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Polytope of Type {22,32}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,32}*1408
Also Known As : {22,32|2}. if this polytope has another name.
Group : SmallGroup(1408,6806)
Rank : 3
Schlafli Type : {22,32}
Number of vertices, edges, etc : 22, 352, 32
Order of s0s1s2 : 352
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 : {22,16}*704
   4-fold quotients : {22,8}*352
   8-fold quotients : {22,4}*176
   11-fold quotients : {2,32}*128
   16-fold quotients : {22,2}*88
   22-fold quotients : {2,16}*64
   32-fold quotients : {11,2}*44
   44-fold quotients : {2,8}*32
   88-fold quotients : {2,4}*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 := (  1,178)(  2,177)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)(  8,182)
(  9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)( 16,196)
( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,211)( 24,210)
( 25,220)( 26,219)( 27,218)( 28,217)( 29,216)( 30,215)( 31,214)( 32,213)
( 33,212)( 34,200)( 35,199)( 36,209)( 37,208)( 38,207)( 39,206)( 40,205)
( 41,204)( 42,203)( 43,202)( 44,201)( 45,244)( 46,243)( 47,253)( 48,252)
( 49,251)( 50,250)( 51,249)( 52,248)( 53,247)( 54,246)( 55,245)( 56,255)
( 57,254)( 58,264)( 59,263)( 60,262)( 61,261)( 62,260)( 63,259)( 64,258)
( 65,257)( 66,256)( 67,222)( 68,221)( 69,231)( 70,230)( 71,229)( 72,228)
( 73,227)( 74,226)( 75,225)( 76,224)( 77,223)( 78,233)( 79,232)( 80,242)
( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)( 88,234)
( 89,310)( 90,309)( 91,319)( 92,318)( 93,317)( 94,316)( 95,315)( 96,314)
( 97,313)( 98,312)( 99,311)(100,321)(101,320)(102,330)(103,329)(104,328)
(105,327)(106,326)(107,325)(108,324)(109,323)(110,322)(111,343)(112,342)
(113,352)(114,351)(115,350)(116,349)(117,348)(118,347)(119,346)(120,345)
(121,344)(122,332)(123,331)(124,341)(125,340)(126,339)(127,338)(128,337)
(129,336)(130,335)(131,334)(132,333)(133,266)(134,265)(135,275)(136,274)
(137,273)(138,272)(139,271)(140,270)(141,269)(142,268)(143,267)(144,277)
(145,276)(146,286)(147,285)(148,284)(149,283)(150,282)(151,281)(152,280)
(153,279)(154,278)(155,299)(156,298)(157,308)(158,307)(159,306)(160,305)
(161,304)(162,303)(163,302)(164,301)(165,300)(166,288)(167,287)(168,297)
(169,296)(170,295)(171,294)(172,293)(173,292)(174,291)(175,290)(176,289)
(353,618)(354,617)(355,627)(356,626)(357,625)(358,624)(359,623)(360,622)
(361,621)(362,620)(363,619)(364,629)(365,628)(366,638)(367,637)(368,636)
(369,635)(370,634)(371,633)(372,632)(373,631)(374,630)(375,651)(376,650)
(377,660)(378,659)(379,658)(380,657)(381,656)(382,655)(383,654)(384,653)
(385,652)(386,640)(387,639)(388,649)(389,648)(390,647)(391,646)(392,645)
(393,644)(394,643)(395,642)(396,641)(397,684)(398,683)(399,693)(400,692)
(401,691)(402,690)(403,689)(404,688)(405,687)(406,686)(407,685)(408,695)
(409,694)(410,704)(411,703)(412,702)(413,701)(414,700)(415,699)(416,698)
(417,697)(418,696)(419,662)(420,661)(421,671)(422,670)(423,669)(424,668)
(425,667)(426,666)(427,665)(428,664)(429,663)(430,673)(431,672)(432,682)
(433,681)(434,680)(435,679)(436,678)(437,677)(438,676)(439,675)(440,674)
