Overview
- Group
- SmallGroup(300,25)
- Rank
- 3
- Schläfli Type
- {6,3}
- Vertices, edges, …
- 50, 75, 25
- Order of s0s1s2
- 10
- Order of s0s1s2s1
- 6
- Also known as
- {6,3}(5,0), {6,3}10. if this polytope has another name.
Special Properties
- Toroidal
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-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 := ( 6,23)( 7,24)( 8,25)( 9,21)(10,22)(11,20)(12,16)(13,17)(14,18)(15,19);; s1 := ( 2, 8)( 3,15)( 4,17)( 5,24)( 6,18)( 7,25)(10,11)(13,19)(14,21)(16,22);; s2 := ( 1, 2)( 3, 5)( 6,10)( 7, 9)(11,13)(14,15)(17,20)(18,19)(21,24)(22,23);; 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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(25)!( 6,23)( 7,24)( 8,25)( 9,21)(10,22)(11,20)(12,16)(13,17)(14,18)(15,19); s1 := Sym(25)!( 2, 8)( 3,15)( 4,17)( 5,24)( 6,18)( 7,25)(10,11)(13,19)(14,21)(16,22); s2 := Sym(25)!( 1, 2)( 3, 5)( 6,10)( 7, 9)(11,13)(14,15)(17,20)(18,19)(21,24)(22,23); 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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.