Polytope of Type {60,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,4,2}*960c
if this polytope has a name.
Group : SmallGroup(960,11090)
Rank : 4
Schlafli Type : {60,4,2}
Number of vertices, edges, etc : 60, 120, 4, 2
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{60,4,2,2} of size 1920
Vertex Figure Of :
{2,60,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {30,4,2}*480b
4-fold quotients : {15,4,2}*240
5-fold quotients : {12,4,2}*192c
10-fold quotients : {6,4,2}*96c
20-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {60,4,2}*1920b
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 17)( 6, 19)( 7, 18)( 8, 20)( 9, 13)( 10, 15)( 11, 14)( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)( 27, 58)( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)( 35, 50)( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)( 66, 79)( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)( 82,103)( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)( 90,115)( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)( 98,107)( 99,106)(100,108)(121,181)(122,183)(123,182)(124,184)(125,197)(126,199)(127,198)(128,200)(129,193)(130,195)(131,194)(132,196)(133,189)(134,191)(135,190)(136,192)(137,185)(138,187)(139,186)(140,188)(141,221)(142,223)(143,222)(144,224)(145,237)(146,239)(147,238)(148,240)(149,233)(150,235)(151,234)(152,236)(153,229)(154,231)(155,230)(156,232)(157,225)(158,227)(159,226)(160,228)(161,201)(162,203)(163,202)(164,204)(165,217)(166,219)(167,218)(168,220)(169,213)(170,215)(171,214)(172,216)(173,209)(174,211)(175,210)(176,212)(177,205)(178,207)(179,206)(180,208);;
s1 := ( 1,145)( 2,146)( 3,148)( 4,147)( 5,141)( 6,142)( 7,144)( 8,143)( 9,157)( 10,158)( 11,160)( 12,159)( 13,153)( 14,154)( 15,156)( 16,155)( 17,149)( 18,150)( 19,152)( 20,151)( 21,125)( 22,126)( 23,128)( 24,127)( 25,121)( 26,122)( 27,124)( 28,123)( 29,137)( 30,138)( 31,140)( 32,139)( 33,133)( 34,134)( 35,136)( 36,135)( 37,129)( 38,130)( 39,132)( 40,131)( 41,165)( 42,166)( 43,168)( 44,167)( 45,161)( 46,162)( 47,164)( 48,163)( 49,177)( 50,178)( 51,180)( 52,179)( 53,173)( 54,174)( 55,176)( 56,175)( 57,169)( 58,170)( 59,172)( 60,171)( 61,205)( 62,206)( 63,208)( 64,207)( 65,201)( 66,202)( 67,204)( 68,203)( 69,217)( 70,218)( 71,220)( 72,219)( 73,213)( 74,214)( 75,216)( 76,215)( 77,209)( 78,210)( 79,212)( 80,211)( 81,185)( 82,186)( 83,188)( 84,187)( 85,181)( 86,182)( 87,184)( 88,183)( 89,197)( 90,198)( 91,200)( 92,199)( 93,193)( 94,194)( 95,196)( 96,195)( 97,189)( 98,190)( 99,192)(100,191)(101,225)(102,226)(103,228)(104,227)(105,221)(106,222)(107,224)(108,223)(109,237)(110,238)(111,240)(112,239)(113,233)(114,234)(115,236)(116,235)(117,229)(118,230)(119,232)(120,231);;
s2 := ( 1, 64)( 2, 63)( 3, 62)( 4, 61)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 72)( 10, 71)( 11, 70)( 12, 69)( 13, 76)( 14, 75)( 15, 74)( 16, 73)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 88)( 26, 87)( 27, 86)( 28, 85)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 96)( 34, 95)( 35, 94)( 36, 93)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41,104)( 42,103)( 43,102)( 44,101)( 45,108)( 46,107)( 47,106)( 48,105)( 49,112)( 50,111)( 51,110)( 52,109)( 53,116)( 54,115)( 55,114)( 56,113)( 57,120)( 58,119)( 59,118)( 60,117)(121,184)(122,183)(123,182)(124,181)(125,188)(126,187)(127,186)(128,185)(129,192)(130,191)(131,190)(132,189)(133,196)(134,195)(135,194)(136,193)(137,200)(138,199)(139,198)(140,197)(141,204)(142,203)(143,202)(144,201)(145,208)(146,207)(147,206)(148,205)(149,212)(150,211)(151,210)(152,209)(153,216)(154,215)(155,214)(156,213)(157,220)(158,219)(159,218)(160,217)(161,224)(162,223)(163,222)(164,221)(165,228)(166,227)(167,226)(168,225)(169,232)(170,231)(171,230)(172,229)(173,236)(174,235)(175,234)(176,233)(177,240)(178,239)(179,238)(180,237);;
