Overview
- Group
- SmallGroup(1920,150669)
- 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)( 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)( 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)( 94, 97)( 95, 96)( 98,103)( 99,107)(100,106)(101,105)(102,104)(109,112)(110,111)(113,118)(114,122)(115,121)(116,120)(117,119)(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)( 63,204)( 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 := ( 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*s3*s2*s1*s2*s1*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 ];;
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)( 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)( 94, 97)( 95, 96)( 98,103)( 99,107)(100,106)(101,105)(102,104)(109,112)(110,111)(113,118)(114,122)(115,121)(116,120)(117,119)(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)( 63,204)( 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)!( 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*s3*s2*s1*s2*s1*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 >;