Polytope of Type {4,60}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,60}*1920d
if this polytope has a name.
Group : SmallGroup(1920,239398)
Rank : 3
Schlafli Type : {4,60}
Number of vertices, edges, etc : 16, 480, 240
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,60}*960b, {4,30}*960b, {4,60}*960c
   4-fold quotients : {4,60}*480a, {4,60}*480b, {4,60}*480c, {4,30}*480
   5-fold quotients : {4,12}*384d
   8-fold quotients : {2,60}*240, {4,30}*240a, {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {4,12}*192b, {4,6}*192b, {4,12}*192c
   12-fold quotients : {4,20}*160
   16-fold quotients : {4,15}*120, {2,30}*120
   20-fold quotients : {4,12}*96a, {4,12}*96b, {4,12}*96c, {4,6}*96
   24-fold quotients : {2,20}*80, {4,10}*80
   32-fold quotients : {2,15}*60
   40-fold quotients : {2,12}*48, {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*32
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1> of order 2.
      160 facets:
         80 of {2}*4
         80 of {4}*8
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      120 facets:
         120 of {4}*8
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      120 facets:
         120 of {4}*8
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*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> of order 2.
      120 facets:
         120 of {4}*8
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*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> of order 2.
      120 facets:
         120 of {4}*8
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<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> of order 3.
      80 facets:
         80 of {4}*8
      8 vertex figures:
         4 of {20}*40
         4 of {60}*120
   P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      100 facets:
         20 of {4}*8
         80 of {2}*4
      4 vertex figures:
         4 of {60}*120
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*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> of order 4.
      60 facets:
         60 of {4}*8
      4 vertex figures:
         4 of {60}*120
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*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> of order 4.
      60 facets:
         60 of {4}*8
      4 vertex figures:
         4 of {60}*120

Permutation Representation (GAP) :

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,363)(242,364)(243,361)(244,362)(245,367)(246,368)(247,365)(248,366)(249,371)(250,372)(251,369)(252,370)(253,375)(254,376)(255,373)(256,374)(257,379)(258,380)(259,377)(260,378)(261,383)(262,384)(263,381)(264,382)(265,387)(266,388)(267,385)(268,386)(269,391)(270,392)(271,389)(272,390)(273,395)(274,396)(275,393)(276,394)(277,399)(278,400)(279,397)(280,398)(281,403)(282,404)(283,401)(284,402)(285,407)(286,408)(287,405)(288,406)(289,411)(290,412)(291,409)(292,410)(293,415)(294,416)(295,413)(296,414)(297,419)(298,420)(299,417)(300,418)(301,423)(302,424)(303,421)(304,422)(305,427)(306,428)(307,425)(308,426)(309,431)(310,432)(311,429)(312,430)(313,435)(314,436)(315,433)(316,434)(317,439)(318,440)(319,437)(320,438)(321,443)(322,444)(323,441)(324,442)(325,447)(326,448)(327,445)(328,446)(329,451)(330,452)(331,449)(332,450)(333,455)(334,456)(335,453)(336,454)(337,459)(338,460)(339,457)(340,458)(341,463)(342,464)(343,461)(344,462)(345,467)(346,468)(347,465)(348,466)(349,471)(350,472)(351,469)(352,470)(353,475)(354,476)(355,473)(356,474)(357,479)(358,480)(359,477)(360,478);;
s1 := (  1,241)(  2,242)(  3,244)(  4,243)(  5,257)(  6,258)(  7,260)(  8,259)(  9,253)( 10,254)( 11,256)( 12,255)( 13,249)( 14,250)( 15,252)( 16,251)( 17,245)( 18,246)( 19,248)( 20,247)( 21,281)( 22,282)( 23,284)( 24,283)( 25,297)( 26,298)( 27,300)( 28,299)( 29,293)( 30,294)( 31,296)( 32,295)( 33,289)( 34,290)( 35,292)( 36,291)( 37,285)( 38,286)( 39,288)( 40,287)( 41,261)( 42,262)( 43,264)( 44,263)( 45,277)( 46,278)( 47,280)( 48,279)( 49,273)( 50,274)( 51,276)( 52,275)( 53,269)( 54,270)( 55,272)( 56,271)( 57,265)( 58,266)( 59,268)( 60,267)( 61,301)( 62,302)( 63,304)( 64,303)( 65,317)( 66,318)( 67,320)( 68,319)( 69,313)( 70,314)( 71,316)( 72,315)( 73,309)( 74,310)( 75,312)( 76,311)( 77,305)( 78,306)( 