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