Polytope of Type {80,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {80,12}*1920a
Also Known As : {80,12|2}. if this polytope has another name.
Group : SmallGroup(1920,41747)
Rank : 3
Schlafli Type : {80,12}
Number of vertices, edges, etc : 80, 480, 12
Order of s0s1s2 : 240
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 : {80,6}*960, {40,12}*960a
   3-fold quotients : {80,4}*640a
   4-fold quotients : {40,6}*480, {20,12}*480
   5-fold quotients : {16,12}*384a
   6-fold quotients : {40,4}*320a, {80,2}*320
   8-fold quotients : {10,12}*240, {20,6}*240a
   10-fold quotients : {8,12}*192a, {16,6}*192
   12-fold quotients : {20,4}*160, {40,2}*160
   15-fold quotients : {16,4}*128a
   16-fold quotients : {10,6}*120
   20-fold quotients : {4,12}*96a, {8,6}*96
   24-fold quotients : {20,2}*80, {10,4}*80
   30-fold quotients : {8,4}*64a, {16,2}*64
   40-fold quotients : {2,12}*48, {4,6}*48a
   48-fold quotients : {10,2}*40
   60-fold quotients : {4,4}*32, {8,2}*32
   80-fold quotients : {2,6}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16, {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 := (  1,721)(  2,725)(  3,724)(  4,723)(  5,722)(  6,726)(  7,730)(  8,729)(  9,728)( 10,727)( 11,731)( 12,735)( 13,734)( 14,733)( 15,732)( 16,736)( 17,740)( 18,739)( 19,738)( 20,737)
( 21,741)( 22,745)( 23,744)( 24,743)( 25,742)( 26,746)( 27,750)( 28,749)( 29,748)( 30,747)( 31,766)( 32,770)( 33,769)( 34,768)( 35,767)( 36,771)( 37,775)( 38,774)( 39,773)( 40,772)( 41,776)( 42,780)( 43,779)( 44,778)( 45,777)( 46,751)( 47,755)( 48,754)( 49,753)( 50,752)( 51,756)( 52,760)( 53,759)( 54,758)( 55,757)( 56,761)( 57,765)( 58,764)( 59,763)( 60,762)( 61,781)( 62,785)( 63,784)( 64,783)( 65,782)( 66,786)( 67,790)( 68,789)( 69,788)( 70,787)( 71,791)( 72,795)( 73,794)( 74,793)( 75,792)( 76,796)( 77,800)( 78,799)( 79,798)( 80,797)( 81,801)( 82,805)( 83,804)( 84,803)( 85,802)( 86,806)( 87,810)( 88,809)( 89,808)( 90,807)( 91,826)( 92,830)( 93,829)( 94,828)( 95,827)( 96,831)( 97,835)( 98,834)( 99,833)(100,832)(101,836)(102,840)(103,839)(104,838)(105,837)(106,811)(107,815)(108,814)(109,813)(110,812)(111,816)(112,820)(113,819)(114,818)(115,817)(116,821)(117,825)(118,824)(119,823)(120,822)(121,871)(122,875)(123,874)(124,873)(125,872)(126,876)(127,880)(128,879)(129,878)(130,877)(131,881)(132,885)(133,884)(134,883)(135,882)(136,886)(137,890)(138,889)(139,888)(140,887)(141,891)(142,895)(143,894)(144,893)(145,892)(146,896)(147,900)(148,899)(149,898)(150,897)(151,841)(152,845)(153,844)(154,843)(155,842)(156,846)(157,850)(158,849)(159,848)(160,847)(161,851)(162,855)(163,854)(164,853)(165,852)(166,856)(167,860)(168,859)(169,858)(170,857)(171,861)(172,865)(173,864)(174,863)(175,862)(176,866)(177,870)(178,869)(179,868)(180,867)(181,931)(182,935)(183,934)(184,933)(185,932)(186,936)(187,940)(188,939)(189,938)(190,937)(191,941)(192,945)(193,944)(194,943)(195,942)(196,946)(197,950)(198,949)(199,948)(200,947)(201,951)(202,955)(203,954)(204,953)(205,952)(206,956)(207,960)(208,959)(209,958)(210,957)(211,901)(212,905)(213,904)(214,903)(215,902)(216,906)(217,910)(218,909)(219,908)(220,907)(221,911)(222,915)(223,914)(224,913)(225,912)(226,916)(227,920)(228,919)(229,918)(230,917)(231,921)(232,925)(233,924)(234,923)(235,922)(236,926)(237,930)(238,929)(239,928)(240,927)(241,481)(242,485)(243,484)(244,483)(245,482)(246,486)(247,490)(248,489)(249,488)(250,487)(251,491)(252,495)(253,494)(254,493)(255,492)(256,496)(257,500)(258,499)(259,498)(260,497)(261,501)(262,505)(263,504)(264,503)(265,502)(266,506)(267,510)(268,509)(269,508)(270,507)(271,526)(272,530)(273,529)(274,528)(275,527)(276,531)(277,535)(278,534)(279,533)(280,532)(281,536)(282,540)(283,539)(284,538)(285,537)(286,511)(287,515)(288,514)(289,513)(290,512)(291,516)(292,520)(293,519)(294,518)(295,517)(296,521)(297,525)(298,524)(299,523)(300,522)(301,541)(302,545)(303,544)(304,543)(305,542)(306,546)(307,550)(308,549)(309,548)(310,547)(311,551)(312,555)(313,554)(314,553)(315,552)(316,556)(317,560)(318,559)(319,558)(320,557)(321,561)(322,565)(323,564)(324,563)(325,562)(326,566)(327,570)(328,569)(329,568)(330,567)(331,586)(332,590)(333,589)(334,588)(335,587)(336,591)(337,595)(338,594)(339,593)(340,592)(341,596)(342,600)(343,599)(344,598)(345,597)(346,571)(347,575)(348,574)(349,573)(350,572)(351,576)(352,580)(353,579)(354,578)(355,577)(356,581)(357,585)(358,584)(359,583)(360,582)(361,631)(362,635)(363,634)(364,633)(365,632)(366,636)(367,640)(368,639)(369,638)(370,637)(371,641)(372,645)(373,644)(374,643)(375,642)(376,646)(377,650)(378,649)(379,648)(380,647)(381,651)(382,655)(383,654)(384,653)(385,652)(386,656)(387,660)(388,659)(389,658)(390,657)(391,601)(392,605)(393,604)(394,603)(395,602)(396,606)(397,610)(398,609)(399,608)(400,607)(401,611)(402,615)(403,614)(404,613)(405,612)(406,616)(407,620)(408,619)(409,618)(410,617)(411,621)(412,625)(413,624)(414,623)(415,622)(416,626)(417,630)(418,629)(419,628)(420,627)(421,691)(422,695)(423,694)(424,693)(425,692)(426,696)(427,700)(428,699)(429,698)(430,697)(431,701)(432,705)(433,704)(434,703)(435,702)(436,706)(437,710)(438,709)(439,708)(440,707)(441,711)(442,715)(443,714)(444,713)(445,712)(446,716)(447,720)(448,719)(449,718)(450,717)(451,661)(452,665)(453,664)(454,663)(455,662)(456,666)(457,670)(458,669)(459,668)(460,667)(461,671)(462,675)(463,674)(464,673)(465,672)(466,676)(467,680)(468,679)(469,678)(470,677)(471,681)(472,685)(473,684)(474,683)
(475,682)(476,686)(477,690)(478,689)(479,688)(480,687);;
s1 := (  1,  2)(  3,  5)(  6, 12)(  7, 11)(  8, 15)(  9, 14)( 10, 13)( 16, 17)( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 47)( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 57)
( 37, 56)( 38, 60)( 39, 59)( 40, 58)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 61, 62)( 63, 65)( 66, 72)( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 77)( 78, 80)( 81, 87)( 82, 86)( 83, 90)( 84, 89)( 85, 88)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)( 96,117)( 97,116)( 98,120)( 99,119)(100,118)(101,112)(102,111)(103,115)(104,114)(105,113)(121,152)(122,151)(123,155)(124,154)(125,153)(126,162)(127,161)(128,165)(129,164)(130,163)(131,157)(132,156)(133,160)(134,159)(135,158)(136,167)(137,166)(138,170)(139,169)(140,168)(141,177)(142,176)(143,180)(144,179)(145,178)(146,172)(147,171)(148,175)(149,174)(150,173)(181,212)(182,211)(183,215)(184,214)(185,213)(186,222)(187,221)(188,225)(189,224)(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)(196,227)(197,226)(198,230)(199,229)(200,228)(201,237)(202,236)(203,240)(204,239)(205,238)(206,232)(207,231)(208,235)(209,234)(210,233)(241,302)(242,301)(243,305)(244,304)(245,303)(246,312)(247,311)(248,315)(249,314)(250,313)(251,307)(252,306)(253,310)(254,309)(255,308)(256,317)(257,316)(258,320)(259,319)(260,318)(261,327)(262,326)(263,330)(264,329)(265,328)(266,322)(267,321)(268,325)(269,324)(270,323)(271,347)(272,346)(273,350)(274,349)(275,348)(276,357)(277,356)(278,360)(279