Polytope of Type {32,30}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,30}*1920
Also Known As : {32,30|2}. if this polytope has another name.
Group : SmallGroup(1920,44837)
Rank : 3
Schlafli Type : {32,30}
Number of vertices, edges, etc : 32, 480, 30
Order of s0s1s2 : 480
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 : {16,30}*960
   3-fold quotients : {32,10}*640
   4-fold quotients : {8,30}*480
   5-fold quotients : {32,6}*384
   6-fold quotients : {16,10}*320
   8-fold quotients : {4,30}*240a
   10-fold quotients : {16,6}*192
   12-fold quotients : {8,10}*160
   15-fold quotients : {32,2}*128
   16-fold quotients : {2,30}*120
   20-fold quotients : {8,6}*96
   24-fold quotients : {4,10}*80
   30-fold quotients : {16,2}*64
   32-fold quotients : {2,15}*60
   40-fold quotients : {4,6}*48a
   48-fold quotients : {2,10}*40
   60-fold quotients : {8,2}*32
   80-fold quotients : {2,6}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {4,2}*16
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := ( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 98)( 69, 99)( 70,100)( 71,101)( 72,102)( 73,103)( 74,104)( 75,105)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,113)( 84,114)( 85,115)( 86,116)( 87,117)( 88,118)( 89,119)( 90,120)(121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)(129,189)(130,190)(131,191)(132,192)(133,193)(134,194)(135,195)(136,196)(137,197)(138,198)(139,199)(140,200)(141,201)(142,202)(143,203)(144,204)(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,226)(152,227)(153,228)(154,229)(155,230)(156,231)(157,232)(158,233)(159,234)(160,235)(161,236)(162,237)(163,238)(164,239)(165,240)(166,211)(167,212)(168,213)(169,214)(170,215)(171,216)(172,217)(173,218)(174,219)(175,220)(176,221)(177,222)(178,223)(179,224)(180,225)(271,286)(272,287)(273,288)(274,289)(275,290)(276,291)(277,292)(278,293)(279,294)(280,295)(281,296)(282,297)(283,298)(284,299)(285,300)(301,331)(302,332)(303,333)(304,334)(305,335)(306,336)(307,337)(308,338)(309,339)(310,340)(311,341)(312,342)(313,343)(314,344)(315,345)(316,346)(317,347)(318,348)(319,349)(320,350)(321,351)(322,352)(323,353)(324,354)(325,355)(326,356)(327,357)(328,358)(329,359)(330,360)(361,421)(362,422)(363,423)(364,424)(365,425)(366,426)(367,427)(368,428)(369,429)(370,430)(371,431)(372,432)(373,433)(374,434)(375,435)(376,436)(377,437)(378,438)(379,439)(380,440)(381,441)(382,442)(383,443)(384,444)(385,445)(386,446)(387,447)(388,448)(389,449)(390,450)(391,466)(392,467)(393,468)(394,469)(395,470)(396,471)(397,472)(398,473)(399,474)(400,475)(401,476)(402,477)(403,478)(404,479)(405,480)(406,451)(407,452)(408,453)(409,454)(410,455)(411,456)(412,457)(413,458)(414,459)(415,460)(416,461)(417,462)(418,463)(419,464)(420,465)(481,601)(482,602)(483,603)(484,604)(485,605)(486,606)(487,607)(488,608)(489,609)(490,610)(491,611)(492,612)(493,613)(494,614)(495,615)(496,616)(497,617)(498,618)(499,619)(500,620)(501,621)(502,622)(503,623)(504,624)(505,625)(506,626)(507,627)(508,628)(509,629)(510,630)(511,646)(512,647)(513,648)(514,649)(515,650)(516,651)(517,652)(518,653)(519,654)(520,655)(521,656)(522,657)(523,658)(524,659)(525,660)(526,631)(527,632)(528,633)(529,634)(530,635)(531,636)(532,637)(533,638)(534,639)(535,640)(536,641)(537,642)(538,643)(539,644)(540,645)(541,691)