Overview
- Group
- SmallGroup(1920,148923)
- Rank
- 4
- Schläfli Type
- {2,20,24}
- Vertices, edges, …
- 2, 20, 240, 24
- 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)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)(120,121)(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)( 33,169)( 34,168)( 35,172)( 36,171)( 37,170)( 38,179)( 39,178)( 40,182)( 41,181)( 42,180)( 43,174)( 44,173)( 45,177)( 46,176)( 47,175)( 48,154)( 49,153)( 50,157)( 51,156)( 52,155)( 53,164)( 54,163)( 55,167)( 56,166)( 57,165)( 58,159)( 59,158)( 60,162)( 61,161)( 62,160)( 63,184)( 64,183)( 65,187)( 66,186)( 67,185)( 68,194)( 69,193)( 70,197)( 71,196)( 72,195)( 73,189)( 74,188)( 75,192)( 76,191)( 77,190)( 78,199)( 79,198)( 80,202)( 81,201)( 82,200)( 83,209)( 84,208)( 85,212)( 86,211)( 87,210)( 88,204)( 89,203)( 90,207)( 91,206)( 92,205)( 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, 53)( 34, 54)( 35, 55)( 36, 56)( 37, 57)( 38, 48)( 39, 49)( 40, 50)( 41, 51)( 42, 52)( 43, 58)( 44, 59)( 45, 60)( 46, 61)( 47, 62)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93,113)( 94,114)( 95,115)( 96,116)( 97,117)( 98,108)( 99,109)(100,110)(101,111)(102,112)(103,118)(104,119)(105,120)(106,121)(107,122)(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, 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,
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)!( 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)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)(120,121)(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)( 33,169)( 34,168)( 35,172)( 36,171)( 37,170)( 38,179)( 39,178)( 40,182)( 41,181)( 42,180)( 43,174)( 44,173)( 45,177)( 46,176)( 47,175)( 48,154)( 49,153)( 50,157)( 51,156)( 52,155)( 53,164)( 54,163)( 55,167)( 56,166)( 57,165)( 58,159)( 59,158)( 60,162)( 61,161)( 62,160)( 63,184)( 64,183)( 65,187)( 66,186)( 67,185)( 68,194)( 69,193)( 70,197)( 71,196)( 72,195)( 73,189)( 74,188)( 75,192)( 76,191)( 77,190)( 78,199)( 79,198)( 80,202)( 81,201)( 82,200)( 83,209)( 84,208)( 85,212)( 86,211)( 87,210)( 88,204)( 89,203)( 90,207)( 91,206)( 92,205)( 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, 53)( 34, 54)( 35, 55)( 36, 56)( 37, 57)( 38, 48)( 39, 49)( 40, 50)( 41, 51)( 42, 52)( 43, 58)( 44, 59)( 45, 60)( 46, 61)( 47, 62)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93,113)( 94,114)( 95,115)( 96,116)( 97,117)( 98,108)( 99,109)(100,110)(101,111)(102,112)(103,118)(104,119)(105,120)(106,121)(107,122)(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, 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, 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 >;