Overview
- Group
- SmallGroup(1440,5871)
- Rank
- 4
- Schläfli Type
- {10,6,3}
- Vertices, edges, …
- 10, 120, 36, 12
- 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
3-fold
4-fold
5-fold
12-fold
15-fold
20-fold
24-fold
30-fold
60-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=<s1*s2*s1*s3*(s2*s1)^2*s3*s2> of order 2
6 facets
- 6 of {10,6}*120
10 vertex figures
- 10 of 2-fold non-regular quotient of {6,3}*144
P/N, where N=<(s1*s2)^2> of order 3
6 facets
- 3 of {10,2}*40
- 3 of {10,6}*120
10 vertex figures
- 10 of 3-fold non-regular quotient of {6,3}*144
Representations
Permutation Representation (GAP)
s0 := ( 5,17)( 6,18)( 7,19)( 8,20)( 9,13)(10,14)(11,15)(12,16)(25,37)(26,38)(27,39)(28,40)(29,33)(30,34)(31,35)(32,36)(45,57)(46,58)(47,59)(48,60)(49,53)(50,54)(51,55)(52,56);; s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,17)(10,18)(11,20)(12,19)(15,16)(21,25)(22,26)(23,28)(24,27)(29,37)(30,38)(31,40)(32,39)(35,36)(41,45)(42,46)(43,48)(44,47)(49,57)(50,58)(51,60)(52,59)(55,56);; s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(21,41)(22,44)(23,43)(24,42)(25,45)(26,48)(27,47)(28,46)(29,49)(30,52)(31,51)(32,50)(33,53)(34,56)(35,55)(36,54)(37,57)(38,60)(39,59)(40,58);; s3 := ( 1,22)( 2,21)( 3,23)( 4,24)( 5,26)( 6,25)( 7,27)( 8,28)( 9,30)(10,29)(11,31)(12,32)(13,34)(14,33)(15,35)(16,36)(17,38)(18,37)(19,39)(20,40)(41,42)(45,46)(49,50)(53,54)(57,58);; 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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(60)!( 5,17)( 6,18)( 7,19)( 8,20)( 9,13)(10,14)(11,15)(12,16)(25,37)(26,38)(27,39)(28,40)(29,33)(30,34)(31,35)(32,36)(45,57)(46,58)(47,59)(48,60)(49,53)(50,54)(51,55)(52,56); s1 := Sym(60)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,17)(10,18)(11,20)(12,19)(15,16)(21,25)(22,26)(23,28)(24,27)(29,37)(30,38)(31,40)(32,39)(35,36)(41,45)(42,46)(43,48)(44,47)(49,57)(50,58)(51,60)(52,59)(55,56); s2 := Sym(60)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(21,41)(22,44)(23,43)(24,42)(25,45)(26,48)(27,47)(28,46)(29,49)(30,52)(31,51)(32,50)(33,53)(34,56)(35,55)(36,54)(37,57)(38,60)(39,59)(40,58); s3 := Sym(60)!( 1,22)( 2,21)( 3,23)( 4,24)( 5,26)( 6,25)( 7,27)( 8,28)( 9,30)(10,29)(11,31)(12,32)(13,34)(14,33)(15,35)(16,36)(17,38)(18,37)(19,39)(20,40)(41,42)(45,46)(49,50)(53,54)(57,58); poly := sub<Sym(60)|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, s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.