Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,15}

Atlas Canonical Name {8,15}*1920c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1920,240273)
Rank
3
Schläfli Type
{8,15}
Vertices, edges, …
64, 480, 120
Order of s0s1s2
60
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

12-fold

32-fold

96-fold

160-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*(s1*s0)^2*s2> of order 2

60 facets

32 vertex figures

P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 2

60 facets

32 vertex figures

P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s1*s0)^2*s2*s1*s0*s1*s2> of order 4

30 facets

16 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle