Polytope of Type {8,88}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,88}*1408b
if this polytope has a name.
Group : SmallGroup(1408,3566)
Rank : 3
Schlafli Type : {8,88}
Number of vertices, edges, etc : 8, 352, 88
Order of s0s1s2 : 88
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 : {4,88}*704a, {8,44}*704b
4-fold quotients : {4,44}*352, {2,88}*352
8-fold quotients : {2,44}*176, {4,22}*176
11-fold quotients : {8,8}*128a
16-fold quotients : {2,22}*88
22-fold quotients : {4,8}*64a, {8,4}*64b
32-fold quotients : {2,11}*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)( 2,178)( 3,179)( 4,180)( 5,181)( 6,182)( 7,183)( 8,184)
( 9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)( 16,192)
( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)( 24,200)
( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)( 32,208)
( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)( 40,216)
( 41,217)( 42,218)( 43,219)( 44,220)( 45,232)( 46,233)( 47,234)( 48,235)
( 49,236)( 50,237)( 51,238)( 52,239)( 53,240)( 54,241)( 55,242)( 56,221)
( 57,222)( 58,223)( 59,224)( 60,225)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,231)( 67,254)( 68,255)( 69,256)( 70,257)( 71,258)( 72,259)
( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,243)( 79,244)( 80,245)
( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)( 88,253)
( 89,276)( 90,277)( 91,278)( 92,279)( 93,280)( 94,281)( 95,282)( 96,283)
( 97,284)( 98,285)( 99,286)(100,265)(101,266)(102,267)(103,268)(104,269)
(105,270)(106,271)(107,272)(108,273)(109,274)(110,275)(111,298)(112,299)
(113,300)(114,301)(115,302)(116,303)(117,304)(118,305)(119,306)(120,307)
(121,308)(122,287)(123,288)(124,289)(125,290)(126,291)(127,292)(128,293)
(129,294)(130,295)(131,296)(132,297)(133,309)(134,310)(135,311)(136,312)
(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)(144,320)
(145,321)(146,322)(147,323)(148,324)(149,325)(150,326)(151,327)(152,328)
(153,329)(154,330)(155,331)(156,332)(157,333)(158,334)(159,335)(160,336)
(161,337)(162,338)(163,339)(164,340)(165,341)(166,342)(167,343)(168,344)
(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)(176,352)
(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)(360,536)
(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)(368,544)
(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)(376,552)
(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)(384,560)
(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)(392,568)
(393,569)(394,570)(395,571)(396,572)(397,584)(398,585)(399,586)(400,587)
(401,588)(402,589)(403,590)(404,591)(405,592)(406,593)(407,594)(408,573)
(409,574)(410,575)(411,576)(412,577)(413,578)(414,579)(415,580)(416,581)
(417,582)(418,583)(419,606)(420,607)(421,608)(422,609)(423,610)(424,611)
(425,612)(426,613)(427,614)(428,615)(429,616)(430,595)(431,596)(432,597)
(433,598)(434,599)(435,600)(436,601)(437,602)(438,603)(439,604)(440,605)
(441,628)(442,629)(443,630)(444,631)(445,632)(446,633)(447,634)(448,635)
(449,636)(450,637)(451,638)(452,617)(453,618)(454,619)(455,620)(456,621)
(457,622)(458,623)(459,624)(460,625)(461,626)(462,627)(463,650)(464,651)
(465,652)(466,653)(467,654)(468,655)(469,656)(470,657)(471,658)(472,659)
(473,660)(474,639)(475,640)(476,641)(477,642)(478,643)(479,644)(480,645)
(481,646)(482,647)(483,648)(484,649)(485,661)(486,662)(487,663)(488,664)
