Polytope of Type {60,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,4}*960a
if this polytope has a name.
Group : SmallGroup(960,5037)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 120, 240, 8
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {60,4,2} of size 1920
Vertex Figure Of :
   {2,60,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,4}*480a
   3-fold quotients : {20,4}*320
   4-fold quotients : {60,2}*240, {30,4}*240a
   5-fold quotients : {12,4}*192a
   6-fold quotients : {20,4}*160
   8-fold quotients : {30,2}*120
   10-fold quotients : {12,4}*96a
   12-fold quotients : {20,2}*80, {10,4}*80
   15-fold quotients : {4,4}*64
   16-fold quotients : {15,2}*60
   20-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {10,2}*40
   30-fold quotients : {4,4}*32
   40-fold quotients : {6,2}*24
   48-fold quotients : {5,2}*20
   60-fold quotients : {2,4}*16, {4,2}*16
   80-fold quotients : {3,2}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,8}*1920a, {120,4}*1920a, {60,4}*1920a, {120,4}*1920b, {60,8}*1920b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2> of order 2.
      4 facets:
         4 of {60}*120
      90 vertex figures:
         60 of {2}*4
         30 of {4}*8
   P/N, where N=<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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      6 facets:
         4 of {30}*60
         2 of {60}*120
      60 vertex figures:
         60 of {4}*8

Permutation Representation (GAP) : 
s0 := (  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 62, 65)( 63, 64)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)(104,113)(105,112)(121,181)(122,185)(123,184)(124,183)(125,182)(126,191)(127,195)(128,194)(129,193)(130,192)(131,186)(132,190)(133,189)(134,188)(135,187)(136,196)(137,200)(138,199)(139,198)(140,197)(141,206)(142,210)(143,209)(144,208)(145,207)(146,201)(147,205)(148,204)(149,203)(150,202)(151,226)(152,230)(153,229)(154,228)(155,227)(156,236)(157,240)(158,239)(159,238)(160,237)(161,231)(162,235)(163,234)(164,233)(165,232)(166,211)(167,215)(168,214)(169,213)(170,212)(171,221)(172,225)(173,224)(174,223)(175,222)(176,216)(177,220)(178,219)(179,218)(180,217);;
s1 := (  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)(  8,125)(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,157)( 32,156)( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)( 40,153)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)( 48,175)( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,187)( 62,186)( 63,190)( 64,189)( 65,188)( 66,182)( 67,181)( 68,185)( 69,184)( 70,183)( 71,192)( 72,191)( 73,195)( 74,194)( 75,193)( 76,202)( 77,201)( 78,205)( 79,204)( 80,203)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,207)( 87,206)( 88,210)( 89,209)( 90,208)( 91,217)( 92,216)( 93,220)( 94,219)( 95,218)( 96,212)( 97,211)( 98,215)( 99,214)(100,213)(101,222)(102,221)(103,225)(104,224)(105,223)(106,232)(107,231)(108,235)(109,234)(110,233)(111,227)(112,226)(113,230)(114,229)(115,228)(116,237)(117,236)(118,240)(119,239)(120,238);;
s2 := ( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(181,226)(182,227)(183,228)(184,229)(185,230)(186,231)(187,232)(188,233)(189,234)(190,235)(191,236)(192,237)(193,238)(194,239)(195,240)(196,211)(197,212)(198,213)(199,214)(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)(208,223)(209,224)(210,225);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(240)!(  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 62, 65)( 63, 64)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)(104,113)(105,112)(121,181)(122,185)(123,184)(124,183)(125,182)(126,191)(127,195)(128,194)(129,193)(130,192)(131,186)(132,190)(133,189)(134,188)(135,187)(136,196)(137,200)(138,199)(139,198)(140,197)(141,206)(142,210)(143,209)(144,208)(145,207)(146,201)(147,205)(148,204)(149,203)(150,202)(151,226)(152,230)(153,229)(154,228)(155,227)(156,236)(157,240)(158,239)(159,238)(160,237)(161,231)(162,235)(163,234)(164,233)(165,232)(166,211)(167,215)(168,214)(169,213)(170,212)(171,221)(172,225)(173,224)(174,223)(175,222)(176,216)(177,220)(178,219)(179,218)(180,217);
s1 := Sym(240)!(  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)(  8,125)(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,157)( 32,156)( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)( 40,153)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)( 48,175)( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,187)( 62,186)( 63,190)( 64,189)( 65,188)( 66,182)( 67,181)( 68,185)( 69,184)( 70,183)( 71,192)( 72,191)( 73,195)( 74,194)( 75,193)( 76,202)( 77,201)( 78,205)( 79,204)( 80,203)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,207)( 87,206)( 88,210)( 89,209)( 90,208)( 91,217)( 92,216)( 93,220)( 94,219)( 95,218)( 96,212)( 97,211)( 98,215)( 99,214)(100,213)(101,222)(102,221)(103,225)(104,224)(105,223)(106,232)(107,231)(108,235)(109,234)(110,233)(111,227)(112,226)(113,230)(114,229)(115,228)(116,237)(117,236)(118,240)(119,239)(120,238);
s2 := Sym(240)!( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(181,226)(182,227)(183,228)(184,229)(185,230)(186,231)(187,232)(188,233)(189,234)(190,235)(191,236)(192,237)(193,238)(194,239)(195,240)(196,211)(197,212)(198,213)(199,214)(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)(208,223)(209,224)(210,225);
poly := sub<Sym(240)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*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*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 >;
References : None.
to this polytope

Twisty Puzzle