Polytope of Type {4,176}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,176}*1408b
if this polytope has a name.
Group : SmallGroup(1408,6458)
Rank : 3
Schlafli Type : {4,176}
Number of vertices, edges, etc : 4, 352, 176
Order of s0s1s2 : 176
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
4-fold quotients : {4,44}*352, {2,88}*352
8-fold quotients : {2,44}*176, {4,22}*176
11-fold quotients : {4,16}*128b
16-fold quotients : {2,22}*88
22-fold quotients : {4,8}*64a
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)( 45,221)( 46,222)( 47,223)( 48,224)
( 49,225)( 50,226)( 51,227)( 52,228)( 53,229)( 54,230)( 55,231)( 56,232)
( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)( 64,240)
( 65,241)( 66,242)( 67,243)( 68,244)( 69,245)( 70,246)( 71,247)( 72,248)
( 73,249)( 74,250)( 75,251)( 76,252)( 77,253)( 78,254)( 79,255)( 80,256)
( 81,257)( 82,258)( 83,259)( 84,260)( 85,261)( 86,262)( 87,263)( 88,264)
( 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)(133,320)(134,321)(135,322)(136,323)
(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)(144,309)
(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)(152,317)
(153,318)(154,319)(155,342)(156,343)(157,344)(158,345)(159,346)(160,347)
(161,348)(162,349)(163,350)(164,351)(165,352)(166,331)(167,332)(168,333)
(169,334)(170,335)(171,336)(172,337)(173,338)(174,339)(175,340)(176,341)
(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)(397,573)(398,574)(399,575)(400,576)
(401,577)(402,578)(403,579)(404,580)(405,581)(406,582)(407,583)(408,584)
(409,585)(410,586)(411,587)(412,588)(413,589)(414,590)(415,591)(416,592)
(417,593)(418,594)(419,595)(420,596)(421,597)(422,598)(423,599)(424,600)
(425,601)(426,602)(427,603)(428,604)(429,605)(430,606)(431,607)(432,608)
(433,609)(434,610)(435,611)(436,612)(437,613)(438,614)(439,615)(440,616)
(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)(485,672)(486,673)(487,674)(488,675)
(489,676)(490,677)(491,678)(492,679)(493,680)(494,681)(495,682)(496,661)
(497,662)(498,663)(499,664)(500,665)(501,666)(502,667)(503,668)(504,669)
(505,670)(506,671)(507,694)(508,695)(509,696)(510,697)(511,698)(512,699)
(513,700)(514,701)(515,702)(516,703)(517,704)(518,683)(519,684)(520,685)
(521,686)(522,687)(523,688)(524,689)(525,690)(526,691)(527,692)(528,693);;
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)(529,672)(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)(551,683)(552,693)(553,692)(554,691)
(555,690)(556,689)(557,688)(558,687)(559,686)(560,685)(561,684)(562,694)
(563,704)(564,703)(565,702)(566,701)(567,700)(568,699)(569,698)(570,697)
(571,696)(572,695)(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)
(595,639)(596,649)(597,648)(598,647)(599,646)(600,645)(601,644)(602,643)
(603,642)(604,641)(605,640)(606,650)(607,660)(608,659)(609,658)(610,657)
(611,656)(612,655)(613,654)(614,653)(615,652)(616,651);;
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)( 23,387)( 24,386)
( 25,396)( 26,395)( 27,394)( 28,393)( 29,392)( 30,391)( 31,390)( 32,389)
( 33,388)( 34,376)( 35,375)( 36,385)( 37,384)( 38,383)( 39,382)( 40,381)
( 41,380)( 42,379)( 43,378)( 44,377)( 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)( 67,420)( 68,419)( 69,429)( 70,428)( 71,427)( 72,426)
( 73,425)( 74,424)( 75,423)( 76,422)( 77,421)( 78,431)( 79,430)( 80,440)
( 81,439)( 82,438)( 83,437)( 84,436)( 85,435)( 86,434)( 87,433)( 88,432)
( 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)(199,563)(200,562)
(201,572)(202,571)(203,570)(204,569)(205,568)(206,567)(207,566)(208,565)
(209,564)(210,552)(211,551)(212,561)(213,560)(214,559)(215,558)(216,557)
(217,556)(218,555)(219,554)(220,553)(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)(243,596)(244,595)(245,605)(246,604)(247,603)(248,602)
(249,601)(250,600)(251,599)(252,598)(253,597)(254,607)(255,606)(256,616)