(489,665)(490,666)(491,667)(492,668)(493,669)(494,670)(495,671)(496,672)
(497,673)(498,674)(499,675)(500,676)(501,677)(502,678)(503,679)(504,680)
(505,681)(506,682)(507,683)(508,684)(509,685)(510,686)(511,687)(512,688)
(513,689)(514,690)(515,691)(516,692)(517,693)(518,694)(519,695)(520,696)
(521,697)(522,698)(523,699)(524,700)(525,701)(526,702)(527,703)(528,704);;
s1 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)( 48, 64)
( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 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)
(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)
(141,169)(142,168)(143,167)(144,155)(145,165)(146,164)(147,163)(148,162)
(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(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)(199,243)(200,253)(201,252)(202,251)
(203,250)(204,249)(205,248)(206,247)(207,246)(208,245)(209,244)(210,254)
(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,258)(218,257)
(219,256)(220,255)(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)(375,463)(376,473)(377,472)(378,471)
(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,474)
(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)
(395,476)(396,475)(397,496)(398,506)(399,505)(400,504)(401,503)(402,502)
(403,501)(404,500)(405,499)(406,498)(407,497)(408,485)(409,495)(410,494)
(411,493)(412,492)(413,491)(414,490)(415,489)(416,488)(417,487)(418,486)
(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)(529,672)(530,682)
(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)(538,674)
(539,673)(540,661)(541,671)(542,670)(543,669)(544,668)(545,667)(546,666)
(547,665)(548,664)(549,663)(550,662)(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)(573,628)(574,638)(575,637)(576,636)(577,635)(578,634)
(579,633)(580,632)(581,631)(582,630)(583,629)(584,617)(585,627)(586,626)
(587,625)(588,624)(589,623)(590,622)(591,621)(592,620)(593,619)(594,618)
(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 := ( 1,354)( 2,353)( 3,363)( 4,362)( 5,361)( 6,360)( 7,359)( 8,358)
( 9,357)( 10,356)( 11,355)( 12,365)( 13,364)( 14,374)( 15,373)( 16,372)
( 17,371)( 18,370)( 19,369)( 20,368)( 21,367)( 22,366)( 23,376)( 24,375)
( 25,385)( 26,384)( 27,383)( 28,382)( 29,381)( 30,380)( 31,379)( 32,378)
( 33,377)( 34,387)( 35,386)( 36,396)( 37,395)( 38,394)( 39,393)( 40,392)
( 41,391)( 42,390)( 43,389)( 44,388)( 45,409)( 46,408)( 47,418)( 48,417)
( 49,416)( 50,415)( 51,414)( 52,413)( 53,412)( 54,411)( 55,410)( 56,398)
( 57,397)( 58,407)( 59,406)( 60,405)( 61,404)( 62,403)( 63,402)( 64,401)
( 65,400)( 66,399)( 67,431)( 68,430)( 69,440)( 70,439)( 71,438)( 72,437)
( 73,436)( 74,435)( 75,434)( 76,433)( 77,432)( 78,420)( 79,419)( 80,429)
( 81,428)( 82,427)( 83,426)( 84,425)( 85,424)( 86,423)( 87,422)( 88,421)
( 89,464)( 90,463)( 91,473)( 92,472)( 93,471)( 94,470)( 95,469)( 96,468)
( 97,467)( 98,466)( 99,465)(100,475)(101,474)(102,484)(103,483)(104,482)
(105,481)(106,480)(107,479)(108,478)(109,477)(110,476)(111,442)(112,441)
(113,451)(114,450)(115,449)(116,448)(117,447)(118,446)(119,445)(120,444)
(121,443)(122,453)(123,452)(124,462)(125,461)(126,460)(127,459)(128,458)
(129,457)(130,456)(131,455)(132,454)(133,519)(134,518)(135,528)(136,527)
(137,526)(138,525)(139,524)(140,523)(141,522)(142,521)(143,520)(144,508)
(145,507)(146,517)(147,516)(148,515)(149,514)(150,513)(151,512)(152,511)
