)(105,461)(106,462)(107,463)(108,464)(109,465)(110,466)(111,467)
(112,468)(113,469)(114,470)(115,471)(116,472)(117,473)(118,474)(119,475)
(120,476)(121,477)(122,478)(123,479)(124,480)(125,481)(126,482)(127,483)
(128,484)(129,485)(130,486)(131,487)(132,488)(133,489)(134,490)(135,491)
(136,492)(137,493)(138,494)(139,495)(140,496)(141,497)(142,498)(143,499)
(144,500)(145,501)(146,502)(147,503)(148,504)(149,505)(150,506)(151,507)
(152,508)(153,509)(154,510)(155,511)(156,512)(157,513)(158,514)(159,515)
(160,516)(161,517)(162,518)(163,519)(164,520)(165,521)(166,522)(167,523)
(168,524)(169,525)(170,526)(171,527)(172,528)(173,529)(174,530)(175,531)
(176,532)(177,533)(178,534)(179,535)(180,536)(181,537)(182,538)(183,539)
(184,540)(185,541)(186,542)(187,543)(188,544)(189,545)(190,546)(191,547)
(192,548)(193,549)(194,550)(195,551)(196,552)(197,553)(198,554)(199,555)
(200,556)(201,557)(202,558)(203,559)(204,560)(205,561)(206,562)(207,563)
(208,564)(209,565)(210,566)(211,567)(212,568)(213,569)(214,570)(215,571)
(216,572)(217,573)(218,574)(219,575)(220,576)(221,577)(222,578)(223,579)
(224,580)(225,581)(226,582)(227,583)(228,584)(229,585)(230,586)(231,587)
(232,588)(233,589)(234,590)(235,591)(236,592)(237,593)(238,594)(239,595)
(240,596)(241,597)(242,598)(243,599)(244,600)(245,601)(246,602)(247,603)
(248,604)(249,605)(250,606)(251,607)(252,608)(253,609)(254,610)(255,611)
(256,612)(257,613)(258,614)(259,615)(260,616)(261,617)(262,618)(263,619)
(264,620)(265,621)(266,622)(267,623)(268,624)(269,625)(270,626)(271,627)
(272,628)(273,629)(274,630)(275,631)(276,632)(277,633)(278,634)(279,635)
(280,636)(281,637)(282,638)(283,639)(284,640)(285,641)(286,642)(287,643)
(288,644)(289,645)(290,646)(291,647)(292,648)(293,649)(294,650)(295,651)
(296,652)(297,653)(298,654)(299,655)(300,656)(301,657)(302,658)(303,659)
(304,660)(305,661)(306,662)(307,663)(308,664)(309,665)(310,666)(311,667)
(312,668)(313,669)(314,670)(315,671)(316,672)(317,673)(318,674)(319,675)
(320,676)(321,677)(322,678)(323,679)(324,680)(325,681)(326,682)(327,683)
(328,684)(329,685)(330,686)(331,687)(332,688)(333,689)(334,690)(335,691)
(336,692)(337,693)(338,694)(339,695)(340,696)(341,697)(342,698)(343,699)
(344,700)(345,701)(346,702)(347,703)(348,704)(349,705)(350,706)(351,707)
(352,708)(353,709)(354,710)(355,711)(356,712);
poly := sub<Sym(712)|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, 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*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*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*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