Polytope of Type {120,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,239539)
Rank : 3
Schlafli Type : {120,4}
Number of vertices, edges, etc : 240, 480, 8
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {120,4}*960c, {120,4}*960d, {60,4}*960b
   4-fold quotients : {120,2}*480, {60,4}*480b, {60,4}*480c, {30,4}*480
   5-fold quotients : {24,4}*384c
   8-fold quotients : {60,2}*240, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {24,4}*192c, {24,4}*192d, {12,4}*192b
   12-fold quotients : {40,2}*160
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {24,2}*96, {12,4}*96b, {12,4}*96c, {6,4}*96
   24-fold quotients : {20,2}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   60-fold quotients : {8,2}*32
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {4,2}*16
   160-fold quotients : {3,2}*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):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      4 facets:
         4 of {120}*240
      160 vertex figures:
         80 of {4}*8
         80 of {2}*4

Permutation Representation (GAP) :

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

Polytope of Type {120,4}

Twisty Puzzle