Polytope of Type {15,2} with group SmallGroup(60,12) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(60,12)
Rank: 3
Schläfli Type: {15,2}
Vertices, edges, …: 15, 15, 2
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{5,2}*20

5-fold

{3,2}*12

Covers minimal covers in bold

2-fold

{30,2}*120

3-fold

4-fold

5-fold

6-fold

7-fold

{105,2}*420

8-fold

9-fold

10-fold

11-fold

{165,2}*660

12-fold

13-fold

{195,2}*780

14-fold

15-fold

16-fold

17-fold

{255,2}*1020

18-fold

19-fold

{285,2}*1140

20-fold

21-fold

22-fold

23-fold

{345,2}*1380

24-fold

25-fold

26-fold

27-fold

28-fold

29-fold

{435,2}*1740

30-fold

31-fold

{465,2}*1860

32-fold

33-fold

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s2 := (16,17);;
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, s1*s2*s1*s2, 
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(17)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(17)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s2 := Sym(17)!(16,17);
poly := sub<Sym(17)|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, 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 >;