Overview
- Group
- SmallGroup(240,194)
- Rank
- 3
- Schläfli Type
- {6,15}
- Vertices, edges, …
- 8, 60, 20
- Order of s0s1s2
- 20
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
5-fold
10-fold
12-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)(11,12)(15,16)(19,20);; s1 := ( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16);; s2 := ( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,18)(10,17)(11,19)(12,20)(13,14);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(20)!( 3, 4)( 7, 8)(11,12)(15,16)(19,20); s1 := Sym(20)!( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16); s2 := Sym(20)!( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,18)(10,17)(11,19)(12,20)(13,14); poly := sub<Sym(20)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;
References
None.
to this polytope.