Polytope of Type {88,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {88,8}*1408a
if this polytope has a name.
Group : SmallGroup(1408,3565)
Rank : 3
Schlafli Type : {88,8}
Number of vertices, edges, etc : 88, 352, 8
Order of s0s1s2 : 88
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {88,4}*704b, {44,8}*704a
4-fold quotients : {44,4}*352, {22,8}*352
8-fold quotients : {44,2}*176, {22,4}*176
11-fold quotients : {8,8}*128a
16-fold quotients : {22,2}*88
22-fold quotients : {4,8}*64a, {8,4}*64b
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)( 45,232)( 46,242)( 47,241)( 48,240)
( 49,239)( 50,238)( 51,237)( 52,236)( 53,235)( 54,234)( 55,233)( 56,221)
( 57,231)( 58,230)( 59,229)( 60,228)( 61,227)( 62,226)( 63,225)( 64,224)
( 65,223)( 66,222)( 67,254)( 68,264)( 69,263)( 70,262)( 71,261)( 72,260)
( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,243)( 79,253)( 80,252)
( 81,251)( 82,250)( 83,249)( 84,248)( 85,247)( 86,246)( 87,245)( 88,244)
( 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)(133,309)(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)(397,584)(398,594)(399,593)(400,592)
(401,591)(402,590)(403,589)(404,588)(405,587)(406,586)(407,585)(408,573)
(409,583)(410,582)(411,581)(412,580)(413,579)(414,578)(415,577)(416,576)
(417,575)(418,574)(419,606)(420,616)(421,615)(422,614)(423,613)(424,612)
(425,611)(426,610)(427,609)(428,608)(429,607)(430,595)(431,605)(432,604)
(433,603)(434,602)(435,601)(436,600)(437,599)(438,598)(439,597)(440,596)
(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)(485,661)(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, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)
( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 57)( 46, 56)( 47, 66)( 48, 65)
( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 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)
(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)
(141,170)(142,169)(143,168)(144,156)(145,155)(146,165)(147,164)(148,163)
(149,162)(150,161)(151,160)(152,159)(153,158)(154,157)(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)(199,244)(200,243)(201,253)(202,252)
(203,251)(204,250)(205,249)(206,248)(207,247)(208,246)(209,245)(210,255)
(211,254)(212,264)(213,263)(214,262)(215,261)(216,260)(217,259)(218,258)
(219,257)(220,256)(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)(375,464)(376,463)(377,473)(378,472)
(379,471)(380,470)(381,469)(382,468)(383,467)(384,466)(385,465)(386,475)
(387,474)(388,484)(389,483)(390,482)(391,481)(392,480)(393,479)(394,478)
(395,477)(396,476)(397,497)(398,496)(399,506)(400,505)(401,504)(402,503)
(403,502)(404,501)(405,500)(406,499)(407,498)(408,486)(409,485)(410,495)
(411,494)(412,493)(413,492)(414,491)(415,490)(416,489)(417,488)(418,487)
(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)(551,695)(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)(573,629)(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)
(595,651)(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)( 23,375)( 24,376)
( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)( 32,384)
( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)( 40,392)
( 41,393)( 42,394)( 43,395)( 44,396)( 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)( 67,430)( 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)(133,518)(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)(199,551)(200,552)
(201,553)(202,554)(203,555)(204,556)(205,557)(206,558)(207,559)(208,560)
(209,561)(210,562)(211,563)(212,564)(213,565)(214,566)(215,567)(216,568)
(217,569)(218,570)(219,571)(220,572)(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)(243,606)(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)(309,694)(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,
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*s2*s1*s0*s1*s0*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 ];;
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)( 45,232)( 46,242)( 47,241)
( 48,240)( 49,239)( 50,238)( 51,237)( 52,236)( 53,235)( 54,234)( 55,233)
( 56,221)( 57,231)( 58,230)( 59,229)( 60,228)( 61,227)( 62,226)( 63,225)
( 64,224)( 65,223)( 66,222)( 67,254)( 68,264)( 69,263)( 70,262)( 71,261)
( 72,260)( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,243)( 79,253)
( 80,252)( 81,251)( 82,250)( 83,249)( 84,248)( 85,247)( 86,246)( 87,245)
( 88,244)( 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)(133,309)(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)(397,584)(398,594)(399,593)
(400,592)(401,591)(402,590)(403,589)(404,588)(405,587)(406,586)(407,585)
(408,573)(409,583)(410,582)(411,581)(412,580)(413,579)(414,578)(415,577)
(416,576)(417,575)(418,574)(419,606)(420,616)(421,615)(422,614)(423,613)
(424,612)(425,611)(426,610)(427,609)(428,608)(429,607)(430,595)(431,605)
(432,604)(433,603)(434,602)(435,601)(436,600)(437,599)(438,598)(439,597)
(440,596)(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)(485,661)(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, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 57)( 46, 56)( 47, 66)
( 48, 65)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)
( 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)(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)
(140,171)(141,170)(142,169)(143,168)(144,156)(145,155)(146,165)(147,164)
(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157)(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)(199,244)(200,243)(201,253)
(202,252)(203,251)(204,250)(205,249)(206,248)(207,247)(208,246)(209,245)
(210,255)(211,254)(212,264)(213,263)(214,262)(215,261)(216,260)(217,259)
(218,258)(219,257)(220,256)(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)(375,464)(376,463)(377,473)
(378,472)(379,471)(380,470)(381,469)(382,468)(383,467)(384,466)(385,465)
(386,475)(387,474)(388,484)(389,483)(390,482)(391,481)(392,480)(393,479)
(394,478)(395,477)(396,476)(397,497)(398,496)(399,506)(400,505)(401,504)
(402,503)(403,502)(404,501)(405,500)(406,499)(407,498)(408,486)(409,485)
(410,495)(411,494)(412,493)(413,492)(414,491)(415,490)(416,489)(417,488)
(418,487)(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)(551,695)(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)(573,629)(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)(595,651)(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)( 23,375)
( 24,376)( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)
( 32,384)( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)
( 40,392)( 41,393)( 42,394)( 43,395)( 44,396)( 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)( 67,430)( 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)(133,518)(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)(199,551)
(200,552)(201,553)(202,554)(203,555)(204,556)(205,557)(206,558)(207,559)
(208,560)(209,561)(210,562)(211,563)(212,564)(213,565)(214,566)(215,567)
(216,568)(217,569)(218,570)(219,571)(220,572)(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)(243,606)(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)(309,694)(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,
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*s2*s1*s0*s1*s0*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 >;
References : None.
to this polytope