Polytope of Type {24,40}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,40}*1920a
Also Known As : {24,40|2}. if this polytope has another name.
Group : SmallGroup(1920,14533)
Rank : 3
Schlafli Type : {24,40}
Number of vertices, edges, etc : 24, 480, 40
Order of s₀s₁s₂ : 120
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 : {24,20}*960a, {12,40}*960a
   3-fold quotients : {8,40}*640b
   4-fold quotients : {24,10}*480, {6,40}*480, {12,20}*480
   5-fold quotients : {24,8}*384b
   6-fold quotients : {4,40}*320a, {8,20}*320a
   8-fold quotients : {12,10}*240, {6,20}*240a
   10-fold quotients : {24,4}*192a, {12,8}*192a
   12-fold quotients : {4,20}*160, {2,40}*160, {8,10}*160
   15-fold quotients : {8,8}*128b
   16-fold quotients : {6,10}*120
   20-fold quotients : {12,4}*96a, {24,2}*96, {6,8}*96
   24-fold quotients : {2,20}*80, {4,10}*80
   30-fold quotients : {4,8}*64a, {8,4}*64a
   40-fold quotients : {12,2}*48, {6,4}*48a
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
   80-fold quotients : {6,2}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16, {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):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {24,40}

Twisty Puzzle