(542,692)(543,693)(544,694)(545,695)(546,696)(547,697)(548,698)(549,699)(550,700)(551,701)(552,702)(553,703)(554,704)(555,705)(556,706)(557,707)(558,708)(559,709)(560,710)(561,711)(562,712)(563,713)(564,714)(565,715)(566,716)(567,717)(568,718)(569,719)(570,720)(571,661)(572,662)(573,663)(574,664)(575,665)(576,666)(577,667)(578,668)(579,669)(580,670)(581,671)(582,672)(583,673)(584,674)(585,675)(586,676)(587,677)(588,678)(589,679)(590,680)(591,681)(592,682)(593,683)(594,684)(595,685)(596,686)(597,687)(598,688)(599,689)(600,690)(721,841)(722,842)(723,843)(724,844)(725,845)(726,846)(727,847)(728,848)(729,849)(730,850)(731,851)(732,852)(733,853)(734,854)(735,855)(736,856)(737,857)(738,858)(739,859)(740,860)(741,861)(742,862)(743,863)(744,864)(745,865)(746,866)(747,867)(748,868)(749,869)(750,870)(751,886)(752,887)(753,888)(754,889)(755,890)(756,891)(757,892)(758,893)(759,894)(760,895)(761,896)(762,897)(763,898)(764,899)(765,900)(766,871)(767,872)(768,873)(769,874)(770,875)(771,876)(772,877)(773,878)(774,879)(775,880)(776,881)(777,882)(778,883)(779,884)(780,885)(781,931)(782,932)(783,933)(784,934)(785,935)(786,936)(787,937)(788,938)(789,939)(790,940)(791,941)(792,942)(793,943)(794,944)(795,945)(796,946)(797,947)(798,948)(799,949)(800,950)(801,951)(802,952)(803,953)(804,954)(805,955)(806,956)(807,957)(808,958)(809,959)(810,960)(811,901)(812,902)(813,903)(814,904)(815,905)(816,906)(817,907)(818,908)(819,909)(820,910)(821,911)(822,912)(823,913)(824,914)(825,915)(826,916)(827,917)(828,918)(829,919)(830,920)(831,921)(832,922)(833,923)(834,924)(835,925)(836,926)(837,927)(838,928)(839,929)(840,930);;
s1 := (  1,721)(  2,725)(  3,724)(  4,723)(  5,722)(  6,731)(  7,735)(  8,734)(  9,733)( 10,732)( 11,726)( 12,730)( 13,729)( 14,728)( 15,727)( 16,736)( 17,740)( 18,739)( 19,738)( 20,737)
( 21,746)( 22,750)( 23,749)( 24,748)( 25,747)( 26,741)( 27,745)( 28,744)( 29,743)( 30,742)( 31,766)( 32,770)( 33,769)( 34,768)( 35,767)( 36,776)( 37,780)( 38,779)( 39,778)( 40,777)( 41,771)( 42,775)( 43,774)( 44,773)( 45,772)( 46,751)( 47,755)( 48,754)( 49,753)( 50,752)( 51,761)( 52,765)( 53,764)( 54,763)( 55,762)( 56,756)( 57,760)( 58,759)( 59,758)( 60,757)( 61,811)( 62,815)( 63,814)( 64,813)( 65,812)( 66,821)( 67,825)( 68,824)( 69,823)( 70,822)( 71,816)( 72,820)( 73,819)( 74,818)( 75,817)( 76,826)( 77,830)( 78,829)( 79,828)( 80,827)( 81,836)( 82,840)( 83,839)( 84,838)( 85,837)( 86,831)( 87,835)( 88,834)( 89,833)( 90,832)( 91,781)( 92,785)( 93,784)( 94,783)( 95,782)( 96,791)( 97,795)( 98,794)( 99,793)(100,792)(101,786)(102,790)(103,789)(104,788)(105,787)(106,796)(107,800)(108,799)(109,798)(110,797)(111,806)(112,810)(113,809)(114,808)(115,807)(116,801)(117,805)(118,804)(119,803)(120,802)(121,901)(122,905)(123,904)(124,903)(125,902)(126,911)(127,915)(128,914)(129,913)(130,912)(131,906)(132,910)(133,909)(134,908)(135,907)(136,916)(137,920)(138,919)(139,918)(140,917)(141,926)(142,930)(143,929)(144,928)(145,927)(146,921)(147,925)(148,924)(149,923)(150,922)(151,946)(152,950)(153,949)(154,948)(155,947)(156,956)(157,960)(158,959)(159,958)(160,957)(161,951)(162,955)(163,954)(164,953)(165,952)(166,931)(167,935)(168,934)(169,933)(170,932)(171,941)(172,945)(173,944)(174,943)(175,942)(176,936)(177,940)(178,939)(179,938)(180,937)(181,841)(182,845)(183,844)(184,843)(185,842