,359)(280,358)(281,352)(282,351)(283,355)(284,354)(285,353)(286,332)(287,331)(288,335)(289,334)(290,333)(291,342)(292,341)(293,345)(294,344)(295,343)(296,337)(297,336)(298,340)(299,339)(300,338)(361,452)(362,451)(363,455)(364,454)(365,453)(366,462)(367,461)(368,465)(369,464)(370,463)(371,457)(372,456)(373,460)(374,459)(375,458)(376,467)(377,466)(378,470)(379,469)(380,468)(381,477)(382,476)(383,480)(384,479)(385,478)(386,472)(387,471)(388,475)(389,474)(390,473)(391,422)(392,421)(393,425)(394,424)(395,423)(396,432)(397,431)(398,435)(399,434)(400,433)(401,427)(402,426)(403,430)(404,429)(405,428)(406,437)(407,436)(408,440)(409,439)(410,438)(411,447)(412,446)(413,450)(414,449)(415,448)(416,442)(417,441)(418,445)(419,444)(420,443)(481,602)(482,601)(483,605)(484,604)(485,603)(486,612)(487,611)(488,615)(489,614)(490,613)(491,607)(492,606)(493,610)(494,609)(495,608)(496,617)(497,616)(498,620)(499,619)(500,618)(501,627)(502,626)(503,630)(504,629)(505,628)(506,622)(507,621)(508,625)(509,624)(510,623)(511,647)(512,646)(513,650)(514,649)(515,648)(516,657)(517,656)(518,660)(519,659)(520,658)(521,652)(522,651)(523,655)(524,654)(525,653)(526,632)(527,631)(528,635)(529,634)(530,633)(531,642)(532,641)(533,645)(534,644)(535,643)(536,637)(537,636)(538,640)(539,639)(540,638)(541,662)(542,661)(543,665)(544,664)(545,663)(546,672)(547,671)(548,675)(549,674)(550,673)(551,667)(552,666)(553,670)(554,669)(555,668)(556,677)(557,676)(558,680)(559,679)(560,678)(561,687)(562,686)(563,690)(564,689)(565,688)(566,682)(567,681)(568,685)(569,684)(570,683)(571,707)(572,706)(573,710)(574,709)(575,708)(576,717)(577,716)(578,720)(579,719)(580,718)(581,712)(582,711)(583,715)(584,714)(585,713)(586,692)(587,691)(588,695)(589,694)(590,693)(591,702)(592,701)(593,705)(594,704)(595,703)(596,697)(597,696)(598,700)(599,699)(600,698)(721,902)(722,901)(723,905)(724,904)(725,903)(726,912)(727,911)(728,915)(729,914)(730,913)(731,907)(732,906)(733,910)(734,909)(735,908)(736,917)(737,916)(738,920)(739,919)(740,918)(741,927)(742,926)(743,930)(744,929)(745,928)(746,922)(747,921)(748,925)(749,924)(750,923)(751,947)(752,946)(753,950)(754,949)(755,948)(756,957)(757,956)(758,960)(759,959)(760,958)(761,952)(762,951)(763,955)(764,954)(765,953)(766,932)(767,931)(768,935)(769,934)(770,933)(771,942)(772,941)(773,945)(774,944)(775,943)(776,937)(777,936)(778,940)(779,939)(780,938)(781,842)(782,841)(783,845)(784,844)(785,843)(786,852)(787,851)(788,855)(789,854)(790,853)(791,847)(792,846)(793,850)(794,849)(795,848)(796,857)(797,856)(798,860)(799,859)(800,858)(801,867)(802,866)(803,870)(804,869)(805,868)(806,862)(807,861)(808,865)(809,864)(810,863)(811,887)(812,886)(813,890)(814,889)(815,888)(816,897)(817,896)(818,900)(819,899)(820,898)(821,892)(822,891)(823,895)(824,894)(825,893)(826,872)(827,871)(828,875)(829,874)(830,873)(831,882)(832,881)(833,885)(834,884)(835,883)(836,877)
(837,876)(838,880)(839,879)(840,878);;
s2 := (  1,246)(  2,247)(  3,248)(  4,249)(  5,250)(  6,241)(  7,242)(  8,243)(  9,244)( 10,245)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,261)( 17,262)( 18,263)( 19,264)( 20,265)
