Overview
- Group
- SmallGroup(1920,148921)
- Rank
- 4
- Schläfli Type
- {2,40,12}
- Vertices, edges, …
- 2, 40, 240, 12
- 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
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)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)( 63, 78)( 64, 82)( 65, 81)( 66, 80)( 67, 79)( 68, 83)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 88)( 74, 92)( 75, 91)( 76, 90)( 77, 89)( 93,108)( 94,112)( 95,111)( 96,110)( 97,109)( 98,113)( 99,117)(100,116)(101,115)(102,114)(103,118)(104,122)(105,121)(106,120)(107,119)(123,183)(124,187)(125,186)(126,185)(127,184)(128,188)(129,192)(130,191)(131,190)(132,189)(133,193)(134,197)(135,196)(136,195)(137,194)(138,198)(139,202)(140,201)(141,200)(142,199)(143,203)(144,207)(145,206)(146,205)(147,204)(148,208)(149,212)(150,211)(151,210)(152,209)(153,213)(154,217)(155,216)(156,215)(157,214)(158,218)(159,222)(160,221)(161,220)(162,219)(163,223)(164,227)(165,226)(166,225)(167,224)(168,228)(169,232)(170,231)(171,230)(172,229)(173,233)(174,237)(175,236)(176,235)(177,234)(178,238)(179,242)(180,241)(181,240)(182,239);; s2 := ( 3,124)( 4,123)( 5,127)( 6,126)( 7,125)( 8,134)( 9,133)( 10,137)( 11,136)( 12,135)( 13,129)( 14,128)( 15,132)( 16,131)( 17,130)( 18,139)( 19,138)( 20,142)( 21,141)( 22,140)( 23,149)( 24,148)( 25,152)( 26,151)( 27,150)( 28,144)( 29,143)( 30,147)( 31,146)( 32,145)( 33,154)( 34,153)( 35,157)( 36,156)( 37,155)( 38,164)( 39,163)( 40,167)( 41,166)( 42,165)( 43,159)( 44,158)( 45,162)( 46,161)( 47,160)( 48,169)( 49,168)( 50,172)( 51,171)( 52,170)( 53,179)( 54,178)( 55,182)( 56,181)( 57,180)( 58,174)( 59,173)( 60,177)( 61,176)( 62,175)( 63,199)( 64,198)( 65,202)( 66,201)( 67,200)( 68,209)( 69,208)( 70,212)( 71,211)( 72,210)( 73,204)( 74,203)( 75,207)( 76,206)( 77,205)( 78,184)( 79,183)( 80,187)( 81,186)( 82,185)( 83,194)( 84,193)( 85,197)( 86,196)( 87,195)( 88,189)( 89,188)( 90,192)( 91,191)( 92,190)( 93,229)( 94,228)( 95,232)( 96,231)( 97,230)( 98,239)( 99,238)(100,242)(101,241)(102,240)(103,234)(104,233)(105,237)(106,236)(107,235)(108,214)(109,213)(110,217)(111,216)(112,215)(113,224)(114,223)(115,227)(116,226)(117,225)(118,219)(119,218)(120,222)(121,221)(122,220);; s3 := ( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)( 20, 25)( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)( 48, 53)( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)( 94, 99)( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)(112,117)(123,158)(124,159)(125,160)(126,161)(127,162)(128,153)(129,154)(130,155)(131,156)(132,157)(133,163)(134,164)(135,165)(136,166)(137,167)(138,173)(139,174)(140,175)(141,176)(142,177)(143,168)(144,169)(145,170)(146,171)(147,172)(148,178)(149,179)(150,180)(151,181)(152,182)(183,218)(184,219)(185,220)(186,221)(187,222)(188,213)(189,214)(190,215)(191,216)(192,217)(193,223)(194,224)(195,225)(196,226)(197,227)(198,233)(199,234)(200,235)(201,236)(202,237)(203,228)(204,229)(205,230)(206,231)(207,232)(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*s2*s3*s2*s3*s2*s3*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(242)!