Overview
- Group
- SmallGroup(100,13)
- Rank
- 3
- Schläfli Type
- {5,10}
- Vertices, edges, …
- 5, 25, 10
- 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
- Flat
Quotients maximal quotients in bold
5-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
9-fold
10-fold
11-fold
12-fold
13-fold
14-fold
15-fold
16-fold
- {80,10}*1600b
- {20,40}*1600a
- {20,20}*1600c
- {20,40}*1600b
- {40,20}*1600d
- {40,20}*1600f
- {10,80}*1600c
- {5,10}*1600
- {5,20}*1600
17-fold
18-fold
19-fold
20-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,18)(16,21)(17,20)(22,25)(23,24);; s1 := ( 1, 7)( 2, 4)( 3,14)( 5,16)( 6,10)( 8,12)( 9,18)(11,22)(13,17)(15,20)(19,24)(21,23);; s2 := ( 4, 5)( 7, 8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);; 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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(25)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,18)(16,21)(17,20)(22,25)(23,24); s1 := Sym(25)!( 1, 7)( 2, 4)( 3,14)( 5,16)( 6,10)( 8,12)( 9,18)(11,22)(13,17)(15,20)(19,24)(21,23); s2 := Sym(25)!( 4, 5)( 7, 8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25); 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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.