(441,530)(442,529)(443,539)(444,538)(445,537)(446,536)(447,535)(448,534)
(449,533)(450,532)(451,531)(452,541)(453,540)(454,550)(455,549)(456,548)
(457,547)(458,546)(459,545)(460,544)(461,543)(462,542)(463,563)(464,562)
(465,572)(466,571)(467,570)(468,569)(469,568)(470,567)(471,566)(472,565)
(473,564)(474,552)(475,551)(476,561)(477,560)(478,559)(479,558)(480,557)
(481,556)(482,555)(483,554)(484,553)(485,596)(486,595)(487,605)(488,604)
(489,603)(490,602)(491,601)(492,600)(493,599)(494,598)(495,597)(496,607)
(497,606)(498,616)(499,615)(500,614)(501,613)(502,612)(503,611)(504,610)
(505,609)(506,608)(507,574)(508,573)(509,583)(510,582)(511,581)(512,580)
(513,579)(514,578)(515,577)(516,576)(517,575)(518,585)(519,584)(520,594)
(521,593)(522,592)(523,591)(524,590)(525,589)(526,588)(527,587)(528,586);;
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)( 45,419)( 46,420)( 47,421)( 48,422)
( 49,423)( 50,424)( 51,425)( 52,426)( 53,427)( 54,428)( 55,429)( 56,430)
( 57,431)( 58,432)( 59,433)( 60,434)( 61,435)( 62,436)( 63,437)( 64,438)
( 65,439)( 66,440)( 67,397)( 68,398)( 69,399)( 70,400)( 71,401)( 72,402)
( 73,403)( 74,404)( 75,405)( 76,406)( 77,407)( 78,408)( 79,409)( 80,410)
( 81,411)( 82,412)( 83,413)( 84,414)( 85,415)( 86,416)( 87,417)( 88,418)
( 89,485)( 90,486)( 91,487)( 92,488)( 93,489)( 94,490)( 95,491)( 96,492)
( 97,493)( 98,494)( 99,495)(100,496)(101,497)(102,498)(103,499)(104,500)
(105,501)(106,502)(107,503)(108,504)(109,505)(110,506)(111,518)(112,519)
(113,520)(114,521)(115,522)(116,523)(117,524)(118,525)(119,526)(120,527)
(121,528)(122,507)(123,508)(124,509)(125,510)(126,511)(127,512)(128,513)
(129,514)(130,515)(131,516)(132,517)(133,441)(134,442)(135,443)(136,444)
(137,445)(138,446)(139,447)(140,448)(141,449)(142,450)(143,451)(144,452)
(145,453)(146,454)(147,455)(148,456)(149,457)(150,458)(151,459)(152,460)
(153,461)(154,462)(155,474)(156,475)(157,476)(158,477)(159,478)(160,479)
(161,480)(162,481)(163,482)(164,483)(165,484)(166,463)(167,464)(168,465)
(169,466)(170,467)(171,468)(172,469)(173,470)(174,471)(175,472)(176,473)
(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)(221,595)(222,596)(223,597)(224,598)
(225,599)(226,600)(227,601)(228,602)(229,603)(230,604)(231,605)(232,606)
(233,607)(234,608)(235,609)(236,610)(237,611)(238,612)(239,613)(240,614)
(241,615)(242,616)(243,573)(244,574)(245,575)(246,576)(247,577)(248,578)
(249,579)(250,580)(251,581)(252,582)(253,583)(254,584)(255,585)(256,586)
(257,587)(258,588)(259,589)(260,590)(261,591)(262,592)(263,593)(264,594)
(265,661)(266,662)(267,663)(268,664)(269,665)(270,666)(271,667)(272,668)
(273,669)(274,670)(275,671)(276,672)(277,673)(278,674)(279,675)(280,676)
(281,677)(282,678)(283,679)(284,680)(285,681)(286,682)(287,694)(288,695)
(289,696)(290,697)(291,698)(292,699)(293,700)(294,701)(295,702)(296,703)
(297,704)(298,683)(299,684)(300,685)(301,686)(302,687)(303,688)(304,689)
(305,690)(306,691)(307,692)(308,693)(309,617)(310,618)(311,619)(312,620)
(313,621)(314,622)(315,623)(316,624)(317,625)(318,626)(319,627)(320,628)
(321,629)(322,630)(323,631)(324,632)(325,633)(326,634)(327,635)(328,636)