)(186,851)(187,855)(188,854)(189,853)(190,852)(191,846)(192,850)(193,849)(194,848)(195,847)(196,856)(197,860)(198,859)(199,858)(200,857)(201,866)(202,870)(203,869)(204,868)(205,867)(206,861)(207,865)(208,864)(209,863)(210,862)(211,886)(212,890)(213,889)(214,888)(215,887)(216,896)(217,900)(218,899)(219,898)(220,897)(221,891)(222,895)(223,894)(224,893)(225,892)(226,871)(227,875)(228,874)(229,873)(230,872)(231,881)(232,885)(233,884)(234,883)(235,882)(236,876)(237,880)(238,879)(239,878)(240,877)(241,481)(242,485)(243,484)(244,483)(245,482)(246,491)(247,495)(248,494)(249,493)(250,492)(251,486)(252,490)(253,489)(254,488)(255,487)(256,496)(257,500)(258,499)(259,498)(260,497)(261,506)(262,510)(263,509)(264,508)(265,507)(266,501)(267,505)(268,504)(269,503)(270,502)(271,526)(272,530)(273,529)(274,528)(275,527)(276,536)(277,540)(278,539)(279,538)(280,537)(281,531)(282,535)(283,534)(284,533)(285,532)(286,511)(287,515)(288,514)(289,513)(290,512)(291,521)(292,525)(293,524)(294,523)(295,522)(296,516)(297,520)(298,519)(299,518)(300,517)(301,571)(302,575)(303,574)(304,573)(305,572)(306,581)(307,585)(308,584)(309,583)(310,582)(311,576)(312,580)(313,579)(314,578)(315,577)(316,586)(317,590)(318,589)(319,588)(320,587)(321,596)(322,600)(323,599)(324,598)(325,597)(326,591)(327,595)(328,594)(329,593)(330,592)(331,541)(332,545)(333,544)(334,543)(335,542)(336,551)(337,555)(338,554)(339,553)(340,552)(341,546)(342,550)(343,549)(344,548)(345,547)(346,556)(347,560)(348,559)(349,558)(350,557)(351,566)(352,570)(353,569)(354,568)(355,567)(356,561)(357,565)(358,564)(359,563)(360,562)(361,661)(362,665)(363,664)(364,663)(365,662)(366,671)(367,675)(368,674)(369,673)(370,672)(371,666)(372,670)(373,669)(374,668)(375,667)(376,676)(377,680)(378,679)(379,678)(380,677)(381,686)(382,690)(383,689)(384,688)(385,687)(386,681)(387,685)(388,684)(389,683)(390,682)(391,706)(392,710)(393,709)(394,708)(395,707)(396,716)(397,720)(398,719)(399,718)(400,717)(401,711)(402,715)(403,714)(404,713)(405,712)(406,691)(407,695)(408,694)(409,693)(410,692)(411,701)(412,705)(413,704)(414,703)(415,702)(416,696)(417,700)(418,699)(419,698)(420,697)(421,601)(422,605)(423,604)(424,603)(425,602)(426,611)(427,615)(428,614)(429,613)(430,612)(431,606)(432,610)(433,609)(434,608)(435,607)(436,616)(437,620)(438,619)(439,618)(440,617)(441,626)(442,630)(443,629)(444,628)(445,627)(446,621)(447,625)(448,624)(449,623)(450,622)(451,646)(452,650)(453,649)(454,648)(455,647)(456,656)(457,660)(458,659)(459,658)(460,657)(461,651)(462,655)(463,654)(464,653)(465,652)(466,631)(467,635)(468,634)(469,633)(470,632)(471,641)(472,645)(473,644)(474,643)
(475,642)(476,636)(477,640)(478,639)(479,638)(480,637);;
s2 := (  1,247)(  2,246)(  3,250)(  4,249)(  5,248)(  6,242)(  7,241)(  8,245)(  9,244)( 10,243)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)( 16,262)( 17,261)( 18,265)( 19,264)( 20,263)
