Polytope of Type {2,4,60}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,60}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 4
Schlafli Type : {2,4,60}
Number of vertices, edges, etc : 2, 8, 240, 120
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
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 : {2,4,30}*960
4-fold quotients : {2,4,15}*480, {2,4,30}*480b, {2,4,30}*480c
5-fold quotients : {2,4,12}*384c
8-fold quotients : {2,4,15}*240, {2,2,30}*240
10-fold quotients : {2,4,6}*192
16-fold quotients : {2,2,15}*120
20-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
24-fold quotients : {2,2,10}*80
40-fold quotients : {2,4,3}*48, {2,2,6}*48
48-fold quotients : {2,2,5}*40
80-fold quotients : {2,2,3}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(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 := ( 3,123)( 4,125)( 5,124)( 6,126)( 7,139)( 8,141)( 9,140)( 10,142)
( 11,135)( 12,137)( 13,136)( 14,138)( 15,131)( 16,133)( 17,132)( 18,134)
( 19,127)( 20,129)( 21,128)( 22,130)( 23,163)( 24,165)( 25,164)( 26,166)
( 27,179)( 28,181)( 29,180)( 30,182)( 31,175)( 32,177)( 33,176)( 34,178)
( 35,171)( 36,173)( 37,172)( 38,174)( 39,167)( 40,169)( 41,168)( 42,170)
( 43,143)( 44,145)( 45,144)( 46,146)( 47,159)( 48,161)( 49,160)( 50,162)
( 51,155)( 52,157)( 53,156)( 54,158)( 55,151)( 56,153)( 57,152)( 58,154)
( 59,147)( 60,149)( 61,148)( 62,150)( 63,183)( 64,185)( 65,184)( 66,186)
( 67,199)( 68,201)( 69,200)( 70,202)( 71,195)( 72,197)( 73,196)( 74,198)
( 75,191)( 76,193)( 77,192)( 78,194)( 79,187)( 80,189)( 81,188)( 82,190)
( 83,223)( 84,225)( 85,224)( 86,226)( 87,239)( 88,241)( 89,240)( 90,242)
( 91,235)( 92,237)( 93,236)( 94,238)( 95,231)( 96,233)( 97,232)( 98,234)
( 99,227)(100,229)(101,228)(102,230)(103,203)(104,205)(105,204)(106,206)
(107,219)(108,221)(109,220)(110,222)(111,215)(112,217)(113,216)(114,218)
(115,211)(116,213)(117,212)(118,214)(119,207)(120,209)(121,208)(122,210);;
s3 := ( 3, 47)( 4, 50)( 5, 49)( 6, 48)( 7, 43)( 8, 46)( 9, 45)( 10, 44)
( 11, 59)( 12, 62)( 13, 61)( 14, 60)( 15, 55)( 16, 58)( 17, 57)( 18, 56)
( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 27)( 24, 30)( 25, 29)( 26, 28)
( 31, 39)( 32, 42)( 33, 41)( 34, 40)( 36, 38)( 63,107)( 64,110)( 65,109)
( 66,108)( 67,103)( 68,106)( 69,105)( 70,104)( 71,119)( 72,122)( 73,121)
( 74,120)( 75,115)( 76,118)( 77,117)( 78,116)( 79,111)( 80,114)( 81,113)
( 82,112)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 99)( 92,102)( 93,101)
( 94,100)( 96, 98)(123,227)(124,230)(125,229)(126,228)(127,223)(128,226)
(129,225)(130,224)(131,239)(132,242)(133,241)(134,240)(135,235)(136,238)
(137,237)(138,236)(139,231)(140,234)(141,233)(142,232)(143,207)(144,210)
(145,209)(146,208)(147,203)(148,206)(149,205)(150,204)(151,219)(152,222)
(153,221)(154,220)(155,215)(156,218)(157,217)(158,216)(159,211)(160,214)
(161,213)(162,212)(163,187)(164,190)(165,189)(166,188)(167,183)(168,186)
(169,185)(170,184)(171,199)(172,202)(173,201)(174,200)(175,195)(176,198)
(177,197)(178,196)(179,191)(180,194)(181,193)(182,192);;
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*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*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*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*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(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)!( 3,123)( 4,125)( 5,124)( 6,126)( 7,139)( 8,141)( 9,140)
( 10,142)( 11,135)( 12,137)( 13,136)( 14,138)( 15,131)( 16,133)( 17,132)
( 18,134)( 19,127)( 20,129)( 21,128)( 22,130)( 23,163)( 24,165)( 25,164)
( 26,166)( 27,179)( 28,181)( 29,180)( 30,182)( 31,175)( 32,177)( 33,176)
( 34,178)( 35,171)( 36,173)( 37,172)( 38,174)( 39,167)( 40,169)( 41,168)
( 42,170)( 43,143)( 44,145)( 45,144)( 46,146)( 47,159)( 48,161)( 49,160)
( 50,162)( 51,155)( 52,157)( 53,156)( 54,158)( 55,151)( 56,153)( 57,152)
( 58,154)( 59,147)( 60,149)( 61,148)( 62,150)( 63,183)( 64,185)( 65,184)
( 66,186)( 67,199)( 68,201)( 69,200)( 70,202)( 71,195)( 72,197)( 73,196)
( 74,198)( 75,191)( 76,193)( 77,192)( 78,194)( 79,187)( 80,189)( 81,188)
( 82,190)( 83,223)( 84,225)( 85,224)( 86,226)( 87,239)( 88,241)( 89,240)
( 90,242)( 91,235)( 92,237)( 93,236)( 94,238)( 95,231)( 96,233)( 97,232)
( 98,234)( 99,227)(100,229)(101,228)(102,230)(103,203)(104,205)(105,204)
(106,206)(107,219)(108,221)(109,220)(110,222)(111,215)(112,217)(113,216)
(114,218)(115,211)(116,213)(117,212)(118,214)(119,207)(120,209)(121,208)
(122,210);
s3 := Sym(242)!( 3, 47)( 4, 50)( 5, 49)( 6, 48)( 7, 43)( 8, 46)( 9, 45)
( 10, 44)( 11, 59)( 12, 62)( 13, 61)( 14, 60)( 15, 55)( 16, 58)( 17, 57)
( 18, 56)( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 27)( 24, 30)( 25, 29)
( 26, 28)( 31, 39)( 32, 42)( 33, 41)( 34, 40)( 36, 38)( 63,107)( 64,110)
( 65,109)( 66,108)( 67,103)( 68,106)( 69,105)( 70,104)( 71,119)( 72,122)
( 73,121)( 74,120)( 75,115)( 76,118)( 77,117)( 78,116)( 79,111)( 80,114)
( 81,113)( 82,112)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 99)( 92,102)
( 93,101)( 94,100)( 96, 98)(123,227)(124,230)(125,229)(126,228)(127,223)
(128,226)(129,225)(130,224)(131,239)(132,242)(133,241)(134,240)(135,235)
(136,238)(137,237)(138,236)(139,231)(140,234)(141,233)(142,232)(143,207)
(144,210)(145,209)(146,208)(147,203)(148,206)(149,205)(150,204)(151,219)
(152,222)(153,221)(154,220)(155,215)(156,218)(157,217)(158,216)(159,211)
(160,214)(161,213)(162,212)(163,187)(164,190)(165,189)(166,188)(167,183)
(168,186)(169,185)(170,184)(171,199)(172,202)(173,201)(174,200)(175,195)
(176,198)(177,197)(178,196)(179,191)(180,194)(181,193)(182,192);
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*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*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*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*s1*s2*s3*s2*s3*s2 >;
to this polytope