s3 := (241,242);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*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*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*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!( 2, 3)( 5, 17)( 6, 19)( 7, 18)( 8, 20)( 9, 13)( 10, 15)( 11, 14)( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)( 27, 58)( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)( 35, 50)( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)( 66, 79)( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)( 82,103)( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)( 90,115)( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)( 98,107)( 99,106)(100,108)(121,181)(122,183)(123,182)(124,184)(125,197)(126,199)(127,198)(128,200)(129,193)(130,195)(131,194)(132,196)(133,189)(134,191)(135,190)(136,192)(137,185)(138,187)(139,186)(140,188)(141,221)(142,223)(143,222)(144,224)(145,237)(146,239)(147,238)(148,240)(149,233)(150,235)(151,234)(152,236)(153,229)(154,231)(155,230)(156,232)(157,225)(158,227)(159,226)(160,228)(161,201)(162,203)(163,202)(164,204)(165,217)(166,219)(167,218)(168,220)(169,213)(170,215)(171,214)(172,216)(173,209)(174,211)(175,210)(176,212)(177,205)(178,207)(179,206)(180,208);
s1 := Sym(242)!( 1,145)( 2,146)( 3,148)( 4,147)( 5,141)( 6,142)( 7,144)( 8,143)( 9,157)( 10,158)( 11,160)( 12,159)( 13,153)( 14,154)( 15,156)( 16,155)( 17,149)( 18,150)( 19,152)( 20,151)( 21,125)( 22,126)( 23,128)( 24,127)( 25,121)( 26,122)( 27,124)( 28,123)( 29,137)( 30,138)( 31,140)( 32,139)( 33,133)( 34,134)( 35,136)( 36,135)( 37,129)( 38,130)( 39,132)( 40,131)( 41,165)( 42,166)( 43,168)( 44,167)( 45,161)( 46,162)( 47,164)( 48,163)( 49,177)( 50,178)( 51,180)( 52,179)( 53,173)( 54,174)( 55,176)( 56,175)( 57,169)( 58,170)( 59,172)( 60,171)( 61,205)( 62,206)( 63,208)( 64,207)( 65,201)( 66,202)( 67,204)( 68,203)( 69,217)( 70,218)( 71,220)( 72,219)( 73,213)( 74,214)( 75,216)( 76,215)( 77,209)( 78,210)( 79,212)( 80,211)( 81,185)( 82,186)( 83,188)( 84,187)( 85,181)( 86,182)( 87,184)( 88,183)( 89,197)( 90,198)( 91,200)( 92,199)( 93,193)( 94,194)( 95,196)( 96,195)( 97,189)( 98,190)( 99,192)(100,191)(101,225)(102,226)(103,228)(104,227)(105,221)(106,222)(107,224)(108,223)(109,237)(110,238)(111,240)(112,239)(113,233)(114,234)(115,236)(116,235)(117,229)(118,230)(119,232)(120,231);
s2 := Sym(242)!( 1, 64)( 2, 63)( 3, 62)( 4, 61)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 72)( 10, 71)( 11, 70)( 12, 69)( 13, 76)( 14, 75)( 15, 74)( 16, 73)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 88)( 26, 87)( 27, 86)( 28, 85)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 96)( 34, 95)( 35, 94)( 36, 93)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41,104)( 42,103)( 43,102)( 44,101)( 45,108)( 46,107)( 47,106)( 48,105)( 49,112)( 50,111)( 51,110)( 52,109)( 53,116)( 54,115)( 55,114)( 56,113)( 57,120)( 58,119)( 59,118)( 60,117)(121,184)(122,183)(123,182)(124,181)(125,188)(126,187)(127,186)(128,185)(129,192)(130,191)(131,190)(132,189)(133,196)(134,195)(135,194)(136,193)(137,200)(138,199)(139,198)(140,197)(141,204)(142,203)(143,202)(144,201)(145,208)(146,207)(147,206)(148,205)(149,212)(150,211)(151,210)(152,209)(153,216)(154,215)(155,214)(156,213)(157,220)(158,219)(159,218)(160,217)(161,224)(162,223)(163,222)(164,221)(165,228)(166,227)(167,226)(168,225)(169,232)(170,231)(171,230)(172,229)(173,236)(174,235)(175,234)(176,233)(177,240)(178,239)(179,238)(180,237);
s3 := Sym(242)!(241,242);
poly := sub<Sym(242)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*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*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*s2*s1*s0*s2*s1*s2 >;
to this polytope