(153,510)(154,509)(155,497)(156,496)(157,506)(158,505)(159,504)(160,503)
(161,502)(162,501)(163,500)(164,499)(165,498)(166,486)(167,485)(168,495)
(169,494)(170,493)(171,492)(172,491)(173,490)(174,489)(175,488)(176,487)
(177,530)(178,529)(179,539)(180,538)(181,537)(182,536)(183,535)(184,534)
(185,533)(186,532)(187,531)(188,541)(189,540)(190,550)(191,549)(192,548)
(193,547)(194,546)(195,545)(196,544)(197,543)(198,542)(199,552)(200,551)
(201,561)(202,560)(203,559)(204,558)(205,557)(206,556)(207,555)(208,554)
(209,553)(210,563)(211,562)(212,572)(213,571)(214,570)(215,569)(216,568)
(217,567)(218,566)(219,565)(220,564)(221,585)(222,584)(223,594)(224,593)
(225,592)(226,591)(227,590)(228,589)(229,588)(230,587)(231,586)(232,574)
(233,573)(234,583)(235,582)(236,581)(237,580)(238,579)(239,578)(240,577)
(241,576)(242,575)(243,607)(244,606)(245,616)(246,615)(247,614)(248,613)
(249,612)(250,611)(251,610)(252,609)(253,608)(254,596)(255,595)(256,605)
(257,604)(258,603)(259,602)(260,601)(261,600)(262,599)(263,598)(264,597)
(265,640)(266,639)(267,649)(268,648)(269,647)(270,646)(271,645)(272,644)
(273,643)(274,642)(275,641)(276,651)(277,650)(278,660)(279,659)(280,658)
(281,657)(282,656)(283,655)(284,654)(285,653)(286,652)(287,618)(288,617)
(289,627)(290,626)(291,625)(292,624)(293,623)(294,622)(295,621)(296,620)
(297,619)(298,629)(299,628)(300,638)(301,637)(302,636)(303,635)(304,634)
(305,633)(306,632)(307,631)(308,630)(309,695)(310,694)(311,704)(312,703)
(313,702)(314,701)(315,700)(316,699)(317,698)(318,697)(319,696)(320,684)
(321,683)(322,693)(323,692)(324,691)(325,690)(326,689)(327,688)(328,687)
(329,686)(330,685)(331,673)(332,672)(333,682)(334,681)(335,680)(336,679)
(337,678)(338,677)(339,676)(340,675)(341,674)(342,662)(343,661)(344,671)
(345,670)(346,669)(347,668)(348,667)(349,666)(350,665)(351,664)(352,663);;
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*s0*s1*s2*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*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)!( 1,177)( 2,178)( 3,179)( 4,180)( 5,181)( 6,182)( 7,183)
( 8,184)( 9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)
( 16,192)( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)
( 24,200)( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)
( 32,208)( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)
( 40,216)( 41,217)( 42,218)( 43,219)( 44,220)( 45,232)( 46,233)( 47,234)
( 48,235)( 49,236)( 50,237)( 51,238)( 52,239)( 53,240)( 54,241)( 55,242)
( 56,221)( 57,222)( 58,223)( 59,224)( 60,225)( 61,226)( 62,227)( 63,228)
( 64,229)( 65,230)( 66,231)( 67,254)( 68,255)( 69,256)( 70,257)( 71,258)
( 72,259)( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,243)( 79,244)
( 80,245)( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)
( 88,253)( 89,276)( 90,277)( 91,278)( 92,279)( 93,280)( 94,281)( 95,282)
( 96,283)( 97,284)( 98,285)( 99,286)(100,265)(101,266)(102,267)(103,268)
(104,269)(105,270)(106,271)(107,272)(108,273)(109,274)(110,275)(111,298)
(112,299)(113,300)(114,301)(115,302)(116,303)(117,304)(118,305)(119,306)
(120,307)(121,308)(122,287)(123,288)(124,289)(125,290)(126,291)(127,292)
(128,293)(129,294)(130,295)(131,296)(132,297)(133,309)(134,310)(135,311)
(136,312)(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)
(144,320)(145,321)(146,322)(147,323)(148,324)(149,325)(150,326)(151,327)
