Overview
- Group
- SmallGroup(1920,240291)
- Rank
- 4
- Schläfli Type
- {2,4,30}
- Vertices, edges, …
- 2, 16, 240, 120
- 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
16-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, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)(115,117)(116,118)(119,121)(120,122)(123,185)(124,186)(125,183)(126,184)(127,189)(128,190)(129,187)(130,188)(131,193)(132,194)(133,191)(134,192)(135,197)(136,198)(137,195)(138,196)(139,201)(140,202)(141,199)(142,200)(143,205)(144,206)(145,203)(146,204)(147,209)(148,210)(149,207)(150,208)(151,213)(152,214)(153,211)(154,212)(155,217)(156,218)(157,215)(158,216)(159,221)(160,222)(161,219)(162,220)(163,225)(164,226)(165,223)(166,224)(167,229)(168,230)(169,227)(170,228)(171,233)(172,234)(173,231)(174,232)(175,237)(176,238)(177,235)(178,236)(179,241)(180,242)(181,239)(182,240);; s2 := ( 3,123)( 4,125)( 5,124)( 6,126)( 7,139)( 8,141)( 9,140)( 10,142)( 11,135)( 12,137)( 13,136)( 14,138)( 15,131)( 16,133)( 17,132)( 18,134)( 19,127)( 20,129)( 21,128)( 22,130)( 23,163)( 24,165)( 25,164)( 26,166)( 27,179)( 28,181)( 29,180)( 30,182)( 31,175)( 32,177)( 33,176)( 34,178)( 35,171)( 36,173)( 37,172)( 38,174)( 39,167)( 40,169)( 41,168)( 42,170)( 43,143)( 44,145)( 45,144)( 46,146)( 47,159)( 48,161)( 49,160)( 50,162)( 51,155)( 52,157)( 53,156)( 54,158)( 55,151)( 56,153)( 57,152)( 58,154)( 59,147)( 60,149)( 61,148)( 62,150)( 63,183)( 64,185)( 65,184)( 66,186)( 67,199)( 68,201)( 69,200)( 70,202)( 71,195)( 72,197)( 73,196)( 74,198)( 75,191)( 76,193)( 77,192)( 78,194)( 79,187)( 80,189)( 81,188)( 82,190)( 83,223)( 84,225)( 85,224)( 86,226)( 87,239)( 88,241)( 89,240)( 90,242)( 91,235)( 92,237)( 93,236)( 94,238)( 95,231)( 96,233)( 97,232)( 98,234)( 99,227)(100,229)(101,228)(102,230)(103,203)(104,205)(105,204)(106,206)(107,219)(108,221)(109,220)(110,222)(111,215)(112,217)(113,216)(114,218)(115,211)(116,213)(117,212)(118,214)(119,207)(120,209)(121,208)(122,210);; s3 := ( 3, 47)( 4, 50)( 5, 49)( 6, 48)( 7, 43)( 8, 46)( 9, 45)( 10, 44)( 11, 59)( 12, 62)( 13, 61)( 14, 60)( 15, 55)( 16, 58)( 17, 57)( 18, 56)( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 27)( 24, 30)( 25, 29)( 26, 28)( 31, 39)( 32, 42)( 33, 41)( 34, 40)( 36, 38)( 63,107)( 64,110)( 65,109)( 66,108)( 67,103)( 68,106)( 69,105)( 70,104)( 71,119)( 72,122)( 73,121)( 74,120)( 75,115)( 76,118)( 77,117)( 78,116)( 79,111)( 80,114)( 81,113)( 82,112)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 99)( 92,102)( 93,101)( 94,100)( 96, 98)(123,167)(124,170)(125,169)(126,168)(127,163)(128,166)(129,165)(130,164)(131,179)(132,182)(133,181)(134,180)(135,175)(136,178)(137,177)(138,176)(139,171)(140,174)(141,173)(142,172)(143,147)(144,150)(145,149)(146,148)(151,159)(152,162)(153,161)(154,160)(156,158)(183,227)(184,230)(185,229)(186,228)(187,223)(188,226)(189,225)(190,224)(191,239)(192,242)(193,241)(194,240)(195,235)(196,238)(197,237)(198,236)(199,231)(200,234)(201,233)(202,232)(203,207)(204,210)(205,209)(206,208)(211,219)(212,222)(213,221)(214,220)(216,218);; 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*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*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*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)!( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)(115,117)(116,118)(119,121)(120,122)(123,185)(124,186)(125,183)(126,184)(127,189)(128,190)(129,187)(130,188)(131,193)(132,194)(133,191)(134,192)(135,197)(136,198)(137,195)(138,196)(139,201)(140,202)(141,199)(142,200)(143,205)(144,206)(145,203)(146,204)(147,209)(148,210)(149,207)(150,208)(151,213)(152,214)(153,211)(154,212)(155,217)(156,218)(157,215)(158,216)(159,221)(160,222)(161,219)(162,220)(163,225)(164,226)(165,223)(166,224)(167,229)(168,230)(169,227)(170,228)(171,233)(172,234)(173,231)(174,232)(175,237)(176,238)(177,235)(178,236)(179,241)(180,242)(181,239)(182,240); s2 := Sym(242)!( 3,123)( 4,125)( 5,124)( 6,126)( 7,139)( 8,141)( 9,140)( 10,142)( 11,135)( 12,137)( 13,136)( 14,138)( 15,131)( 16,133)( 17,132)( 18,134)( 19,127)( 20,129)( 21,128)( 22,130)( 23,163)( 24,165)( 25,164)( 26,166)( 27,179)( 28,181)( 29,180)( 30,182)( 31,175)( 32,177)( 33,176)( 34,178)( 35,171)( 36,173)( 37,172)( 38,174)( 39,167)( 40,169)( 41,168)( 42,170)( 43,143)( 44,145)( 45,144)( 46,146)( 47,159)( 48,161)( 49,160)( 50,162)( 51,155)( 52,157)( 53,156)( 54,158)( 55,151)( 56,153)( 57,152)( 58,154)( 59,147)( 60,149)( 61,148)( 62,150)( 63,183)( 64,185)( 65,184)( 66,186)( 67,199)( 68,201)( 69,200)( 70,202)( 71,195)( 72,197)( 73,196)( 74,198)( 75,191)( 76,193)( 77,192)( 78,194)( 79,187)( 80,189)( 81,188)( 82,190)( 83,223)( 84,225)( 85,224)( 86,226)( 87,239)( 88,241)( 89,240)( 90,242)( 91,235)( 92,237)( 93,236)( 94,238)( 95,231)( 96,233)( 97,232)( 98,234)( 99,227)(100,229)(101,228)(102,230)(103,203)(104,205)(105,204)(106,206)(107,219)(108,221)(109,220)(110,222)(111,215)(112,217)(113,216)(114,218)(115,211)(116,213)(117,212)(118,214)(119,207)(120,209)(121,208)(122,210); s3 := Sym(242)!( 3, 47)( 4, 50)( 5, 49)( 6, 48)( 7, 43)( 8, 46)( 9, 45)( 10, 44)( 11, 59)( 12, 62)( 13, 61)( 14, 60)( 15, 55)( 16, 58)( 17, 57)( 18, 56)( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 27)( 24, 30)( 25, 29)( 26, 28)( 31, 39)( 32, 42)( 33, 41)( 34, 40)( 36, 38)( 63,107)( 64,110)( 65,109)( 66,108)( 67,103)( 68,106)( 69,105)( 70,104)( 71,119)( 72,122)( 73,121)( 74,120)( 75,115)( 76,118)( 77,117)( 78,116)( 79,111)( 80,114)( 81,113)( 82,112)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 99)( 92,102)( 93,101)( 94,100)( 96, 98)(123,167)(124,170)(125,169)(126,168)(127,163)(128,166)(129,165)(130,164)(131,179)(132,182)(133,181)(134,180)(135,175)(136,178)(137,177)(138,176)(139,171)(140,174)(141,173)(142,172)(143,147)(144,150)(145,149)(146,148)(151,159)(152,162)(153,161)(154,160)(156,158)(183,227)(184,230)(185,229)(186,228)(187,223)(188,226)(189,225)(190,224)(191,239)(192,242)(193,241)(194,240)(195,235)(196,238)(197,237)(198,236)(199,231)(200,234)(201,233)(202,232)(203,207)(204,210)(205,209)(206,208)(211,219)(212,222)(213,221)(214,220)(216,218); 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*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*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*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 >;