(257,615)(258,614)(259,613)(260,612)(261,611)(262,610)(263,609)(264,608)
(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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*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*s0*s1*s2*s1 ];;
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)( 45,221)( 46,222)( 47,223)
( 48,224)( 49,225)( 50,226)( 51,227)( 52,228)( 53,229)( 54,230)( 55,231)
( 56,232)( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)
( 64,240)( 65,241)( 66,242)( 67,243)( 68,244)( 69,245)( 70,246)( 71,247)
( 72,248)( 73,249)( 74,250)( 75,251)( 76,252)( 77,253)( 78,254)( 79,255)
( 80,256)( 81,257)( 82,258)( 83,259)( 84,260)( 85,261)( 86,262)( 87,263)
( 88,264)( 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)(133,320)(134,321)(135,322)
(136,323)(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)
(144,309)(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)
(152,317)(153,318)(154,319)(155,342)(156,343)(157,344)(158,345)(159,346)
(160,347)(161,348)(162,349)(163,350)(164,351)(165,352)(166,331)(167,332)
(168,333)(169,334)(170,335)(171,336)(172,337)(173,338)(174,339)(175,340)
(176,341)(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)(397,573)(398,574)(399,575)
(400,576)(401,577)(402,578)(403,579)(404,580)(405,581)(406,582)(407,583)
(408,584)(409,585)(410,586)(411,587)(412,588)(413,589)(414,590)(415,591)
(416,592)(417,593)(418,594)(419,595)(420,596)(421,597)(422,598)(423,599)
(424,600)(425,601)(426,602)(427,603)(428,604)(429,605)(430,606)(431,607)
(432,608)(433,609)(434,610)(435,611)(436,612)(437,613)(438,614)(439,615)
(440,616)(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)(485,672)(486,673)(487,674)
(488,675)(489,676)(490,677)(491,678)(492,679)(493,680)(494,681)(495,682)
(496,661)(497,662)(498,663)(499,664)(500,665)(501,666)(502,667)(503,668)
(504,669)(505,670)(506,671)(507,694)(508,695)(509,696)(510,697)(511,698)
(512,699)(513,700)(514,701)(515,702)(516,703)(517,704)(518,683)(519,684)
(520,685)(521,686)(522,687)(523,688)(524,689)(525,690)(526,691)(527,692)
(528,693);
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)(529,672)
(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)(551,683)(552,693)(553,692)
(554,691)(555,690)(556,689)(557,688)(558,687)(559,686)(560,685)(561,684)
(562,694)(563,704)(564,703)(565,702)(566,701)(567,700)(568,699)(569,698)
(570,697)(571,696)(572,695)(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)(595,639)(596,649)(597,648)(598,647)(599,646)(600,645)(601,644)
(602,643)(603,642)(604,641)(605,640)(606,650)(607,660)(608,659)(609,658)
(610,657)(611,656)(612,655)(613,654)(614,653)(615,652)(616,651);
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)( 23,387)
( 24,386)( 25,396)( 26,395)( 27,394)( 28,393)( 29,392)( 30,391)( 31,390)
( 32,389)( 33,388)( 34,376)( 35,375)( 36,385)( 37,384)( 38,383)( 39,382)
( 40,381)( 41,380)( 42,379)( 43,378)( 44,377)( 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)( 67,420)( 68,419)( 69,429)( 70,428)( 71,427)
( 72,426)( 73,425)( 74,424)( 75,423)( 76,422)( 77,421)( 78,431)( 79,430)
( 80,440)( 81,439)( 82,438)( 83,437)( 84,436)( 85,435)( 86,434)( 87,433)
( 88,432)( 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)(199,563)
(200,562)(201,572)(202,571)(203,570)(204,569)(205,568)(206,567)(207,566)
(208,565)(209,564)(210,552)(211,551)(212,561)(213,560)(214,559)(215,558)
(216,557)(217,556)(218,555)(219,554)(220,553)(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)(243,596)(244,595)(245,605)(246,604)(247,603)
(248,602)(249,601)(250,600)(251,599)(252,598)(253,597)(254,607)(255,606)
(256,616)(257,615)(258,614)(259,613)(260,612)(261,611)(262,610)(263,609)
(264,608)(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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*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*s0*s1*s2*s1 >;
References : None.
to this polytope