( 21,256)( 22,257)( 23,258)( 24,259)( 25,260)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,276)( 32,277)( 33,278)( 34,279)( 35,280)( 36,271)( 37,272)( 38,273)( 39,274)( 40,275)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,291)( 47,292)( 48,293)( 49,294)( 50,295)( 51,286)( 52,287)( 53,288)( 54,289)( 55,290)( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,306)( 62,307)( 63,308)( 64,309)( 65,310)( 66,301)( 67,302)( 68,303)( 69,304)( 70,305)( 71,311)( 72,312)( 73,313)( 74,314)( 75,315)( 76,321)( 77,322)( 78,323)( 79,324)( 80,325)( 81,316)( 82,317)( 83,318)( 84,319)( 85,320)( 86,326)( 87,327)( 88,328)( 89,329)( 90,330)( 91,336)( 92,337)( 93,338)( 94,339)( 95,340)( 96,331)( 97,332)( 98,333)( 99,334)(100,335)(101,341)(102,342)(103,343)(104,344)(105,345)(106,351)(107,352)(108,353)(109,354)(110,355)(111,346)(112,347)(113,348)(114,349)(115,350)(116,356)(117,357)(118,358)(119,359)(120,360)(121,366)(122,367)(123,368)(124,369)(125,370)(126,361)(127,362)(128,363)(129,364)(130,365)(131,371)(132,372)(133,373)(134,374)(135,375)(136,381)(137,382)(138,383)(139,384)(140,385)(141,376)(142,377)(143,378)(144,379)(145,380)(146,386)(147,387)(148,388)(149,389)(150,390)(151,396)(152,397)(153,398)(154,399)(155,400)(156,391)(157,392)(158,393)(159,394)(160,395)(161,401)(162,402)(163,403)(164,404)(165,405)(166,411)(167,412)(168,413)(169,414)(170,415)(171,406)(172,407)(173,408)(174,409)(175,410)(176,416)(177,417)(178,418)(179,419)(180,420)(181,426)(182,427)(183,428)(184,429)(185,430)(186,421)(187,422)(188,423)(189,424)(190,425)(191,431)(192,432)(193,433)(194,434)(195,435)(196,441)(197,442)(198,443)(199,444)(200,445)(201,436)(202,437)(203,438)(204,439)(205,440)(206,446)(207,447)(208,448)(209,449)(210,450)(211,456)(212,457)(213,458)(214,459)(215,460)(216,451)(217,452)(218,453)(219,454)(220,455)(221,461)(222,462)(223,463)(224,464)(225,465)(226,471)(227,472)(228,473)(229,474)(230,475)(231,466)(232,467)(233,468)(234,469)(235,470)(236,476)(237,477)(238,478)(239,479)(240,480)(481,726)(482,727)(483,728)(484,729)(485,730)(486,721)(487,722)(488,723)(489,724)(490,725)(491,731)(492,732)(493,733)(494,734)(495,735)(496,741)(497,742)(498,743)(499,744)(500,745)(501,736)(502,737)(503,738)(504,739)(505,740)(506,746)(507,747)(508,748)(509,749)(510,750)(511,756)(512,757)(513,758)(514,759)(515,760)(516,751)(517,752)(518,753)(519,754)(520,755)(521,761)(522,762)(523,763)(524,764)(525,765)(526,771)(527,772)(528,773)(529,774)(530,775)(531,766)(532,767)(533,768)(534,769)(535,770)(536,776)(537,777)(538,778)(539,779)(540,780)(541,786)(542,787)(543,788)(544,789)(545,790)(546,781)(547,782)(548,783)(549,784)(550,785)(551,791)(552,792)(553,793)(554,794)(555,795)(556,801)(557,802)(558,803)(559,804)(560,805)(561,796)(562,797)(563,798)(564,799)(565,800)(566,806)(567,807)(568,808)(569,809)(570,810)(571,816)(572,817)(573,818)(574,819)(575,820)(576,811)(577,812)(578,813)(579,814)(580,815)(581,821)(582,822)(583,823)(584,824)(585,825)(586,831)(587,832)(588,833)(589,834)(590,835)(591,826)(592,827)(593,828)(594,829)(595,830)(596,836)(597,837)(598,838)(599,839)(600,840)(601,846)(602,847)(603,848)(604,849)(605,850)(606,841)(607,842)(608,843)(609,844)(610,845)(611,851)(612,852)(613,853)(614,854)(615,855)(616,861)(617,862)(618,863)(619,864)(620,865)(621,856)(622,857)(623,858)(624,859)(625,860)(626,866)(627,867)(628,868)(629,869)(630,870)(631,876)(632,877)(633,878)(634,879)(635,880)(636,871)(637,872)(638,873)(639,874)(640,875)(641,881)(642,882)(643,883)(644,884)(645,885)(646,891)(647,892)(648,893)(649,894)(650,895)(651,886)(652,887)(653,888)(654,889)(655,890)(656,896)(657,897)(658,898)(659,899)(660,900)(661,906)(662,907)(663,908)(664,909)(665,910)(666,901)(667,902)(668,903)(669,904)(670,905)(671,911)(672,912)(673,913)(674,914)(675,915)(676,921)(677,922)(678,923)(679,924)(680,925)(681,916)(682,917)(683,918)(684,919)(685,920)(686,926)(687,927)(688,928)(689,929)(690,930)(691,936)(692,937)(693,938)(694,939)(695,940)(696,931)(697,932)(698,933)(699,934)(700,935)(701,941)(702,942)(703,943)(704,944)(705,945)(706,951)(707,952)(708,953)(709,954)(710,955)(711,946)(712,947)(713,948)(714,949)