(329,637)(330,638)(331,650)(332,651)(333,652)(334,653)(335,654)(336,655)
(337,656)(338,657)(339,658)(340,659)(341,660)(342,639)(343,640)(344,641)
(345,642)(346,643)(347,644)(348,645)(349,646)(350,647)(351,648)(352,649);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 ];;
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)!(  1,178)(  2,177)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)
(  8,182)(  9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)
( 16,196)( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,211)
( 24,210)( 25,220)( 26,219)( 27,218)( 28,217)( 29,216)( 30,215)( 31,214)
( 32,213)( 33,212)( 34,200)( 35,199)( 36,209)( 37,208)( 38,207)( 39,206)
( 40,205)( 41,204)( 42,203)( 43,202)( 44,201)( 45,244)( 46,243)( 47,253)
( 48,252)( 49,251)( 50,250)( 51,249)( 52,248)( 53,247)( 54,246)( 55,245)
( 56,255)( 57,254)( 58,264)( 59,263)( 60,262)( 61,261)( 62,260)( 63,259)
( 64,258)( 65,257)( 66,256)( 67,222)( 68,221)( 69,231)( 70,230)( 71,229)
( 72,228)( 73,227)( 74,226)( 75,225)( 76,224)( 77,223)( 78,233)( 79,232)
( 80,242)( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)
( 88,234)( 89,310)( 90,309)( 91,319)( 92,318)( 93,317)( 94,316)( 95,315)
( 96,314)( 97,313)( 98,312)( 99,311)(100,321)(101,320)(102,330)(103,329)
(104,328)(105,327)(106,326)(107,325)(108,324)(109,323)(110,322)(111,343)
(112,342)(113,352)(114,351)(115,350)(116,349)(117,348)(118,347)(119,346)
(120,345)(121,344)(122,332)(123,331)(124,341)(125,340)(126,339)(127,338)
(128,337)(129,336)(130,335)(131,334)(132,333)(133,266)(134,265)(135,275)
(136,274)(137,273)(138,272)(139,271)(140,270)(141,269)(142,268)(143,267)
(144,277)(145,276)(146,286)(147,285)(148,284)(149,283)(150,282)(151,281)
(152,280)(153,279)(154,278)(155,299)(156,298)(157,308)(158,307)(159,306)
(160,305)(161,304)(162,303)(163,302)(164,301)(165,300)(166,288)(167,287)
(168,297)(169,296)(170,295)(171,294)(172,293)(173,292)(174,291)(175,290)
(176,289)(353,618)(354,617)(355,627)(356,626)(357,625)(358,624)(359,623)
(360,622)(361,621)(362,620)(363,619)(364,629)(365,628)(366,638)(367,637)
(368,636)(369,635)(370,634)(371,633)(372,632)(373,631)(374,630)(375,651)
(376,650)(377,660)(378,659)(379,658)(380,657)(381,656)(382,655)(383,654)
(384,653)(385,652)(386,640)(387,639)(388,649)(389,648)(390,647)(391,646)
(392,645)(393,644)(394,643)(395,642)(396,641)(397,684)(398,683)(399,693)
(400,692)(401,691)(402,690)(403,689)(404,688)(405,687)(406,686)(407,685)
(408,695)(409,694)(410,704)(411,703)(412,702)(413,701)(414,700)(415,699)
(416,698)(417,697)(418,696)(419,662)(420,661)(421,671)(422,670)(423,669)
(424,668)(425,667)(426,666)(427,665)(428,664)(429,663)(430,673)(431,672)
(432,682)(433,681)(434,680)(435,679)(436,678)(437,677)(438,676)(439,675)
(440,674)(441,530)(442,529)(443,539)(444,538)(445,537)(446,536)(447,535)
(448,534)(449,533)(450,532)(451,531)(452,541)(453,540)(454,550)(455,549)
(456,548)(457,547)(458,546)(459,545)(460,544)(461,543)(462,542)(463,563)
(464,562)(465,572)(466,571)(467,570)(468,569)(469,568)(470,567)(471,566)
(472,565)(473,564)(474,552)(475,551)(476,561)(477,560)(478,559)(479,558)
