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