Polytope of Type {12,30}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,30}*960a
if this polytope has a name.
Group : SmallGroup(960,10958)
Rank : 3
Schlafli Type : {12,30}
Number of vertices, edges, etc : 16, 240, 40
Order of s0s1s2 : 40
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,30,2} of size 1920
Vertex Figure Of :
   {2,12,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,15}*480, {6,30}*480
   4-fold quotients : {6,15}*240
   5-fold quotients : {12,6}*192b
   10-fold quotients : {12,3}*96, {6,6}*96
   20-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {2,10}*40
   40-fold quotients : {3,3}*24
   48-fold quotients : {2,5}*20
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,60}*1920a, {12,60}*1920b, {12,30}*1920
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle