Overview
- Group
- SmallGroup(1920,148887)
- Rank
- 4
- Schläfli Type
- {2,120,4}
- Vertices, edges, …
- 2, 120, 240, 4
- Order of s0s1s2s3
- 120
- 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)( 34, 37)( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 78)( 64, 82)( 65, 81)( 66, 80)( 67, 79)( 68, 88)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 83)( 74, 87)( 75, 86)( 76, 85)( 77, 84)( 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)(153,213)(154,217)(155,216)(156,215)(157,214)(158,223)(159,227)(160,226)(161,225)(162,224)(163,218)(164,222)(165,221)(166,220)(167,219)(168,228)(169,232)(170,231)(171,230)(172,229)(173,238)(174,242)(175,241)(176,240)(177,239)(178,233)(179,237)(180,236)(181,235)(182,234);; 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)( 63,204)( 64,203)( 65,207)( 66,206)( 67,205)( 68,199)( 69,198)( 70,202)( 71,201)( 72,200)( 73,209)( 74,208)( 75,212)( 76,211)( 77,210)( 78,189)( 79,188)( 80,192)( 81,191)( 82,190)( 83,184)( 84,183)( 85,187)( 86,186)( 87,185)( 88,194)( 89,193)( 90,197)( 91,196)( 92,195)( 93,234)( 94,233)( 95,237)( 96,236)( 97,235)( 98,229)( 99,228)(100,232)(101,231)(102,230)(103,239)(104,238)(105,242)(106,241)(107,240)(108,219)(109,218)(110,222)(111,221)(112,220)(113,214)(114,213)(115,217)(116,216)(117,215)(118,224)(119,223)(120,227)(121,226)(122,225);; s3 := (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)(183,213)(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)(190,220)(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)(207,237)(208,238)(209,239)(210,240)(211,241)(212,242);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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*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)( 34, 37)( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 78)( 64, 82)( 65, 81)( 66, 80)( 67, 79)( 68, 88)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 83)( 74, 87)( 75, 86)( 76, 85)( 77, 84)( 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)(153,213)(154,217)(155,216)(156,215)(157,214)(158,223)(159,227)(160,226)(161,225)(162,224)(163,218)(164,222)(165,221)(166,220)(167,219)(168,228)(169,232)(170,231)(171,230)(172,229)(173,238)(174,242)(175,241)(176,240)(177,239)(178,233)(179,237)(180,236)(181,235)(182,234); 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)( 63,204)( 64,203)( 65,207)( 66,206)( 67,205)( 68,199)( 69,198)( 70,202)( 71,201)( 72,200)( 73,209)( 74,208)( 75,212)( 76,211)( 77,210)( 78,189)( 79,188)( 80,192)( 81,191)( 82,190)( 83,184)( 84,183)( 85,187)( 86,186)( 87,185)( 88,194)( 89,193)( 90,197)( 91,196)( 92,195)( 93,234)( 94,233)( 95,237)( 96,236)( 97,235)( 98,229)( 99,228)(100,232)(101,231)(102,230)(103,239)(104,238)(105,242)(106,241)(107,240)(108,219)(109,218)(110,222)(111,221)(112,220)(113,214)(114,213)(115,217)(116,216)(117,215)(118,224)(119,223)(120,227)(121,226)(122,225); s3 := Sym(242)!(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)(183,213)(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)(190,220)(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)(207,237)(208,238)(209,239)(210,240)(211,241)(212,242); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 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*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 >;