(152,328)(153,329)(154,330)(155,331)(156,332)(157,333)(158,334)(159,335)
(160,336)(161,337)(162,338)(163,339)(164,340)(165,341)(166,342)(167,343)
(168,344)(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)
(176,352)(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)
(360,536)(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)
(368,544)(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)
(376,552)(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)
(384,560)(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)
(392,568)(393,569)(394,570)(395,571)(396,572)(397,584)(398,585)(399,586)
(400,587)(401,588)(402,589)(403,590)(404,591)(405,592)(406,593)(407,594)
(408,573)(409,574)(410,575)(411,576)(412,577)(413,578)(414,579)(415,580)
(416,581)(417,582)(418,583)(419,606)(420,607)(421,608)(422,609)(423,610)
(424,611)(425,612)(426,613)(427,614)(428,615)(429,616)(430,595)(431,596)
(432,597)(433,598)(434,599)(435,600)(436,601)(437,602)(438,603)(439,604)
(440,605)(441,628)(442,629)(443,630)(444,631)(445,632)(446,633)(447,634)
(448,635)(449,636)(450,637)(451,638)(452,617)(453,618)(454,619)(455,620)
(456,621)(457,622)(458,623)(459,624)(460,625)(461,626)(462,627)(463,650)
(464,651)(465,652)(466,653)(467,654)(468,655)(469,656)(470,657)(471,658)
(472,659)(473,660)(474,639)(475,640)(476,641)(477,642)(478,643)(479,644)
(480,645)(481,646)(482,647)(483,648)(484,649)(485,661)(486,662)(487,663)
(488,664)(489,665)(490,666)(491,667)(492,668)(493,669)(494,670)(495,671)
(496,672)(497,673)(498,674)(499,675)(500,676)(501,677)(502,678)(503,679)
(504,680)(505,681)(506,682)(507,683)(508,684)(509,685)(510,686)(511,687)
(512,688)(513,689)(514,690)(515,691)(516,692)(517,693)(518,694)(519,695)
(520,696)(521,697)(522,698)(523,699)(524,700)(525,701)(526,702)(527,703)
(528,704);
s1 := Sym(704)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)
( 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)(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)
(140,170)(141,169)(142,168)(143,167)(144,155)(145,165)(146,164)(147,163)
(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(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)(199,243)(200,253)(201,252)
(202,251)(203,250)(204,249)(205,248)(206,247)(207,246)(208,245)(209,244)
(210,254)(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,258)
(218,257)(219,256)(220,255)(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)(375,463)(376,473)(377,472)
(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)
(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)
(394,477)(395,476)(396,475)(397,496)(398,506)(399,505)(400,504)(401,503)
(402,502)(403,501)(404,500)(405,499)(406,498)(407,497)(408,485)(409,495)
(410,494)(411,493)(412,492)(413,491)(414,490)(415,489)(416,488)(417,487)
(418,486)(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)(529,672)
(530,682)(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)
(538,674)(539,673)(540,661)(541,671)(542,670)(543,669)(544,668)(545,667)
(546,666)(547,665)(548,664)(549,663)(550,662)(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)(573,628)(574,638)(575,637)(576,636)(577,635)
(578,634)(579,633)(580,632)(581,631)(582,630)(583,629)(584,617)(585,627)
(586,626)(587,625)(588,624)(589,623)(590,622)(591,621)(592,620)(593,619)
(594,618)(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)!( 1,354)( 2,353)( 3,363)( 4,362)( 5,361)( 6,360)( 7,359)
