Overview
- Group
- SmallGroup(1920,240141)
- Rank
- 4
- Schläfli Type
- {2,20,12}
- Vertices, edges, …
- 2, 40, 240, 24
- Order of s0s1s2s3
- 60
- 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
4-fold
5-fold
8-fold
10-fold
12-fold
20-fold
24-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 := ( 3, 5)( 4, 6)( 7, 21)( 8, 22)( 9, 19)( 10, 20)( 11, 17)( 12, 18)( 13, 15)( 14, 16)( 23, 25)( 24, 26)( 27, 41)( 28, 42)( 29, 39)( 30, 40)( 31, 37)( 32, 38)( 33, 35)( 34, 36)( 43, 45)( 44, 46)( 47, 61)( 48, 62)( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 55)( 54, 56)( 63, 65)( 64, 66)( 67, 81)( 68, 82)( 69, 79)( 70, 80)( 71, 77)( 72, 78)( 73, 75)( 74, 76)( 83, 85)( 84, 86)( 87,101)( 88,102)( 89, 99)( 90,100)( 91, 97)( 92, 98)( 93, 95)( 94, 96)(103,105)(104,106)(107,121)(108,122)(109,119)(110,120)(111,117)(112,118)(113,115)(114,116)(123,125)(124,126)(127,141)(128,142)(129,139)(130,140)(131,137)(132,138)(133,135)(134,136)(143,145)(144,146)(147,161)(148,162)(149,159)(150,160)(151,157)(152,158)(153,155)(154,156)(163,165)(164,166)(167,181)(168,182)(169,179)(170,180)(171,177)(172,178)(173,175)(174,176)(183,185)(184,186)(187,201)(188,202)(189,199)(190,200)(191,197)(192,198)(193,195)(194,196)(203,205)(204,206)(207,221)(208,222)(209,219)(210,220)(211,217)(212,218)(213,215)(214,216)(223,225)(224,226)(227,241)(228,242)(229,239)(230,240)(231,237)(232,238)(233,235)(234,236);; s2 := ( 3, 7)( 4, 9)( 5, 8)( 6, 10)( 11, 19)( 12, 21)( 13, 20)( 14, 22)( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)( 29, 44)( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)( 65, 68)( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)( 84,109)( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)( 92,121)( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)(100,113)(101,112)(102,114)(123,187)(124,189)(125,188)(126,190)(127,183)(128,185)(129,184)(130,186)(131,199)(132,201)(133,200)(134,202)(135,195)(136,197)(137,196)(138,198)(139,191)(140,193)(141,192)(142,194)(143,227)(144,229)(145,228)(146,230)(147,223)(148,225)(149,224)(150,226)(151,239)(152,241)(153,240)(154,242)(155,235)(156,237)(157,236)(158,238)(159,231)(160,233)(161,232)(162,234)(163,207)(164,209)(165,208)(166,210)(167,203)(168,205)(169,204)(170,206)(171,219)(172,221)(173,220)(174,222)(175,215)(176,217)(177,216)(178,218)(179,211)(180,213)(181,212)(182,214);; s3 := ( 3,163)( 4,166)( 5,165)( 6,164)( 7,167)( 8,170)( 9,169)( 10,168)( 11,171)( 12,174)( 13,173)( 14,172)( 15,175)( 16,178)( 17,177)( 18,176)( 19,179)( 20,182)( 21,181)( 22,180)( 23,143)( 24,146)( 25,145)( 26,144)( 27,147)( 28,150)( 29,149)( 30,148)( 31,151)( 32,154)( 33,153)( 34,152)( 35,155)( 36,158)( 37,157)( 38,156)( 39,159)( 40,162)( 41,161)( 42,160)( 43,123)( 44,126)( 45,125)( 46,124)( 47,127)( 48,130)( 49,129)( 50,128)( 51,131)( 52,134)( 53,133)( 54,132)( 55,135)( 56,138)( 57,137)( 58,136)( 59,139)( 60,142)( 61,141)( 62,140)( 63,223)( 64,226)( 65,225)( 66,224)( 67,227)( 68,230)( 69,229)( 70,228)( 71,231)( 72,234)( 73,233)( 74,232)( 75,235)( 76,238)( 77,237)( 78,236)( 79,239)( 80,242)( 81,241)( 82,240)( 83,203)( 84,206)( 85,205)( 86,204)( 87,207)( 88,210)( 89,209)( 90,208)( 91,211)( 92,214)( 93,213)( 94,212)( 95,215)( 96,218)( 97,217)( 98,216)( 99,219)(100,222)(101,221)(102,220)(103,183)(104,186)(105,185)(106,184)(107,187)(108,190)(109,189)(110,188)(111,191)(112,194)(113,193)(114,192)(115,195)(116,198)(117,197)(118,196)(119,199)(120,202)(121,201)(122,200);; 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*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s3*s2,
