Part of the Atlas of Small Regular Polytopes

Polytope of Type {30,8}

Atlas Canonical Name {30,8}*1920k

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1920,240269)
Rank
3
Schläfli Type
{30,8}
Vertices, edges, …
120, 480, 32
Order of s0s1s2
15
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

12-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle