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