79,308)( 80,307)( 81,341)( 82,342)( 83,344)( 84,343)( 85,357)( 86,358)( 87,360)( 88,359)( 89,353)( 90,354)( 91,356)( 92,355)( 93,349)( 94,350)( 95,352)( 96,351)( 97,345)( 98,346)( 99,348)(100,347)(101,321)(102,322)(103,324)(104,323)(105,337)(106,338)(107,340)(108,339)(109,333)(110,334)(111,336)(112,335)(113,329)(114,330)(115,332)(116,331)(117,325)(118,326)(119,328)(120,327)(121,361)(122,362)(123,364)(124,363)(125,377)(126,378)(127,380)(128,379)(129,373)(130,374)(131,376)(132,375)(133,369)(134,370)(135,372)(136,371)(137,365)(138,366)(139,368)(140,367)(141,401)(142,402)(143,404)(144,403)(145,417)(146,418)(147,420)(148,419)(149,413)(150,414)(151,416)(152,415)(153,409)(154,410)(155,412)(156,411)(157,405)(158,406)(159,408)(160,407)(161,381)(162,382)(163,384)(164,383)(165,397)(166,398)(167,400)(168,399)(169,393)(170,394)(171,396)(172,395)(173,389)(174,390)(175,392)(176,391)(177,385)(178,386)(179,388)(180,387)(181,421)(182,422)(183,424)(184,423)(185,437)(186,438)(187,440)(188,439)(189,433)(190,434)(191,436)(192,435)(193,429)(194,430)(195,432)(196,431)(197,425)(198,426)(199,428)(200,427)(201,461)(202,462)(203,464)(204,463)(205,477)(206,478)(207,480)(208,479)(209,473)(210,474)(211,476)(212,475)(213,469)(214,470)(215,472)(216,471)(217,465)(218,466)(219,468)(220,467)(221,441)(222,442)(223,444)(224,443)(225,457)(226,458)(227,460)(228,459)(229,453)(230,454)(231,456)(232,455)(233,449)(234,450)(235,452)(236,451)(237,445)(238,446)(239,448)(240,447);;
s2 := (  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 21)(  6, 24)(  7, 23)(  8, 22)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)(134,156)(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)(162,168)(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)(181,205)(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)(189,217)(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)(197,209)(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)(229,237)(230,240)(231,239)(232,238)(234,236)(241,325)(242,328)(243,327)(244,326)(245,321)(246,324)(247,323)(248,322)(249,337)(250,340)(251,339)(252,338)(253,333)(254,336)(255,335)(256,334)(257,329)(258,332)(259,331)(260,330)(261,305)(262,308)(263,307)(264,306)(265,301)(266,304)(267,303)(268,302)(269,317)(270,320)(271,319)(272,318)(273,313)(274,316)(275,315)(276,314)(277,309)(278,312)(279,311)(280,310)(281,345)(282,348)(283,347)(284,346)(285,341)(286,344)(287,343)(288,342)(289,357)(290,360)(291,359)(292,358)(293,353)(294,356)(295,355)(296,354)(297,349)(298,352)(299,351)(300,350)(361,445)(362,448)(363,447)(364,446)(365,441)(366,444)(367,443)(368,442)(369,457)(370,460)(371,459)(372,458)(373,453)(374,456)(375,455)(376,454)(377,449)(378,452)(379,451)(380,450)(381,425)(382,428)(383,427)(384,426)(385,421)(386,424)(387,423)(388,422)(389,437)(390,440)(391,439)(392,438)(393,433)(394,436)(395,435)(396,434)(397,429)(398,432)(399,431)(400,430)(401,465)(402,468)(403,467)(404,466)(405,461)(406,464)(407,463)(408,462)(409,477)(410,480)(411,479)(412,478)(413,473)(414,476)(415,475)(416,474)(417,469)(418,472)(419,471)(420,470);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0, 
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*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(480)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,363)(242,364)(243,361)(244,362)(245,367)(246,368)(247,365)(248,366)(249,371)(250,372)(251,369)(252,370)(253,375)(254,376)(255,373)(256,374)(257,379)(258,380)(259,377)(260,378)(261,383)(262,384)(263,381)(264,382)(265,387)(266,388)(267,385)(268,386)(269,391)(270,392)(271,389)(272,390)(273,395)(274,396)(275,393)(276,394)(277,399)(278,400)(279,397)(280,398)(281,403)(282,404)(283,401)(284,402)(285,407)(286,408)(287,405)(288,406)(289,411)(290,412)(291,409)(292,410)(293,415)(294,416)(295,413)(296,414)(297,419)(298,420)(299,417)(300,418)(301,423)(302,424)(303,421)(304,422)(305,427)(306,428)(307,425)(308,426)(309,431)(310,432)(311,429)(312,430)(313,435)(314,436)(315,433)(316,434)(317,439)(318,440)(319,437)(320,438)(321,443)(322,444)(323,441)(324,442)(325,447)(326,448)(327,445)(328,446)(329,451)(330,452)(331,449)(332,450)(333,455)(334,456)(335,453)(336,454)(337,459)(338,460)(339,457)(340,458)(341,463)(342,464)(343,461)(344,462)(345,467)(346,468)(347,465)(348,466)(349,471)(350,472)(351,469)(352,470)(353,475)(354,476)(355,473)(356,474)(357,479)(358,480)(359,477)(360,478);
