Overview
- Group
- SmallGroup(1920,151306)
- Rank
- 4
- Schläfli Type
- {4,12,10}
- Vertices, edges, …
- 8, 48, 120, 10
- Order of s0s1s2s3
- 60
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- 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.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<(s0*s1)^2> of order 2
10 facets
- 10 of 2-fold non-regular quotient of {4,12}*192a
4 vertex figures
- 4 of {12,10}*240
P/N, where N=<(s1*s2)^6> of order 2
10 facets
- 10 of 2-fold non-regular quotient of {4,12}*192a
6 vertex figures
- 4 of {6,10}*120
- 2 of {12,10}*240
Representations
Permutation Representation (GAP)
s0 := ( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(151,166)(152,167)(153,168)(154,169)(155,170)(156,171)(157,172)(158,173)(159,174)(160,175)(161,176)(162,177)(163,178)(164,179)(165,180)(211,226)(212,227)(213,228)(214,229)(215,230)(216,231)(217,232)(218,233)(219,234)(220,235)(221,236)(222,237)(223,238)(224,239)(225,240);; s1 := ( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 96,101)( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)(114,119)(115,120)(121,151)(122,152)(123,153)(124,154)(125,155)(126,161)(127,162)(128,163)(129,164)(130,165)(131,156)(132,157)(133,158)(134,159)(135,160)(136,166)(137,167)(138,168)(139,169)(140,170)(141,176)(142,177)(143,178)(144,179)(145,180)(146,171)(147,172)(148,173)(149,174)(150,175)(181,211)(182,212)(183,213)(184,214)(185,215)(186,221)(187,222)(188,223)(189,224)(190,225)(191,216)(192,217)(193,218)(194,219)(195,220)(196,226)(197,227)(198,228)(199,229)(200,230)(201,236)(202,237)(203,238)(204,239)(205,240)(206,231)(207,232)(208,233)(209,234)(210,235);; s2 := ( 1,186)( 2,190)( 3,189)( 4,188)( 5,187)( 6,181)( 7,185)( 8,184)( 9,183)( 10,182)( 11,191)( 12,195)( 13,194)( 14,193)( 15,192)( 16,201)( 17,205)( 18,204)( 19,203)( 20,202)( 21,196)( 22,200)( 23,199)( 24,198)( 25,197)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,216)( 32,220)( 33,219)( 34,218)( 35,217)( 36,211)( 37,215)( 38,214)( 39,213)( 40,212)( 41,221)( 42,225)( 43,224)( 44,223)( 45,222)( 46,231)( 47,235)( 48,234)( 49,233)( 50,232)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)( 56,236)( 57,240)( 58,239)( 59,238)( 60,237)( 61,126)( 62,130)( 63,129)( 64,128)( 65,127)( 66,121)( 67,125)( 68,124)( 69,123)( 70,122)( 71,131)( 72,135)( 73,134)( 74,133)( 75,132)( 76,141)( 77,145)( 78,144)( 79,143)( 80,142)( 81,136)( 82,140)( 83,139)( 84,138)( 85,137)( 86,146)( 87,150)( 88,149)( 89,148)( 90,147)( 91,156)( 92,160)( 93,159)( 94,158)( 95,157)( 96,151)( 97,155)( 98,154)( 99,153)(100,152)(101,161)(102,165)(103,164)(104,163)(105,162)(106,171)(107,175)(108,174)(109,173)(110,172)(111,166)(112,170)(113,169)(114,168)(115,167)(116,176)(117,180)(118,179)(119,178)(120,177);; s3 := ( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 67)( 7, 66)( 8, 70)( 9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)( 24, 84)( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 92)( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,107)( 47,106)( 48,110)( 49,109)( 50,108)( 51,112)( 52,111)( 53,115)( 54,114)( 55,113)( 56,117)( 57,116)( 58,120)( 59,119)( 60,118)(121,182)(122,181)(123,185)(124,184)(125,183)(126,187)(127,186)(128,190)(129,189)(130,188)(131,192)(132,191)(133,195)(134,194)(135,193)(136,197)(137,196)(138,200)(139,199)(140,198)(141,202)(142,201)(143,205)(144,204)(145,203)(146,207)(147,206)(148,210)(149,209)(150,208)(151,212)(152,211)(153,215)(154,214)(155,213)(156,217)(157,216)(158,220)(159,219)(160,218)(161,222)(162,221)(163,225)(164,224)(165,223)(166,227)(167,226)(168,230)(169,229)(170,228)(171,232)(172,231)(173,235)(174,234)(175,233)(176,237)(177,236)(178,240)(179,239)(180,238);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0,
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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(240)!( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(151,166)(152,167)(153,168)(154,169)(155,170)(156,171)(157,172)(158,173)(159,174)(160,175)(161,176)(162,177)(163,178)(164,179)(165,180)(211,226)(212,227)(213,228)(214,229)(215,230)(216,231)(217,232)(218,233)(219,234)(220,235)(221,236)(222,237)(223,238)(224,239)(225,240); s1 := Sym(240)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 96,101)( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)(114,119)(115,120)(121,151)(122,152)(123,153)(124,154)(125,155)(126,161)(127,162)(128,163)(129,164)(130,165)(131,156)(132,157)(133,158)(134,159)(135,160)(136,166)(137,167)(138,168)(139,169)(140,170)(141,176)(142,177)(143,178)(144,179)(145,180)(146,171)(147,172)(148,173)(149,174)(150,175)(181,211)(182,212)(183,213)(184,214)(185,215)(186,221)(187,222)(188,223)(189,224)(190,225)(191,216)(192,217)(193,218)(194,219)(195,220)(196,226)(197,227)(198,228)(199,229)(200,230)(201,236)(202,237)(203,238)(204,239)(205,240)(206,231)(207,232)(208,233)(209,234)(210,235); s2 := Sym(240)!( 1,186)( 2,190)( 3,189)( 4,188)( 5,187)( 6,181)( 7,185)( 8,184)( 9,183)( 10,182)( 11,191)( 12,195)( 13,194)( 14,193)( 15,192)( 16,201)( 17,205)( 18,204)( 19,203)( 20,202)( 21,196)( 22,200)( 23,199)( 24,198)( 25,197)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,216)( 32,220)( 33,219)( 34,218)( 35,217)( 36,211)( 37,215)( 38,214)( 39,213)( 40,212)( 41,221)( 42,225)( 43,224)( 44,223)( 45,222)( 46,231)( 47,235)( 48,234)( 49,233)( 50,232)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)( 56,236)( 57,240)( 58,239)( 59,238)( 60,237)( 61,126)( 62,130)( 63,129)( 64,128)( 65,127)( 66,121)( 67,125)( 68,124)( 69,123)( 70,122)( 71,131)( 72,135)( 73,134)( 74,133)( 75,132)( 76,141)( 77,145)( 78,144)( 79,143)( 80,142)( 81,136)( 82,140)( 83,139)( 84,138)( 85,137)( 86,146)( 87,150)( 88,149)( 89,148)( 90,147)( 91,156)( 92,160)( 93,159)( 94,158)( 95,157)( 96,151)( 97,155)( 98,154)( 99,153)(100,152)(101,161)(102,165)(103,164)(104,163)(105,162)(106,171)(107,175)(108,174)(109,173)(110,172)(111,166)(112,170)(113,169)(114,168)(115,167)(116,176)(117,180)(118,179)(119,178)(120,177); s3 := Sym(240)!( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 67)( 7, 66)( 8, 70)( 9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)( 24, 84)( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 92)( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,107)( 47,106)( 48,110)( 49,109)( 50,108)( 51,112)( 52,111)( 53,115)( 54,114)( 55,113)( 56,117)( 57,116)( 58,120)( 59,119)( 60,118)(121,182)(122,181)(123,185)(124,184)(125,183)(126,187)(127,186)(128,190)(129,189)(130,188)(131,192)(132,191)(133,195)(134,194)(135,193)(136,197)(137,196)(138,200)(139,199)(140,198)(141,202)(142,201)(143,205)(144,204)(145,203)(146,207)(147,206)(148,210)(149,209)(150,208)(151,212)(152,211)(153,215)(154,214)(155,213)(156,217)(157,216)(158,220)(159,219)(160,218)(161,222)(162,221)(163,225)(164,224)(165,223)(166,227)(167,226)(168,230)(169,229)(170,228)(171,232)(172,231)(173,235)(174,234)(175,233)(176,237)(177,236)(178,240)(179,239)(180,238); poly := sub<Sym(240)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 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 >;
References
None.
to this polytope.