s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1,
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)!( 3, 5)( 4, 6)( 7, 21)( 8, 22)( 9, 19)( 10, 20)( 11, 17)( 12, 18)( 13, 15)( 14, 16)( 23, 25)( 24, 26)( 27, 41)( 28, 42)( 29, 39)( 30, 40)( 31, 37)( 32, 38)( 33, 35)( 34, 36)( 43, 45)( 44, 46)( 47, 61)( 48, 62)( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 55)( 54, 56)( 63, 65)( 64, 66)( 67, 81)( 68, 82)( 69, 79)( 70, 80)( 71, 77)( 72, 78)( 73, 75)( 74, 76)( 83, 85)( 84, 86)( 87,101)( 88,102)( 89, 99)( 90,100)( 91, 97)( 92, 98)( 93, 95)( 94, 96)(103,105)(104,106)(107,121)(108,122)(109,119)(110,120)(111,117)(112,118)(113,115)(114,116)(123,125)(124,126)(127,141)(128,142)(129,139)(130,140)(131,137)(132,138)(133,135)(134,136)(143,145)(144,146)(147,161)(148,162)(149,159)(150,160)(151,157)(152,158)(153,155)(154,156)(163,165)(164,166)(167,181)(168,182)(169,179)(170,180)(171,177)(172,178)(173,175)(174,176)(183,185)(184,186)(187,201)(188,202)(189,199)(190,200)(191,197)(192,198)(193,195)(194,196)(203,205)(204,206)(207,221)(208,222)(209,219)(210,220)(211,217)(212,218)(213,215)(214,216)(223,225)(224,226)(227,241)(228,242)(229,239)(230,240)(231,237)(232,238)(233,235)(234,236); s2 := Sym(242)!( 3, 7)( 4, 9)( 5, 8)( 6, 10)( 11, 19)( 12, 21)( 13, 20)( 14, 22)( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)( 29, 44)( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)( 65, 68)( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)( 84,109)( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)( 92,121)( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)(100,113)(101,112)(102,114)(123,187)(124,189)(125,188)(126,190)(127,183)(128,185)(129,184)(130,186)(131,199)(132,201)(133,200)(134,202)(135,195)(136,197)(137,196)(138,198)(139,191)(140,193)(141,192)(142,194)(143,227)(144,229)(145,228)(146,230)(147,223)(148,225)(149,224)(150,226)(151,239)(152,241)(153,240)(154,242)(155,235)(156,237)(157,236)(158,238)(159,231)(160,233)(161,232)(162,234)(163,207)(164,209)(165,208)(166,210)(167,203)(168,205)(169,204)(170,206)(171,219)(172,221)(173,220)(174,222)(175,215)(176,217)(177,216)(178,218)(179,211)(180,213)(181,212)(182,214); s3 := Sym(242)!( 3,163)( 4,166)( 5,165)( 6,164)( 7,167)( 8,170)( 9,169)( 10,168)( 11,171)( 12,174)( 13,173)( 14,172)( 15,175)( 16,178)( 17,177)( 18,176)( 19,179)( 20,182)( 21,181)( 22,180)( 23,143)( 24,146)( 25,145)( 26,144)( 27,147)( 28,150)( 29,149)( 30,148)( 31,151)( 32,154)( 33,153)( 34,152)( 35,155)( 36,158)( 37,157)( 38,156)( 39,159)( 40,162)( 41,161)( 42,160)( 43,123)( 44,126)( 45,125)( 46,124)( 47,127)( 48,130)( 49,129)( 50,128)( 51,131)( 52,134)( 53,133)( 54,132)( 55,135)( 56,138)( 57,137)( 58,136)( 59,139)( 60,142)( 61,141)( 62,140)( 63,223)( 64,226)( 65,225)( 66,224)( 67,227)( 68,230)( 69,229)( 70,228)( 71,231)( 72,234)( 73,233)( 74,232)( 75,235)( 76,238)( 77,237)( 78,236)( 79,239)( 80,242)( 81,241)( 82,240)( 83,203)( 84,206)( 85,205)( 86,204)( 87,207)( 88,210)( 89,209)( 90,208)( 91,211)( 92,214)( 93,213)( 94,212)( 95,215)( 96,218)( 97,217)( 98,216)( 99,219)(100,222)(101,221)(102,220)(103,183)(104,186)(105,185)(106,184)(107,187)(108,190)(109,189)(110,188)(111,191)(112,194)(113,193)(114,192)(115,195)(116,198)(117,197)(118,196)(119,199)(120,202)(121,201)(122,200); 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*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s3*s2, s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;