(715,950)(716,956)(717,957)(718,958)(719,959)(720,960);;
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, 
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*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*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)!(  1,721)(  2,725)(  3,724)(  4,723)(  5,722)(  6,726)(  7,730)(  8,729)(  9,728)( 10,727)( 11,731)( 12,735)( 13,734)( 14,733)( 15,732)( 16,736)( 17,740)( 18,739)( 19,738)
( 20,737)( 21,741)( 22,745)( 23,744)( 24,743)( 25,742)( 26,746)( 27,750)( 28,749)( 29,748)( 30,747)( 31,766)( 32,770)( 33,769)( 34,768)( 35,767)( 36,771)( 37,775)( 38,774)( 39,773)( 40,772)( 41,776)( 42,780)( 43,779)( 44,778)( 45,777)( 46,751)( 47,755)( 48,754)( 49,753)( 50,752)( 51,756)( 52,760)( 53,759)( 54,758)( 55,757)( 56,761)( 57,765)( 58,764)( 59,763)( 60,762)( 61,781)( 62,785)( 63,784)( 64,783)( 65,782)( 66,786)( 67,790)( 68,789)( 69,788)( 70,787)( 71,791)( 72,795)( 73,794)( 74,793)( 75,792)( 76,796)( 77,800)( 78,799)( 79,798)( 80,797)( 81,801)( 82,805)( 83,804)( 84,803)( 85,802)( 86,806)( 87,810)( 88,809)( 89,808)( 90,807)( 91,826)( 92,830)( 93,829)( 94,828)( 95,827)( 96,831)( 97,835)( 98,834)( 99,833)(100,832)(101,836)(102,840)(103,839)(104,838)(105,837)(106,811)(107,815)(108,814)(109,813)(110,812)(111,816)(112,820)(113,819)(114,818)(115,817)(116,821)(117,825)(118,824)(119,823)(120,822)(121,871)(122,875)(123,874)(124,873)(125,872)(126,876)(127,880)(128,879)(129,878)(130,877)(131,881)(132,885)(133,884)(134,883)(135,882)(136,886)(137,890)(138,889)(139,888)(140,887)(141,891)(142,895)(143,894)(144,893)(145,892)(146,896)(147,900)(148,899)(149,898)(150,897)(151,841)(152,845)(153,844)(154,843)(155,842)(156,846)(157,850)(158,849)(159,848)(160,847)(161,851)(162,855)(163,854)(164,853)(165,852)(166,856)(167,860)(168,859)(169,858)(170,857)(171,861)(172,865)(173,864)(174,863)(175,862)(176,866)(177,870)(178,869)(179,868)(180,867)(181,931)(182,935)(183,934)(184,933)(185,932)(186,936)(187,940)(188,939)(189,938)(190,937)(191,941)(192,945)(193,944)(194,943)(195,942)(196,946)(197,950)(198,949)(199,948)(200,947)(201,951)(202,955)(203,954)(204,953)(205,952)(206,956)(207,960)(208,959)(209,958)(210,957)(211,901)(212,905)(213,904)(214,903)(215,902)(216,906)(217,910)(218,909)(219,908)(220,907)(221,911)(222,915)(223,914)(224,913)(225,912)(226,916)(227,920)(228,919)(229,918)(230,917)(231,921)(232,925)(233,924)(234,923)(235,922)(236,926)(237,930)(238,929)(239,928)(240,927)(241,481)(242,485)(243,484)(244,483)(245,482)(246,486)(247,490)(248,489)(249,488)(250,487)(251,491)(252,495)(253,494)(254,493)(255,492)(256,496)(257,500)(258,499)(259,498)(260,497)(261,501)(262,505)(263,504)(264,503)(265,502)(266,506)(267,510)(268,509)(269,508)(270,507)(271,526)(272,530)(273,529)(274,528)(275,527)(276,531)(277,535)(278,534)(279,533)(280,532)(281,536)(282,540)(283,539)(284,538)(285,537)(286,511)(287,515)(288,514)(289,513)(290,512)(291,516)(292,520)(293,519)(294,518)(295,517)(296,521)(297,525)(298,524)(299,523)(300,522)(301,541)(302,545)(303,544)(304,543)(305,542)(306,546)(307,550)(308,549)(309,548)(310,547)(311,551)(312,555)(313,554)(314,553)(315,552)(316,556)(317,560)(318,559)(319,558)(320,557)(321,561