( 21,257)( 22,256)( 23,260)( 24,259)( 25,258)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,277)( 32,276)( 33,280)( 34,279)( 35,278)( 36,272)( 37,271)( 38,275)( 39,274)( 40,273)( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,292)( 47,291)( 48,295)( 49,294)( 50,293)( 51,287)( 52,286)( 53,290)( 54,289)( 55,288)( 56,297)( 57,296)( 58,300)( 59,299)( 60,298)( 61,307)( 62,306)( 63,310)( 64,309)( 65,308)( 66,302)( 67,301)( 68,305)( 69,304)( 70,303)( 71,312)( 72,311)( 73,315)( 74,314)( 75,313)( 76,322)( 77,321)( 78,325)( 79,324)( 80,323)( 81,317)( 82,316)( 83,320)( 84,319)( 85,318)( 86,327)( 87,326)( 88,330)( 89,329)( 90,328)( 91,337)( 92,336)( 93,340)( 94,339)( 95,338)( 96,332)( 97,331)( 98,335)( 99,334)(100,333)(101,342)(102,341)(103,345)(104,344)(105,343)(106,352)(107,351)(108,355)(109,354)(110,353)(111,347)(112,346)(113,350)(114,349)(115,348)(116,357)(117,356)(118,360)(119,359)(120,358)(121,367)(122,366)(123,370)(124,369)(125,368)(126,362)(127,361)(128,365)(129,364)(130,363)(131,372)(132,371)(133,375)(134,374)(135,373)(136,382)(137,381)(138,385)(139,384)(140,383)(141,377)(142,376)(143,380)(144,379)(145,378)(146,387)(147,386)(148,390)(149,389)(150,388)(151,397)(152,396)(153,400)(154,399)(155,398)(156,392)(157,391)(158,395)(159,394)(160,393)(161,402)(162,401)(163,405)(164,404)(165,403)(166,412)(167,411)(168,415)(169,414)(170,413)(171,407)(172,406)(173,410)(174,409)(175,408)(176,417)(177,416)(178,420)(179,419)(180,418)(181,427)(182,426)(183,430)(184,429)(185,428)(186,422)(187,421)(188,425)(189,424)(190,423)(191,432)(192,431)(193,435)(194,434)(195,433)(196,442)(197,441)(198,445)(199,444)(200,443)(201,437)(202,436)(203,440)(204,439)(205,438)(206,447)(207,446)(208,450)(209,449)(210,448)(211,457)(212,456)(213,460)(214,459)(215,458)(216,452)(217,451)(218,455)(219,454)(220,453)(221,462)(222,461)(223,465)(224,464)(225,463)(226,472)(227,471)(228,475)(229,474)(230,473)(231,467)(232,466)(233,470)(234,469)(235,468)(236,477)(237,476)(238,480)(239,479)(240,478)(481,727)(482,726)(483,730)(484,729)(485,728)(486,722)(487,721)(488,725)(489,724)(490,723)(491,732)(492,731)(493,735)(494,734)(495,733)(496,742)(497,741)(498,745)(499,744)(500,743)(501,737)(502,736)(503,740)(504,739)(505,738)(506,747)(507,746)(508,750)(509,749)(510,748)(511,757)(512,756)(513,760)(514,759)(515,758)(516,752)(517,751)(518,755)(519,754)(520,753)(521,762)(522,761)(523,765)(524,764)(525,763)(526,772)(527,771)(528,775)(529,774)(530,773)(531,767)(532,766)(533,770)(534,769)(535,768)(536,777)(537,776)(538,780)(539,779)(540,778)(541,787)(542,786)(543,790)(544,789)(545,788)(546,782)(547,781)(548,785)(549,784)(550,783)(551,792)(552,791)(553,795)(554,794)(555,793)(556,802)(557,801)(558,805)(559,804)(560,803)(561,797)(562,796)(563,800)(564,799)(565,798)(566,807)(567,806)(568,810)(569,809)(570,808)(571,817)(572,816)(573,820)(574,819)(575,818)(576,812)(577,811)(578,815)(579,814)(580,813)(581,822)(582,821)(583,825)(584,824)(585,823)(586,832)(587,831)(588,835)(589,834)(590,833)(591,827)(592,826)(593,830)(594,829)(595,828)(596,837)(597,836)(598,840)(599,839)(600,838)(601,847)(602,846)(603,850)(604,849)(605,848)(606,842)(607,841)(608,845)(609,844)(610,843)(611,852)(612,851)(613,855)(614,854)(615,853)(616,862)(617,861)(618,865)(619,864)(620,863)(621,857)(622,856)(623,860)(624,859)(625,858)(626,867)(627,866)(628,870)(629,869)(630,868)(631,877)(632,876)(633,880)(634,879)(635,878)(636,872)(637,871)(638,875)(639,874)(640,873)(641,882)(642,881)(643,885)(644,884)(645,883)(646,892)(647,891)(648,895)(649,894)(650,893)(651,887)(652,886)(653,890)(654,889)(655,888)(656,897)(657,896)(658,900)(659,899)(660,898)(661,907)(662,906)(663,910)(664,909)(665,908)(666,902)(667,901)(668,905)(669,904)(670,903)(671,912)(672,911)(673,915)(674,914)(675,913)(676,922)(677,921)(678,925)(679,924)(680,923)(681,917)(682,916)(683,920)(684,919)(685,918)(686,927)(687,926)(688,930)(689,929)(690,928)(691,937)(692,936)(693,940)(694,939)(695,938)(696,932)(697,931)(698,935)(699,934)(700,933)(701,942)(702,941)(703,945)(704,944)(705,943)(706,952)(707,951)(708,955)(709,954)(710,953)(711,947)(712,946)(713,950)(714,949)
(715,948)(716,957)(717,956)(718,960)(719,959)(720,958);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(960)!( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 98)( 69, 99)( 70,100)( 71,101)( 72,102)( 73,103)( 74,104)( 75,105)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,113)( 84,114)( 85,115)( 86,116)( 87,117)( 88,118)( 89,119)( 90,120)(121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)(129,189)(130,190)(131,191)(132,192)(133,193)(134,194)(135,195)(136,196)(137,197)(138,198)(139,199)(140,200)(141,201)(142,202)(143,203)(144,204)(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,226)(152,227)(153,228)(154,229)(155,230)(156,231)(157,232)(158,233)(159,234)(160,235)(161,236)(162,237)(163,238)(164,239)(165,240)(166,211)(167,212)(168,213)(169,214)(170,215)(171,216)(172,217)(173,218)(174,219)(175,220)(176,221)(177,222)(178,223)(179,224)(180,225)(271,286)(272,287)(273,288)(274,289)(275,290)(276,291)(277,292)(278,293)(279,294)(280,295)(281,296)(282,297)(283,298)(284,299)(285,300)(301,331)(302,332)(303,333)(304,334)(305,335)(306,336)(307,337)(308,338)(309,339)(310,340)(311,341)(312,342)(313,343)(314,344)(315,345)(316,346)(317,347)(318,348)(319,349)(320,350)(321,351)(322,352)(323,353)(324,354)(325,355)(326,356)(327,357)(328,358)(329,359)(330,360)(361,421)(362,422)(363,423)(364,424)(365,425)(366,426)(367,427)(368,428)(369,429)(370,430)(371,431)(372,432)(373,433)(374,434)(375,435)(376,436)(377,437)(378,438)(379,439)(380,440)(381,441)(382,442)(383,443)(384,444)(385,445)(386,446)(387,447)(388,448)(389,449)(390,450)(391,466)(392,467)(393,468)(394,469)(395,470)(396,471)(397,472)(398,473)(399,474)(400,475)(401,476)(402,477)(403,478)(404,479)(405,480)(406,451)(407,452)(408,453)(409,454)(410,455)(411,456)(412,457)(413,458)(414,459)(415,460)(416,461)(417,462)(418,463)(419,464)(420,465)(481,601)(482,602)(483,603)(484,604)(485,605)(486,606)(487,607)(488,608)(489,609)(490,610)(491,611)(492,612)(493,613)(494,614)(495,615)(496,616)(497,617)(498,618)(499,619)(500,620)(501,621)(502,622)(503,623)(504,624)(505,625)(506,626)(507,627)(508,628)(509,629)(510,630)(511,646)(512,647)(513,648)(514,649)(515,650)(516,651)(517,652)(518,653)(519,654)(520,655)(521,656)(522,657)(523,658)(524,659)(525,660)(526,631)(527,632)(528,633)(529,634)(530,635)(531,636)(532,637)(533,638)(534,639)(535,640)(536,641)(537,642)(538,643)(539,644)(540,645)(541,691)(542,692)(543,693)(544,694)(545,695)(546,696)(547,697)(548,698)(549,699)(550,700)(551,701)(552,702)(553,703)(554,704)(555,705)(556,706)(557,707)(558,708)(559,709)(560,710)(561,711)(562,712)(563,713)(564,714)(565,715)(566,716)(567,717)(568,718)(569,719)(570,720)(571,661)(572,662)(573,663)(574,664)(575,665)(576,666)(577,667)(578,668)(579,669)(580,670)(581,671)(582,672)(583,673)(584,674)(585,675)(586,676)(587,677)(588,678)(589,679)(590,680)(591,681)(592,682)(593,683)(594,684)(595,685)(596,686)(597,687)(598,688)(599,689)(600,690