(480,557)(481,556)(482,555)(483,554)(484,553)(485,596)(486,595)(487,605)
(488,604)(489,603)(490,602)(491,601)(492,600)(493,599)(494,598)(495,597)
(496,607)(497,606)(498,616)(499,615)(500,614)(501,613)(502,612)(503,611)
(504,610)(505,609)(506,608)(507,574)(508,573)(509,583)(510,582)(511,581)
(512,580)(513,579)(514,578)(515,577)(516,576)(517,575)(518,585)(519,584)
(520,594)(521,593)(522,592)(523,591)(524,590)(525,589)(526,588)(527,587)
(528,586);
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)( 45,419)( 46,420)( 47,421)
( 48,422)( 49,423)( 50,424)( 51,425)( 52,426)( 53,427)( 54,428)( 55,429)
( 56,430)( 57,431)( 58,432)( 59,433)( 60,434)( 61,435)( 62,436)( 63,437)
( 64,438)( 65,439)( 66,440)( 67,397)( 68,398)( 69,399)( 70,400)( 71,401)
( 72,402)( 73,403)( 74,404)( 75,405)( 76,406)( 77,407)( 78,408)( 79,409)
( 80,410)( 81,411)( 82,412)( 83,413)( 84,414)( 85,415)( 86,416)( 87,417)
( 88,418)( 89,485)( 90,486)( 91,487)( 92,488)( 93,489)( 94,490)( 95,491)
( 96,492)( 97,493)( 98,494)( 99,495)(100,496)(101,497)(102,498)(103,499)
(104,500)(105,501)(106,502)(107,503)(108,504)(109,505)(110,506)(111,518)
(112,519)(113,520)(114,521)(115,522)(116,523)(117,524)(118,525)(119,526)
(120,527)(121,528)(122,507)(123,508)(124,509)(125,510)(126,511)(127,512)
(128,513)(129,514)(130,515)(131,516)(132,517)(133,441)(134,442)(135,443)
(136,444)(137,445)(138,446)(139,447)(140,448)(141,449)(142,450)(143,451)
(144,452)(145,453)(146,454)(147,455)(148,456)(149,457)(150,458)(151,459)
(152,460)(153,461)(154,462)(155,474)(156,475)(157,476)(158,477)(159,478)
(160,479)(161,480)(162,481)(163,482)(164,483)(165,484)(166,463)(167,464)
(168,465)(169,466)(170,467)(171,468)(172,469)(173,470)(174,471)(175,472)
(176,473)(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)(221,595)(222,596)(223,597)
(224,598)(225,599)(226,600)(227,601)(228,602)(229,603)(230,604)(231,605)
(232,606)(233,607)(234,608)(235,609)(236,610)(237,611)(238,612)(239,613)
(240,614)(241,615)(242,616)(243,573)(244,574)(245,575)(246,576)(247,577)
(248,578)(249,579)(250,580)(251,581)(252,582)(253,583)(254,584)(255,585)
(256,586)(257,587)(258,588)(259,589)(260,590)(261,591)(262,592)(263,593)
(264,594)(265,661)(266,662)(267,663)(268,664)(269,665)(270,666)(271,667)
(272,668)(273,669)(274,670)(275,671)(276,672)(277,673)(278,674)(279,675)
(280,676)(281,677)(282,678)(283,679)(284,680)(285,681)(286,682)(287,694)
(288,695)(289,696)(290,697)(291,698)(292,699)(293,700)(294,701)(295,702)
(296,703)(297,704)(298,683)(299,684)(300,685)(301,686)(302,687)(303,688)
(304,689)(305,690)(306,691)(307,692)(308,693)(309,617)(310,618)(311,619)
(312,620)(313,621)(314,622)(315,623)(316,624)(317,625)(318,626)(319,627)
(320,628)(321,629)(322,630)(323,631)(324,632)(325,633)(326,634)(327,635)
(328,636)(329,637)(330,638)(331,650)(332,651)(333,652)(334,653)(335,654)
(336,655)(337,656)(338,657)(339,658)(340,659)(341,660)(342,639)(343,640)
(344,641)(345,642)(346,643)(347,644)(348,645)(349,646)(350,647)(351,648)
(352,649);
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 >; 
 
References : None.
to this polytope