Overview
- Group
- SmallGroup(1920,148884)
- Rank
- 4
- Schläfli Type
- {2,8,60}
- Vertices, edges, …
- 2, 8, 240, 60
- 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 := ( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 46, 61)( 47, 62)( 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)(183,213)(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);; s2 := ( 3,123)( 4,127)( 5,126)( 6,125)( 7,124)( 8,133)( 9,137)( 10,136)( 11,135)( 12,134)( 13,128)( 14,132)( 15,131)( 16,130)( 17,129)( 18,138)( 19,142)( 20,141)( 21,140)( 22,139)( 23,148)( 24,152)( 25,151)( 26,150)( 27,149)( 28,143)( 29,147)( 30,146)( 31,145)( 32,144)( 33,168)( 34,172)( 35,171)( 36,170)( 37,169)( 38,178)( 39,182)( 40,181)( 41,180)( 42,179)( 43,173)( 44,177)( 45,176)( 46,175)( 47,174)( 48,153)( 49,157)( 50,156)( 51,155)( 52,154)( 53,163)( 54,167)( 55,166)( 56,165)( 57,164)( 58,158)( 59,162)( 60,161)( 61,160)( 62,159)( 63,183)( 64,187)( 65,186)( 66,185)( 67,184)( 68,193)( 69,197)( 70,196)( 71,195)( 72,194)( 73,188)( 74,192)( 75,191)( 76,190)( 77,189)( 78,198)( 79,202)( 80,201)( 81,200)( 82,199)( 83,208)( 84,212)( 85,211)( 86,210)( 87,209)( 88,203)( 89,207)( 90,206)( 91,205)( 92,204)( 93,228)( 94,232)( 95,231)( 96,230)( 97,229)( 98,238)( 99,242)(100,241)(101,240)(102,239)(103,233)(104,237)(105,236)(106,235)(107,234)(108,213)(109,217)(110,216)(111,215)(112,214)(113,223)(114,227)(115,226)(116,225)(117,224)(118,218)(119,222)(120,221)(121,220)(122,219);; s3 := ( 3, 9)( 4, 8)( 5, 12)( 6, 11)( 7, 10)( 13, 14)( 15, 17)( 18, 24)( 19, 23)( 20, 27)( 21, 26)( 22, 25)( 28, 29)( 30, 32)( 33, 39)( 34, 38)( 35, 42)( 36, 41)( 37, 40)( 43, 44)( 45, 47)( 48, 54)( 49, 53)( 50, 57)( 51, 56)( 52, 55)( 58, 59)( 60, 62)( 63, 69)( 64, 68)( 65, 72)( 66, 71)( 67, 70)( 73, 74)( 75, 77)( 78, 84)( 79, 83)( 80, 87)( 81, 86)( 82, 85)( 88, 89)( 90, 92)( 93, 99)( 94, 98)( 95,102)( 96,101)( 97,100)(103,104)(105,107)(108,114)(109,113)(110,117)(111,116)(112,115)(118,119)(120,122)(123,189)(124,188)(125,192)(126,191)(127,190)(128,184)(129,183)(130,187)(131,186)(132,185)(133,194)(134,193)(135,197)(136,196)(137,195)(138,204)(139,203)(140,207)(141,206)(142,205)(143,199)(144,198)(145,202)(146,201)(147,200)(148,209)(149,208)(150,212)(151,211)(152,210)(153,219)(154,218)(155,222)(156,221)(157,220)(158,214)(159,213)(160,217)(161,216)(162,215)(163,224)(164,223)(165,227)(166,226)(167,225)(168,234)(169,233)(170,237)(171,236)(172,235)(173,229)(174,228)(175,232)(176,231)(177,230)(178,239)(179,238)(180,242)(181,241)(182,240);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(242)!(1,2); s1 := Sym(242)!( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 46, 61)( 47, 62)( 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)(183,213)(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); s2 := Sym(242)!( 3,123)( 4,127)( 5,126)( 6,125)( 7,124)( 8,133)( 9,137)( 10,136)( 11,135)( 12,134)( 13,128)( 14,132)( 15,131)( 16,130)( 17,129)( 18,138)( 19,142)( 20,141)( 21,140)( 22,139)( 23,148)( 24,152)( 25,151)( 26,150)( 27,149)( 28,143)( 29,147)( 30,146)( 31,145)( 32,144)( 33,168)( 34,172)( 35,171)( 36,170)( 37,169)( 38,178)( 39,182)( 40,181)( 41,180)( 42,179)( 43,173)( 44,177)( 45,176)( 46,175)( 47,174)( 48,153)( 49,157)( 50,156)( 51,155)( 52,154)( 53,163)( 54,167)( 55,166)( 56,165)( 57,164)( 58,158)( 59,162)( 60,161)( 61,160)( 62,159)( 63,183)( 64,187)( 65,186)( 66,185)( 67,184)( 68,193)( 69,197)( 70,196)( 71,195)( 72,194)( 73,188)( 74,192)( 75,191)( 76,190)( 77,189)( 78,198)( 79,202)( 80,201)( 81,200)( 82,199)( 83,208)( 84,212)( 85,211)( 86,210)( 87,209)( 88,203)( 89,207)( 90,206)( 91,205)( 92,204)( 93,228)( 94,232)( 95,231)( 96,230)( 97,229)( 98,238)( 99,242)(100,241)(101,240)(102,239)(103,233)(104,237)(105,236)(106,235)(107,234)(108,213)(109,217)(110,216)(111,215)(112,214)(113,223)(114,227)(115,226)(116,225)(117,224)(118,218)(119,222)(120,221)(121,220)(122,219); s3 := Sym(242)!( 3, 9)( 4, 8)( 5, 12)( 6, 11)( 7, 10)( 13, 14)( 15, 17)( 18, 24)( 19, 23)( 20, 27)( 21, 26)( 22, 25)( 28, 29)( 30, 32)( 33, 39)( 34, 38)( 35, 42)( 36, 41)( 37, 40)( 43, 44)( 45, 47)( 48, 54)( 49, 53)( 50, 57)( 51, 56)( 52, 55)( 58, 59)( 60, 62)( 63, 69)( 64, 68)( 65, 72)( 66, 71)( 67, 70)( 73, 74)( 75, 77)( 78, 84)( 79, 83)( 80, 87)( 81, 86)( 82, 85)( 88, 89)( 90, 92)( 93, 99)( 94, 98)( 95,102)( 96,101)( 97,100)(103,104)(105,107)(108,114)(109,113)(110,117)(111,116)(112,115)(118,119)(120,122)(123,189)(124,188)(125,192)(126,191)(127,190)(128,184)(129,183)(130,187)(131,186)(132,185)(133,194)(134,193)(135,197)(136,196)(137,195)(138,204)(139,203)(140,207)(141,206)(142,205)(143,199)(144,198)(145,202)(146,201)(147,200)(148,209)(149,208)(150,212)(151,211)(152,210)(153,219)(154,218)(155,222)(156,221)(157,220)(158,214)(159,213)(160,217)(161,216)(162,215)(163,224)(164,223)(165,227)(166,226)(167,225)(168,234)(169,233)(170,237)(171,236)(172,235)(173,229)(174,228)(175,232)(176,231)(177,230)(178,239)(179,238)(180,242)(181,241)(182,240); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*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*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 >;