)(721,841)(722,842)(723,843)(724,844)(725,845)(726,846)(727,847)(728,848)(729,849)(730,850)(731,851)(732,852)(733,853)(734,854)(735,855)(736,856)(737,857)(738,858)(739,859)(740,860)(741,861)(742,862)(743,863)(744,864)(745,865)(746,866)(747,867)(748,868)(749,869)(750,870)(751,886)(752,887)(753,888)(754,889)(755,890)(756,891)(757,892)(758,893)(759,894)(760,895)(761,896)(762,897)(763,898)(764,899)(765,900)(766,871)(767,872)(768,873)(769,874)(770,875)(771,876)(772,877)(773,878)(774,879)(775,880)(776,881)(777,882)(778,883)(779,884)(780,885)(781,931)(782,932)(783,933)(784,934)(785,935)(786,936)(787,937)(788,938)(789,939)(790,940)(791,941)(792,942)(793,943)(794,944)(795,945)(796,946)(797,947)(798,948)(799,949)(800,950)(801,951)(802,952)(803,953)(804,954)(805,955)(806,956)(807,957)(808,958)(809,959)(810,960)(811,901)(812,902)(813,903)(814,904)(815,905)(816,906)(817,907)(818,908)(819,909)(820,910)(821,911)(822,912)(823,913)(824,914)(825,915)(826,916)(827,917)(828,918)(829,919)(830,920)(831,921)(832,922)(833,923)(834,924)(835,925)(836,926)(837,927)(838,928)(839,929)(840,930);
s1 := Sym(960)!(  1,721)(  2,725)(  3,724)(  4,723)(  5,722)(  6,731)(  7,735)(  8,734)(  9,733)( 10,732)( 11,726)( 12,730)( 13,729)( 14,728)( 15,727)( 16,736)( 17,740)( 18,739)( 19,738)
( 20,737)( 21,746)( 22,750)( 23,749)( 24,748)( 25,747)( 26,741)( 27,745)( 28,744)( 29,743)( 30,742)( 31,766)( 32,770)( 33,769)( 34,768)( 35,767)( 36,776)( 37,780)( 38,779)( 39,778)( 40,777)( 41,771)( 42,775)( 43,774)( 44,773)( 45,772)( 46,751)( 47,755)( 48,754)( 49,753)( 50,752)( 51,761)( 52,765)( 53,764)( 54,763)( 55,762)( 56,756)( 57,760)( 58,759)( 59,758)( 60,757)( 61,811)( 62,815)( 63,814)( 64,813)( 65,812)( 66,821)( 67,825)( 68,824)( 69,823)( 70,822)( 71,816)( 72,820)( 73,819)( 74,818)( 75,817)( 76,826)( 77,830)( 78,829)( 79,828)( 80,827)( 81,836)( 82,840)( 83,839)( 84,838)( 85,837)( 86,831)( 87,835)( 88,834)( 89,833)( 90,832)( 91,781)( 92,785)( 93,784)( 94,783)( 95,782)( 96,791)( 97,795)( 98,794)( 99,793)(100,792)(101,786)(102,790)(103,789)(104,788)(105,787)(106,796)(107,800)(108,799)(109,798)(110,797)(111,806)(112,810)(113,809)(114,808)(115,807)(116,801)(117,805)(118,804)(119,803)(120,802)(121,901)(122,905)(123,904)(124,903)(125,902)(126,911)(127,915)(128,914)(129,913)(130,912)(131,906)(132,910)(133,909)(134,908)(135,907)(136,916)(137,920)(138,919)(139,918)(140,917)(141,926)(142,930)(143,929)(144,928)(145,927)(146,921)(147,925)(148,924)(149,923)(150,922)(151,946)(152,950)(153,949)(154,948)(155,947)(156,956)(157,960)(158,959)(159,958)(160,957)(161,951)(162,955)(163,954)(164,953)(165,952)(166,931)(167,935)(168,934)(169,933)(170,932)(171,941)(172,945)(173,944)(174,943)(175,942)(176,936)(177,940)(178,939)(179,938)(180,937)(181,841)(182,845)(183,844)(184,843)(185,842)(186,851)(187,855)(188,854)(189,853)(190,852)(191,846)(192,850)(193,849)(194,848)(195,847)(196,856)(197,860)(198,859)(199,858)(200,857)(201,866)(202,870)(203,869)(204,868)(205,867)(206,861)(207,865)(208,864)(209,863)(210,862)(211,886)(212,890)(213,889)(214,888)(215,887)(216,896)(217,900)(218,899)(219,898)(220,897)(221,891)(222,895)(223,894)(224,893)(225,892)(226,871)(227,875)(228,874)(229,873)(230,872)(231,881)(232,885)(233,884)(234,883)(235,882)(236,876)(237,880)(238,879)(239,878)(240,877)(241,481)(242,485)(243,484