Polytope of Type {8,44}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,44}*1408a
if this polytope has a name.
Group : SmallGroup(1408,3429)
Rank : 3
Schlafli Type : {8,44}
Number of vertices, edges, etc : 16, 352, 88
Order of s0s1s2 : 88
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,44}*704, {8,44}*704a, {8,44}*704b
   4-fold quotients : {4,44}*352, {8,22}*352
   8-fold quotients : {2,44}*176, {4,22}*176
   11-fold quotients : {8,4}*128a
   16-fold quotients : {2,22}*88
   22-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   32-fold quotients : {2,11}*44
   44-fold quotients : {4,4}*32, {8,2}*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.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      44 facets:
         44 of {8}*16
      12 vertex figures:
         8 of {22}*44
         4 of {44}*88

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

Twisty Puzzle