)(322,565)(323,564)(324,563)(325,562)(326,566)(327,570)(328,569)(329,568)(330,567)(331,586)(332,590)(333,589)(334,588)(335,587)(336,591)(337,595)(338,594)(339,593)(340,592)(341,596)(342,600)(343,599)(344,598)(345,597)(346,571)(347,575)(348,574)(349,573)(350,572)(351,576)(352,580)(353,579)(354,578)(355,577)(356,581)(357,585)(358,584)(359,583)(360,582)(361,631)(362,635)(363,634)(364,633)(365,632)(366,636)(367,640)(368,639)(369,638)(370,637)(371,641)(372,645)(373,644)(374,643)(375,642)(376,646)(377,650)(378,649)(379,648)(380,647)(381,651)(382,655)(383,654)(384,653)(385,652)(386,656)(387,660)(388,659)(389,658)(390,657)(391,601)(392,605)(393,604)(394,603)(395,602)(396,606)(397,610)(398,609)(399,608)(400,607)(401,611)(402,615)(403,614)(404,613)(405,612)(406,616)(407,620)(408,619)(409,618)(410,617)(411,621)(412,625)(413,624)(414,623)(415,622)(416,626)(417,630)(418,629)(419,628)(420,627)(421,691)(422,695)(423,694)(424,693)(425,692)(426,696)(427,700)(428,699)(429,698)(430,697)(431,701)(432,705)(433,704)(434,703)(435,702)(436,706)(437,710)(438,709)(439,708)(440,707)(441,711)(442,715)(443,714)(444,713)(445,712)(446,716)(447,720)(448,719)(449,718)(450,717)(451,661)(452,665)(453,664)(454,663)(455,662)(456,666)(457,670)(458,669)(459,668)(460,667)(461,671)(462,675)(463,674)(464,673)(465,672)(466,676)(467,680)(468,679)(469,678)(470,677)(471,681)(472,685)(473,684)
(474,683)(475,682)(476,686)(477,690)(478,689)(479,688)(480,687);
s1 := Sym(960)!(  1,  2)(  3,  5)(  6, 12)(  7, 11)(  8, 15)(  9, 14)( 10, 13)( 16, 17)( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 47)( 32, 46)( 33, 50)( 34, 49)( 35, 48)
( 36, 57)( 37, 56)( 38, 60)( 39, 59)( 40, 58)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 61, 62)( 63, 65)( 66, 72)( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 77)( 78, 80)( 81, 87)( 82, 86)( 83, 90)( 84, 89)( 85, 88)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)( 96,117)( 97,116)( 98,120)( 99,119)(100,118)(101,112)(102,111)(103,115)(104,114)(105,113)(121,152)(122,151)(123,155)(124,154)(125,153)(126,162)(127,161)(128,165)(129,164)(130,163)(131,157)(132,156)(133,160)(134,159)(135,158)(136,167)(137,166)(138,170)(139,169)(140,168)(141,177)(142,176)(143,180)(144,179)(145,178)(146,172)(147,171)(148,175)(149,174)(150,173)(181,212)(182,211)(183,215)(184,214)(185,213)(186,222)(187,221)(188,225)(189,224)(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)(196,227)(197,226)(198,230)(199,229)(200,228)(201,237)(202,236)(203,240)(204,239)(205,238)(206,232)(207,231)(208,235)(209,234)(210,233)(241,302)(242,301)(243,305)(244,304)(245,303)(246,312)(247,311)(248,315)(249,314)(250,313)(251,307)(252,306)(253,310)(254,309)(255,308)(256,317)(257,316)(258,320)(259,319)(260,318)(261,327)(262,326)(263,330)(264,329)(265,328)(266,322)(267,321)(268,325)(269,324)(270,323)(271,347)(272,346)(273,350)(274,349)(275,348)(276,357)(277,356)(278,360)(279,359)(280,358)(281,352)(282,351)(283,355)(284,354)(285,353)(286,332)(287,331)(288,335)(289,334)(290,333)(291,342)(292,341)(293,345)(294,344)(295,343)(296,337)(297,336)(298,340)(299,339)(300,338)(361,452)(362,451)(363,455)(364,454)(365,453)(366,462)(367,461)(368,465)(369,464)(370,463)(371,457)(372,456)(373,460)(374,459)(375,458)(376,467)(377,466)(378,470)(379,469)(380,468)(381,477)(382,476)(383,480)(384,479)(385,478)(386,472)(387,471)(388,475)(389,474)(390,473)(391,422)(392,421)(393,425)(394,424)(395,423)(396,432)(397,431)(398,435)(399,434)(400,433)(401,427)(402,426)(403,430)(404,429)(405,428)(406,437)(407,436)(408,440)(409,439)(410,438)(411,447)(412,446)(413,450)(414,449)(415,448)(416,442)(417,441)(418,445)(419,444)(420,443)(481,602)(482,601)(483,605)(484,604)(485,603)(486,612)(487,611)(488,615)(489,614)(490,613)(491,607)(492,606)(493,610)(494,609)(495,608)(496,617)(497,616)(498,620)(499,619)(500,618)(501,627)(502,626)(503,630)(504,629)(505,628)(506,622)(507,621)(508,625)(509,624)(510,623)(511,647)(512,646)(513,650)(514,649)(515,648)(516,657)(517,656)(518,660)(519,659)(520,658)(521,652)(522,651)(523,655)(524,654)(525,653)(526,632)(527,631)(528,635)(529,634)(530,633)(531,642)(532,641)(533,645)(534,644)(535,643)(536,637)(537,636)(538,640)(539,639)(540,638)(541,662)(542,661)(543,665)(544,664)(545,663)(546,672)(547,671)(548,675)(549,674)(550,673)(551,667)(552,666)(553,670)(554,669)(555,668)(556,677)(557,676)(558,680)(559,679)(560,678)(561,687)(562,686)(563,690)(564,689)(565,688)(566,682)(567,681)(568,685)(569,684)(570,683)(571,707)(572,706)(573,710)(574,709)(575,708)(576,717)(577,716)(578,720)(579,719)(580,718)(581,712)(582,711)(583,715)(584,714)(585,713)(586,692)(587,691)(588,695)(589,694)(590,693)(591,702)(592,701)(593,705)(594,704)(595,703)(596,697)(597,696)(598,700)(599,699)(600,698)(721,902)(722,901)(723,905)(724,904)(725,903)(726,912)(727,911)(728,915)(729,914)(730,913)(731,907)(732,906)(733,910)(734,909)(735,908)(736,917)(737,916)(738,920)(739,919)(740,918)(741,927)(742,926)(743,930)(744,929)(745,928)(746,922)(747,921)(748,925)(749,924)(750,923)(751,947)(752,946)(753,950)(754,949)(755,948)(756,957)(757,956)(758,960)(759,959)(760,958)(761,952)(762,951)(763,955)(764,954)(765,953)(766,932)(767,931)(768,935)(769,934)(770,933)(771,942)(772,941)(773,945)(774,944)(775,943)(776,937)(777,936)(778,940)(779,939)(780,938)(781,842)(782,841)(783,845)(784,844)(785,843)(786,852)(787,851)(788,855)(789,854)(790,853)(791,847)(792,846)(793,850)(794,849)(795,848)(796,857)(797,856)(798,860)(799,859)(800,858)(801,867)(802,866)(803,870)(804,869)(805,868)(806,862)(807,861)(808,865)(809,864)(810,863)(811,887)(812,886)(813,890)(814,889)(815,888)(816,897)(817,896)(818,900)(819,899)(820,898)(821,892)(822,891)(823,895)(824,894)(825,893)(826,872)(827,871)(828,875)(829,874)(830,873)(831,882)(832,881)(833,885)(834,884)(835,883)
(836,877)(837,876)(838,880)(839,879)(840,878);
s2 := Sym(960)!(  1,246)(  2,247)(  3,248)(  4,249)(  5,250)(  6,241)(  7,242)(  8,243)(  9,244)( 10,245)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,261)( 17,262)( 18,263)( 19,264)
( 20,265)( 21,256)( 22,257)( 23,258)( 24,259)( 25,260)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,276)( 32,277)( 33,278)( 34,279)( 35,280)( 36,271)( 37,272)( 38,273)( 39,274)( 40,275)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,291)( 47,292)( 48,293)( 49,294)( 50,295)( 51,286)( 52,287)( 53,288)( 54,289)( 55,290)( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,306)( 62,307)( 63,308)( 64,309)( 65,310)( 66,301)( 67,302)( 68,303)( 69,304)( 70,305)( 71,311)( 72,312)( 73,313)( 74,314)( 75,315)( 76,321)( 77,322)( 78,323)( 79,324)( 80,325)( 81,316)( 82,317)( 83,318)( 84,319)( 85,320)( 86,326)( 87,327)( 88,328)( 89,329)( 90,330)( 91,336)( 92,337)( 93,338)( 94,339)( 95,340)( 96,331)( 97,332)( 98,333)( 99,334)(100,335)(101,341)(102,342)(103,343)(104,344)(105,345)(106,351)(107,352)(108,353)(109,354)(110,355)(111,346)(112,347)(113,348)(114,349)(115,350)(116,356)(117,357)(118,358)(119,359)(120,360)(121,366)(122,367)(123,368)(124,369)(125,370)(126,361)(127,362)(128,363)(129,364)(130,365)(131,371)(132,372)(133,373)(134,374)(135,375)(136,381)(137,382)(138,383)(139,384)(140,385)(141,376)(142,377)(143,378)(144,379)(145,380)(146,386)(147,387)(148,388)(149,389)(150,390)(151,396)(152,397)(153,398)(154,399)(155,400)(156,391)(157,392)(158,393)(159,394)(160,395)(161,401)(162,402)(163,403)(164,404)(165,405)(166,411)(167,412)(168,413)(169,414)(170,415)(171,406)(172,407)(173,408)(174,409)(175,410)(176,416)(177,417)(178,418)(179,419)(180,420)(181,426)(182,427)(183,428)(184,429)(185,430)(186,421)(187,422)(188,423)(189,424)(190,425)(191,431)(192,432)(193,433)(194,434)(195,435)(196,441)(197,442)(198,443)(199,444)(200,445)(201,436)(202,437)(203,438)(204,439)(205,440)(206,446)(207,447)(208,448)(209,449)(210,450)(211,456)(212,457)(213,458)(214,459)(215,460)(216,451)(217,452)(218,453)(219,454)(220,455)(221,461)(222,462)(223,463)(224,464)(225,465)(226,471)(227,472)(228,473)(229,474)(230,475)(231,466)(232,467)(233,468)(234,469)(235,470)(236,476)(237,477)(238,478)(239,479)(240,480)(481,726)(482,727)(483,728)(484,729)(485,730)(486,721)(487,722)(488,723)(489,724)(490,725)(491,731)(492,732)(493,733)(494,734)(495,735)(496,741)(497,742)(498,743)(499,744)(500,745)(501,736)(502,737)(503,738)(504,739)(505,740)(506,746)(507,747)(508,748)(509,749)(510,750)(511,756)(512,757)(513,758)(514,759)(515,760)(516,751)(517,752)(518,753)(519,754)(520,755)(521,761)(522,762)(523,763)(524,764)(525,765)(526,771)(527,772)(528,773)(529,774)(530,775)(531,766)(532,767)(533,768)(534,769)(535,770)(536,776)(537,777)(538,778)(539,779)(540,780)(541,786)(542,787)(543,788)(544,789)(545,790)(546,781)(547,782)(548,783)(549,784)(550,785)(551,791)(552,792)(553,793)(554,794)(555,795)(556,801)(557,802)(558,803)(559,804)(560,805)(561,796)(562,797)(563,798)(564,799)(565,800)(566,806)(567,807)(568,808)(569,809)(570,810)(571,816)(572,817)(573,818)(574,819)(575,820)(576,811)(577,812)(578,813)(579,814)(580,815)(581,821)(582,822)(583,823)(584,824)(585,825)(586,831)(587,832)(588,833)(589,834)(590,835)(591,826)(592,827)(593,828)(594,829)(595,830)(596,836)(597,837)(598,838)(599,839)(600,840)(601,846)(602,847)(603,848)(604,849)(605,850)(606,841)(607,842)(608,843)(609,844)(610,845)(611,851)(612,852)(613,853)(614,854)(615,855)(616,861)(617,862)(618,863)(619,864)(620,865)(621,856)(622,857)(623,858)(624,859)(625,860)(626,866)(627,867)(628,868)(629,869)(630,870)(631,876)(632,877)(633,878)(634,879)(635,880)(636,871)(637,872)(638,873)(639,874)(640,875)(641,881)(642,882)(643,883)(644,884)(645,885)(646,891)(647,892)(648,893)(649,894)(650,895)(651,886)(652,887)(653,888)(654,889)(655,890)(656,896)(657,897)(658,898)(659,899)(660,900)(661,906)(662,907)(663,908)(664,909)(665,910)(666,901)(667,902)(668,903)(669,904)(670,905)(671,911)(672,912)(673,913)(674,914)(675,915)(676,921)(677,922)(678,923)(679,924)(680,925)(681,916)(682,917)(683,918)(684,919)(685,920)(686,926)(687,927)(688,928)(689,929)(690,930)(691,936)(692,937)(693,938)(694,939)(695,940)(696,931)(697,932)(698,933)(699,934)(700,935)(701,941)(702,942)(703,943)(704,944)(705,945)(706,951)(707,952)(708,953)(709,954)(710,955)(711,946)(712,947)(713,948)
(714,949)(715,950)(716,956)(717,957)(718,958)(719,959)(720,960);
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, 
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*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*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