)(244,483)(245,482)(246,491)(247,495)(248,494)(249,493)(250,492)(251,486)(252,490)(253,489)(254,488)(255,487)(256,496)(257,500)(258,499)(259,498)(260,497)(261,506)(262,510)(263,509)(264,508)(265,507)(266,501)(267,505)(268,504)(269,503)(270,502)(271,526)(272,530)(273,529)(274,528)(275,527)(276,536)(277,540)(278,539)(279,538)(280,537)(281,531)(282,535)(283,534)(284,533)(285,532)(286,511)(287,515)(288,514)(289,513)(290,512)(291,521)(292,525)(293,524)(294,523)(295,522)(296,516)(297,520)(298,519)(299,518)(300,517)(301,571)(302,575)(303,574)(304,573)(305,572)(306,581)(307,585)(308,584)(309,583)(310,582)(311,576)(312,580)(313,579)(314,578)(315,577)(316,586)(317,590)(318,589)(319,588)(320,587)(321,596)(322,600)(323,599)(324,598)(325,597)(326,591)(327,595)(328,594)(329,593)(330,592)(331,541)(332,545)(333,544)(334,543)(335,542)(336,551)(337,555)(338,554)(339,553)(340,552)(341,546)(342,550)(343,549)(344,548)(345,547)(346,556)(347,560)(348,559)(349,558)(350,557)(351,566)(352,570)(353,569)(354,568)(355,567)(356,561)(357,565)(358,564)(359,563)(360,562)(361,661)(362,665)(363,664)(364,663)(365,662)(366,671)(367,675)(368,674)(369,673)(370,672)(371,666)(372,670)(373,669)(374,668)(375,667)(376,676)(377,680)(378,679)(379,678)(380,677)(381,686)(382,690)(383,689)(384,688)(385,687)(386,681)(387,685)(388,684)(389,683)(390,682)(391,706)(392,710)(393,709)(394,708)(395,707)(396,716)(397,720)(398,719)(399,718)(400,717)(401,711)(402,715)(403,714)(404,713)(405,712)(406,691)(407,695)(408,694)(409,693)(410,692)(411,701)(412,705)(413,704)(414,703)(415,702)(416,696)(417,700)(418,699)(419,698)(420,697)(421,601)(422,605)(423,604)(424,603)(425,602)(426,611)(427,615)(428,614)(429,613)(430,612)(431,606)(432,610)(433,609)(434,608)(435,607)(436,616)(437,620)(438,619)(439,618)(440,617)(441,626)(442,630)(443,629)(444,628)(445,627)(446,621)(447,625)(448,624)(449,623)(450,622)(451,646)(452,650)(453,649)(454,648)(455,647)(456,656)(457,660)(458,659)(459,658)(460,657)(461,651)(462,655)(463,654)(464,653)(465,652)(466,631)(467,635)(468,634)(469,633)(470,632)(471,641)(472,645)(473,644)
(474,643)(475,642)(476,636)(477,640)(478,639)(479,638)(480,637);
s2 := Sym(960)!(  1,247)(  2,246)(  3,250)(  4,249)(  5,248)(  6,242)(  7,241)(  8,245)(  9,244)( 10,243)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)( 16,262)( 17,261)( 18,265)( 19,264)
( 20,263)( 21,257)( 22,256)( 23,260)( 24,259)( 25,258)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,277)( 32,276)( 33,280)( 34,279)( 35,278)( 36,272)( 37,271)( 38,275)( 39,274)( 40,273)( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,292)( 47,291)( 48,295)( 49,294)( 50,293)( 51,287)( 52,286)( 53,290)( 54,289)( 55,288)( 56,297)( 57,296)( 58,300)( 59,299)( 60,298)( 61,307)( 62,306)( 63,310)( 64,309)( 65,308)( 66,302)( 67,301)( 68,305)( 69,304)( 70,303)( 71,312)( 72,311)( 73,315)( 74,314)( 75,313)( 76,322)( 77,321)( 78,325)( 79,324)( 80,323)( 81,317)( 82,316)( 83,320)( 84,319)( 85,318)( 86,327)( 87,326)( 88,330)( 89,329)( 90,328)( 91,337)( 92,336)( 93,340)( 94,339)( 95,338)( 96,332)( 97,331)( 98,335)( 