Overview
- Group
- SmallGroup(500,27)
- Rank
- 3
- Schläfli Type
- {5,10}
- Vertices, edges, …
- 25, 125, 50
- Order of s0s1s2
- 10
- Order of s0s1s2s1
- 10
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
5-fold
25-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 6,21)( 7,22)( 8,23)( 9,24)(10,25)(11,16)(12,17)(13,18)(14,19)(15,20);; s1 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5, 6)(11,23)(12,24)(13,25)(14,21)(15,22);; s2 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)(14,18)(15,17);; 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*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(25)!( 6,21)( 7,22)( 8,23)( 9,24)(10,25)(11,16)(12,17)(13,18)(14,19)(15,20); s1 := Sym(25)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5, 6)(11,23)(12,24)(13,25)(14,21)(15,22); s2 := Sym(25)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)(14,18)(15,17); poly := sub<Sym(25)|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*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.