(1,2); s1 := Sym(242)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)( 63, 78)( 64, 82)( 65, 81)( 66, 80)( 67, 79)( 68, 83)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 88)( 74, 92)( 75, 91)( 76, 90)( 77, 89)( 93,108)( 94,112)( 95,111)( 96,110)( 97,109)( 98,113)( 99,117)(100,116)(101,115)(102,114)(103,118)(104,122)(105,121)(106,120)(107,119)(123,183)(124,187)(125,186)(126,185)(127,184)(128,188)(129,192)(130,191)(131,190)(132,189)(133,193)(134,197)(135,196)(136,195)(137,194)(138,198)(139,202)(140,201)(141,200)(142,199)(143,203)(144,207)(145,206)(146,205)(147,204)(148,208)(149,212)(150,211)(151,210)(152,209)(153,213)(154,217)(155,216)(156,215)(157,214)(158,218)(159,222)(160,221)(161,220)(162,219)(163,223)(164,227)(165,226)(166,225)(167,224)(168,228)(169,232)(170,231)(171,230)(172,229)(173,233)(174,237)(175,236)(176,235)(177,234)(178,238)(179,242)(180,241)(181,240)(182,239); s2 := Sym(242)!( 3,124)( 4,123)( 5,127)( 6,126)( 7,125)( 8,134)( 9,133)( 10,137)( 11,136)( 12,135)( 13,129)( 14,128)( 15,132)( 16,131)( 17,130)( 18,139)( 19,138)( 20,142)( 21,141)( 22,140)( 23,149)( 24,148)( 25,152)( 26,151)( 27,150)( 28,144)( 29,143)( 30,147)( 31,146)( 32,145)( 33,154)( 34,153)( 35,157)( 36,156)( 37,155)( 38,164)( 39,163)( 40,167)( 41,166)( 42,165)( 43,159)( 44,158)( 45,162)( 46,161)( 47,160)( 48,169)( 49,168)( 50,172)( 51,171)( 52,170)( 53,179)( 54,178)( 55,182)( 56,181)( 57,180)( 58,174)( 59,173)( 60,177)( 61,176)( 62,175)( 63,199)( 64,198)( 65,202)( 66,201)( 67,200)( 68,209)( 69,208)( 70,212)( 71,211)( 72,210)( 73,204)( 74,203)( 75,207)( 76,206)( 77,205)( 78,184)( 79,183)( 80,187)( 81,186)( 82,185)( 83,194)( 84,193)( 85,197)( 86,196)( 87,195)( 88,189)( 89,188)( 90,192)( 91,191)( 92,190)( 93,229)( 94,228)( 95,232)( 96,231)( 97,230)( 98,239)( 99,238)(100,242)(101,241)(102,240)(103,234)(104,233)(105,237)(106,236)(107,235)(108,214)(109,213)(110,217)(111,216)(112,215)(113,224)(114,223)(115,227)(116,226)(117,225)(118,219)(119,218)(120,222)(121,221)(122,220); s3 := Sym(242)!( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)( 20, 25)( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)( 48, 53)( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)( 94, 99)( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)(112,117)(123,158)(124,159)(125,160)(126,161)(127,162)(128,153)(129,154)(130,155)(131,156)(132,157)(133,163)(134,164)(135,165)(136,166)(137,167)(138,173)(139,174)(140,175)(141,176)(142,177)(143,168)(144,169)(145,170)(146,171)(147,172)(148,178)(149,179)(150,180)(151,181)(152,182)(183,218)(184,219)(185,220)(186,221)(187,222)(188,213)(189,214)(190,215)(191,216)(192,217)(193,223)(194,224)(195,225)(196,226)(197,227)(198,233)(199,234)(200,235)(201,236)(202,237)(203,228)(204,229)(205,230)(206,231)(207,232)(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*s2*s3*s2*s3*s2*s3*s2*s3*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 >;