99,334)(100,333)(101,342)(102,341)(103,345)(104,344)(105,343)(106,352)(107,351)(108,355)(109,354)(110,353)(111,347)(112,346)(113,350)(114,349)(115,348)(116,357)(117,356)(118,360)(119,359)(120,358)(121,367)(122,366)(123,370)(124,369)(125,368)(126,362)(127,361)(128,365)(129,364)(130,363)(131,372)(132,371)(133,375)(134,374)(135,373)(136,382)(137,381)(138,385)(139,384)(140,383)(141,377)(142,376)(143,380)(144,379)(145,378)(146,387)(147,386)(148,390)(149,389)(150,388)(151,397)(152,396)(153,400)(154,399)(155,398)(156,392)(157,391)(158,395)(159,394)(160,393)(161,402)(162,401)(163,405)(164,404)(165,403)(166,412)(167,411)(168,415)(169,414)(170,413)(171,407)(172,406)(173,410)(174,409)(175,408)(176,417)(177,416)(178,420)(179,419)(180,418)(181,427)(182,426)(183,430)(184,429)(185,428)(186,422)(187,421)(188,425)(189,424)(190,423)(191,432)(192,431)(193,435)(194,434)(195,433)(196,442)(197,441)(198,445)(199,444)(200,443)(201,437)(202,436)(203,440)(204,439)(205,438)(206,447)(207,446)(208,450)(209,449)(210,448)(211,457)(212,456)(213,460)(214,459)(215,458)(216,452)(217,451)(218,455)(219,454)(220,453)(221,462)(222,461)(223,465)(224,464)(225,463)(226,472)(227,471)(228,475)(229,474)(230,473)(231,467)(232,466)(233,470)(234,469)(235,468)(236,477)(237,476)(238,480)(239,479)(240,478)(481,727)(482,726)(483,730)(484,729)(485,728)(486,722)(487,721)(488,725)(489,724)(490,723)(491,732)(492,731)(493,735)(494,734)(495,733)(496,742)(497,741)(498,745)(499,744)(500,743)(501,737)(502,736)(503,740)(504,739)(505,738)(506,747)(507,746)(508,750)(509,749)(510,748)(511,757)(512,756)(513,760)(514,759)(515,758)(516,752)(517,751)(518,755)(519,754)(520,753)(521,762)(522,761)(523,765)(524,764)(525,763)(526,772)(527,771)(528,775)(529,774)(530,773)(531,767)(532,766)(533,770)(534,769)(535,768)(536,777)(537,776)(538,780)(539,779)(540,778)(541,787)(542,786)(543,790)(544,789)(545,788)(546,782)(547,781)(548,785)(549,784)(550,783)(551,792)(552,791)(553,795)(554,794)(555,793)(556,802)(557,801)(558,805)(559,804)(560,803)(561,797)(562,796)(563,800)(564,799)(565,798)(566,807)(567,806)(568,810)(569,809)(570,808)(571,817)(572,816)(573,820)(574,819)(575,818)(576,812)(577,811)(578,815)(579,814)(580,813)(581,822)(582,821)(583,825)(584,824)(585,823)(586,832)(587,831)(588,835)(589,834)(590,833)(591,827)(592,826)(593,830)(594,829)(595,828)(596,837)(597,836)(598,840)(599,839)(600,838)(601,847)(602,846)(603,850)(604,849)(605,848)(606,842)(607,841)(608,845)(609,844)(610,843)(611,852)(612,851)(613,855)(614,854)(615,853)(616,862)(617,861)(618,865)(619,864)(620,863)(621,857)(622,856)(623,860)(624,859)(625,858)(626,867)(627,866)(628,870)(629,869)(630,868)(631,877)(632,876)(633,880)(634,879)(635,878)(636,872)(637,871)(638,875)(639,874)(640,873)(641,882)(642,881)(643,885)(644,884)(645,883)(646,892)(647,891)(648,895)(649,894)(650,893)(651,887)(652,886)(653,890)(654,889)(655,888)(656,897)(657,896)(658,900)(659,899)(660,898)(661,907)(662,906)(663,910)(664,909)(665,908)(666,902)(667,901)(668,905)(669,904)(670,903)(671,912)(672,911)(673,915)(674,914)(675,913)(676,922)(677,921)(678,925)(679,924)(680,923)(681,917)(682,916)(683,920)(684,919)(685,918)(686,927)(687,926)(688,930)(689,929)(690,928)(691,937)(692,936)(693,940)(694,939)(695,938)(696,932)(697,931)(698,935)(699,934)(700,933)(701,942)(702,941)(703,945)(704,944)(705,943)(706,952)(707,951)(708,955)(709,954)(710,953)(711,947)(712,946)(713,950)
(714,949)(715,948)(716,957)(717,956)(718,960)(719,959)(720,958);
poly := sub<Sym(960)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle