Polytope of Type {30,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239473)
Rank : 3
Schlafli Type : {30,8}
Number of vertices, edges, etc : 120, 480, 32
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,8}*960a
   4-fold quotients : {30,4}*480
   5-fold quotients : {6,8}*384e
   8-fold quotients : {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {3,8}*192
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {6,4}*96
   32-fold quotients : {15,2}*60
   40-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   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=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 2.
      16 facets:
         16 of {30}*60
      80 vertex figures:
         40 of {8}*16
         40 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 2.
      16 facets:
         16 of {30}*60
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 2.
      16 facets:
         16 of {30}*60
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      8 facets:
         8 of {30}*60
      60 vertex figures:
         20 of {8}*16
         40 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         20 of {8}*16
         20 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         20 of {8}*16
         20 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*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*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         20 of {8}*16
         20 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*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*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         20 of {8}*16
         20 of {4}*8

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