s1 := Sym(480)!(  1,241)(  2,242)(  3,244)(  4,243)(  5,257)(  6,258)(  7,260)(  8,259)(  9,253)( 10,254)( 11,256)( 12,255)( 13,249)( 14,250)( 15,252)( 16,251)( 17,245)( 18,246)( 19,248)( 20,247)( 21,281)( 22,282)( 23,284)( 24,283)( 25,297)( 26,298)( 27,300)( 28,299)( 29,293)( 30,294)( 31,296)( 32,295)( 33,289)( 34,290)( 35,292)( 36,291)( 37,285)( 38,286)( 39,288)( 40,287)( 41,261)( 42,262)( 43,264)( 44,263)( 45,277)( 46,278)( 47,280)( 48,279)( 49,273)( 50,274)( 51,276)( 52,275)( 53,269)( 54,270)( 55,272)( 56,271)( 57,265)( 58,266)( 59,268)( 60,267)( 61,301)( 62,302)( 63,304)( 64,303)( 65,317)( 66,318)( 67,320)( 68,319)( 69,313)( 70,314)( 71,316)( 72,315)( 73,309)( 74,310)( 75,312)( 76,311)( 77,305)( 78,306)( 79,308)( 80,307)( 81,341)( 82,342)( 83,344)( 84,343)( 85,357)( 86,358)( 87,360)( 88,359)( 89,353)( 90,354)( 91,356)( 92,355)( 93,349)( 94,350)( 95,352)( 96,351)( 97,345)( 98,346)( 99,348)(100,347)(101,321)(102,322)(103,324)(104,323)(105,337)(106,338)(107,340)(108,339)(109,333)(110,334)(111,336)(112,335)(113,329)(114,330)(115,332)(116,331)(117,325)(118,326)(119,328)(120,327)(121,361)(122,362)(123,364)(124,363)(125,377)(126,378)(127,380)(128,379)(129,373)(130,374)(131,376)(132,375)(133,369)(134,370)(135,372)(136,371)(137,365)(138,366)(139,368)(140,367)(141,401)(142,402)(143,404)(144,403)(145,417)(146,418)(147,420)(148,419)(149,413)(150,414)(151,416)(152,415)(153,409)(154,410)(155,412)(156,411)(157,405)(158,406)(159,408)(160,407)(161,381)(162,382)(163,384)(164,383)(165,397)(166,398)(167,400)(168,399)(169,393)(170,394)(171,396)(172,395)(173,389)(174,390)(175,392)(176,391)(177,385)(178,386)(179,388)(180,387)(181,421)(182,422)(183,424)(184,423)(185,437)(186,438)(187,440)(188,439)(189,433)(190,434)(191,436)(192,435)(193,429)(194,430)(195,432)(196,431)(197,425)(198,426)(199,428)(200,427)(201,461)(202,462)(203,464)(204,463)(205,477)(206,478)(207,480)(208,479)(209,473)(210,474)(211,476)(212,475)(213,469)(214,470)(215,472)(216,471)(217,465)(218,466)(219,468)(220,467)(221,441)(222,442)(223,444)(224,443)(225,457)(226,458)(227,460)(228,459)(229,453)(230,454)(231,456)(232,455)(233,449)(234,450)(235,452)(236,451)(237,445)(238,446)(239,448)(240,447);
s2 := Sym(480)!(  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 21)(  6, 24)(  7, 23)(  8, 22)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)(134,156)(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)(162,168)(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)(181,205)(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)(189,217)(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)(197,209)(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)(229,237)(230,240)(231,239)(232,238)(234,236)(241,325)(242,328)(243,327)(244,326)(245,321)(246,324)(247,323)(248,322)(249,337)(250,340)(251,339)(252,338)(253,333)(254,336)(255,335)(256,334)(257,329)(258,332)(259,331)(260,330)(261,305)(262,308)(263,307)(264,306)(265,301)(266,304)(267,303)(268,302)(269,317)(270,320)(271,319)(272,318)(273,313)(274,316)(275,315)(276,314)(277,309)(278,312)(279,311)(280,310)(281,345)(282,348)(283,347)(284,346)(285,341)(286,344)(287,343)(288,342)(289,357)(290,360)(291,359)(292,358)(293,353)(294,356)(295,355)(296,354)(297,349)(298,352)(299,351)(300,350)(361,445)(362,448)(363,447)(364,446)(365,441)(366,444)(367,443)(368,442)(369,457)(370,460)(371,459)(372,458)(373,453)(374,456)(375,455)(376,454)(377,449)(378,452)(379,451)(380,450)(381,425)(382,428)(383,427)(384,426)(385,421)(386,424)(387,423)(388,422)(389,437)(390,440)(391,439)(392,438)(393,433)(394,436)(395,435)(396,434)(397,429)(398,432)(399,431)(400,430)(401,465)(402,468)(403,467)(404,466)(405,461)(406,464)(407,463)(408,462)(409,477)(410,480)(411,479)(412,478)(413,473)(414,476)(415,475)(416,474)(417,469)(418,472)(419,471)(420,470);
poly := sub<Sym(480)|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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0, 
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*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 {4,60}

Twisty Puzzle