Overview
- Group
- SmallGroup(1920,151302)
- Rank
- 4
- Schläfli Type
- {2,60,4}
- Vertices, edges, …
- 2, 120, 240, 8
- Order of s0s1s2s3
- 60
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
5-fold
6-fold
8-fold
10-fold
12-fold
15-fold
16-fold
20-fold
24-fold
30-fold
40-fold
48-fold
60-fold
80-fold
120-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 5, 6)( 8, 13)( 9, 17)( 10, 16)( 11, 15)( 12, 14)( 19, 22)( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 33, 48)( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 58)( 39, 62)( 40, 61)( 41, 60)( 42, 59)( 43, 53)( 44, 57)( 45, 56)( 46, 55)( 47, 54)( 64, 67)( 65, 66)( 68, 73)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)( 85, 91)( 86, 90)( 87, 89)( 93,108)( 94,112)( 95,111)( 96,110)( 97,109)( 98,118)( 99,122)(100,121)(101,120)(102,119)(103,113)(104,117)(105,116)(106,115)(107,114)(123,183)(124,187)(125,186)(126,185)(127,184)(128,193)(129,197)(130,196)(131,195)(132,194)(133,188)(134,192)(135,191)(136,190)(137,189)(138,198)(139,202)(140,201)(141,200)(142,199)(143,208)(144,212)(145,211)(146,210)(147,209)(148,203)(149,207)(150,206)(151,205)(152,204)(153,228)(154,232)(155,231)(156,230)(157,229)(158,238)(159,242)(160,241)(161,240)(162,239)(163,233)(164,237)(165,236)(166,235)(167,234)(168,213)(169,217)(170,216)(171,215)(172,214)(173,223)(174,227)(175,226)(176,225)(177,224)(178,218)(179,222)(180,221)(181,220)(182,219);; s2 := ( 3,129)( 4,128)( 5,132)( 6,131)( 7,130)( 8,124)( 9,123)( 10,127)( 11,126)( 12,125)( 13,134)( 14,133)( 15,137)( 16,136)( 17,135)( 18,144)( 19,143)( 20,147)( 21,146)( 22,145)( 23,139)( 24,138)( 25,142)( 26,141)( 27,140)( 28,149)( 29,148)( 30,152)( 31,151)( 32,150)( 33,159)( 34,158)( 35,162)( 36,161)( 37,160)( 38,154)( 39,153)( 40,157)( 41,156)( 42,155)( 43,164)( 44,163)( 45,167)( 46,166)( 47,165)( 48,174)( 49,173)( 50,177)( 51,176)( 52,175)( 53,169)( 54,168)( 55,172)( 56,171)( 57,170)( 58,179)( 59,178)( 60,182)( 61,181)( 62,180)( 63,189)( 64,188)( 65,192)( 66,191)( 67,190)( 68,184)( 69,183)( 70,187)( 71,186)( 72,185)( 73,194)( 74,193)( 75,197)( 76,196)( 77,195)( 78,204)( 79,203)( 80,207)( 81,206)( 82,205)( 83,199)( 84,198)( 85,202)( 86,201)( 87,200)( 88,209)( 89,208)( 90,212)( 91,211)( 92,210)( 93,219)( 94,218)( 95,222)( 96,221)( 97,220)( 98,214)( 99,213)(100,217)(101,216)(102,215)(103,224)(104,223)(105,227)(106,226)(107,225)(108,234)(109,233)(110,237)(111,236)(112,235)(113,229)(114,228)(115,232)(116,231)(117,230)(118,239)(119,238)(120,242)(121,241)(122,240);; s3 := ( 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)( 76, 91)( 77, 92)( 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)(106,121)(107,122)(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)(151,181)(152,182)(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)(196,241)(197,242)(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)(211,226)(212,227);; 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*s3*s2*s3*s2*s1*s2*s1*s3*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*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*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(242)!(1,2); s1 := Sym(242)!( 4, 7)( 5, 6)( 8, 13)( 9, 17)( 10, 16)( 11, 15)( 12, 14)( 19, 22)( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 33, 48)( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 58)( 39, 62)( 40, 61)( 41, 60)( 42, 59)( 43, 53)( 44, 57)( 45, 56)( 46, 55)( 47, 54)( 64, 67)( 65, 66)( 68, 73)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)( 85, 91)( 86, 90)( 87, 89)( 93,108)( 94,112)( 95,111)( 96,110)( 97,109)( 98,118)( 99,122)(100,121)(101,120)(102,119)(103,113)(104,117)(105,116)(106,115)(107,114)(123,183)(124,187)(125,186)(126,185)(127,184)(128,193)(129,197)(130,196)(131,195)(132,194)(133,188)(134,192)(135,191)(136,190)(137,189)(138,198)(139,202)(140,201)(141,200)(142,199)(143,208)(144,212)(145,211)(146,210)(147,209)(148,203)(149,207)(150,206)(151,205)(152,204)(153,228)(154,232)(155,231)(156,230)(157,229)(158,238)(159,242)(160,241)(161,240)(162,239)(163,233)(164,237)(165,236)(166,235)(167,234)(168,213)(169,217)(170,216)(171,215)(172,214)(173,223)(174,227)(175,226)(176,225)(177,224)(178,218)(179,222)(180,221)(181,220)(182,219); s2 := Sym(242)!( 3,129)( 4,128)( 5,132)( 6,131)( 7,130)( 8,124)( 9,123)( 10,127)( 11,126)( 12,125)( 13,134)( 14,133)( 15,137)( 16,136)( 17,135)( 18,144)( 19,143)( 20,147)( 21,146)( 22,145)( 23,139)( 24,138)( 25,142)( 26,141)( 27,140)( 28,149)( 29,148)( 30,152)( 31,151)( 32,150)( 33,159)( 34,158)( 35,162)( 36,161)( 37,160)( 38,154)( 39,153)( 40,157)( 41,156)( 42,155)( 43,164)( 44,163)( 45,167)( 46,166)( 47,165)( 48,174)( 49,173)( 50,177)( 51,176)( 52,175)( 53,169)( 54,168)( 55,172)( 56,171)( 57,170)( 58,179)( 59,178)( 60,182)( 61,181)( 62,180)( 63,189)( 64,188)( 65,192)( 66,191)( 67,190)( 68,184)( 69,183)( 70,187)( 71,186)( 72,185)( 73,194)( 74,193)( 75,197)( 76,196)( 77,195)( 78,204)( 79,203)( 80,207)( 81,206)( 82,205)( 83,199)( 84,198)( 85,202)( 86,201)( 87,200)( 88,209)( 89,208)( 90,212)( 91,211)( 92,210)( 93,219)( 94,218)( 95,222)( 96,221)( 97,220)( 98,214)( 99,213)(100,217)(101,216)(102,215)(103,224)(104,223)(105,227)(106,226)(107,225)(108,234)(109,233)(110,237)(111,236)(112,235)(113,229)(114,228)(115,232)(116,231)(117,230)(118,239)(119,238)(120,242)(121,241)(122,240); s3 := Sym(242)!( 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)( 76, 91)( 77, 92)( 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)(106,121)(107,122)(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)(151,181)(152,182)(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)(196,241)(197,242)(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)(211,226)(212,227); 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*s3*s2*s3*s2*s1*s2*s1*s3*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*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*s2*s1*s2 >;