Overview
- Group
- SmallGroup(60,12)
- Rank
- 2
- Schläfli Type
- {30}
- Vertices, edges, …
- 30, 30
- Order of s0s1
- 30
- Also known as
- 30-gon, {30}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
10-fold
15-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
17-fold
18-fold
19-fold
20-fold
21-fold
22-fold
23-fold
24-fold
25-fold
26-fold
27-fold
28-fold
29-fold
30-fold
31-fold
32-fold
33-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,16)(17,20)(18,19)(21,22)(23,26)(24,25)(27,30)(28,29);; s1 := ( 1,17)( 2,11)( 3, 9)( 4,19)( 5, 7)( 6,27)( 8,13)(10,23)(12,21)(14,29)(15,18)(16,28)(20,25)(22,24)(26,30);; poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(30)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,16)(17,20)(18,19)(21,22)(23,26)(24,25)(27,30)(28,29); s1 := Sym(30)!( 1,17)( 2,11)( 3, 9)( 4,19)( 5, 7)( 6,27)( 8,13)(10,23)(12,21)(14,29)(15,18)(16,28)(20,25)(22,24)(26,30); poly := sub<Sym(30)|s0,s1>;
Finitely Presented Group Representation (Magma)
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.