( 8,358)( 9,357)( 10,356)( 11,355)( 12,365)( 13,364)( 14,374)( 15,373)
( 16,372)( 17,371)( 18,370)( 19,369)( 20,368)( 21,367)( 22,366)( 23,376)
( 24,375)( 25,385)( 26,384)( 27,383)( 28,382)( 29,381)( 30,380)( 31,379)
( 32,378)( 33,377)( 34,387)( 35,386)( 36,396)( 37,395)( 38,394)( 39,393)
( 40,392)( 41,391)( 42,390)( 43,389)( 44,388)( 45,409)( 46,408)( 47,418)
( 48,417)( 49,416)( 50,415)( 51,414)( 52,413)( 53,412)( 54,411)( 55,410)
( 56,398)( 57,397)( 58,407)( 59,406)( 60,405)( 61,404)( 62,403)( 63,402)
( 64,401)( 65,400)( 66,399)( 67,431)( 68,430)( 69,440)( 70,439)( 71,438)
( 72,437)( 73,436)( 74,435)( 75,434)( 76,433)( 77,432)( 78,420)( 79,419)
( 80,429)( 81,428)( 82,427)( 83,426)( 84,425)( 85,424)( 86,423)( 87,422)
( 88,421)( 89,464)( 90,463)( 91,473)( 92,472)( 93,471)( 94,470)( 95,469)
( 96,468)( 97,467)( 98,466)( 99,465)(100,475)(101,474)(102,484)(103,483)
(104,482)(105,481)(106,480)(107,479)(108,478)(109,477)(110,476)(111,442)
(112,441)(113,451)(114,450)(115,449)(116,448)(117,447)(118,446)(119,445)
(120,444)(121,443)(122,453)(123,452)(124,462)(125,461)(126,460)(127,459)
(128,458)(129,457)(130,456)(131,455)(132,454)(133,519)(134,518)(135,528)
(136,527)(137,526)(138,525)(139,524)(140,523)(141,522)(142,521)(143,520)
(144,508)(145,507)(146,517)(147,516)(148,515)(149,514)(150,513)(151,512)
(152,511)(153,510)(154,509)(155,497)(156,496)(157,506)(158,505)(159,504)
(160,503)(161,502)(162,501)(163,500)(164,499)(165,498)(166,486)(167,485)
(168,495)(169,494)(170,493)(171,492)(172,491)(173,490)(174,489)(175,488)
(176,487)(177,530)(178,529)(179,539)(180,538)(181,537)(182,536)(183,535)
(184,534)(185,533)(186,532)(187,531)(188,541)(189,540)(190,550)(191,549)
(192,548)(193,547)(194,546)(195,545)(196,544)(197,543)(198,542)(199,552)
(200,551)(201,561)(202,560)(203,559)(204,558)(205,557)(206,556)(207,555)
(208,554)(209,553)(210,563)(211,562)(212,572)(213,571)(214,570)(215,569)
(216,568)(217,567)(218,566)(219,565)(220,564)(221,585)(222,584)(223,594)
(224,593)(225,592)(226,591)(227,590)(228,589)(229,588)(230,587)(231,586)
(232,574)(233,573)(234,583)(235,582)(236,581)(237,580)(238,579)(239,578)
(240,577)(241,576)(242,575)(243,607)(244,606)(245,616)(246,615)(247,614)
(248,613)(249,612)(250,611)(251,610)(252,609)(253,608)(254,596)(255,595)
(256,605)(257,604)(258,603)(259,602)(260,601)(261,600)(262,599)(263,598)
(264,597)(265,640)(266,639)(267,649)(268,648)(269,647)(270,646)(271,645)
(272,644)(273,643)(274,642)(275,641)(276,651)(277,650)(278,660)(279,659)
(280,658)(281,657)(282,656)(283,655)(284,654)(285,653)(286,652)(287,618)
(288,617)(289,627)(290,626)(291,625)(292,624)(293,623)(294,622)(295,621)
(296,620)(297,619)(298,629)(299,628)(300,638)(301,637)(302,636)(303,635)
(304,634)(305,633)(306,632)(307,631)(308,630)(309,695)(310,694)(311,704)
(312,703)(313,702)(314,701)(315,700)(316,699)(317,698)(318,697)(319,696)
(320,684)(321,683)(322,693)(323,692)(324,691)(325,690)(326,689)(327,688)
(328,687)(329,686)(330,685)(331,673)(332,672)(333,682)(334,681)(335,680)
(336,679)(337,678)(338,677)(339,676)(340,675)(341,674)(342,662)(343,661)
(344,671)(345,670)(346,669)(347,668)(348,667)(349,666)(350,665)(351,664)
(352,663);
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*s0*s1*s2*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*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