Polytope of Type {15,12} with group SmallGroup(1440,5848)

Overview

Group: SmallGroup(1440,5848)
Rank: 3
Schläfli Type: {15,12}
Vertices, edges, …: 60, 360, 48
Order of s₀s₁s₂: 15
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Quotients maximal quotients in bold

4-fold

{15,6}*360

12-fold

{5,6}*120b

24-fold

{5,3}*60

60-fold

{3,4}*24

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s2)^6> of order 2

24 facets

24 of {15}*30

40 vertex figures

20 of {6}*12
20 of {12}*24

Representations

Permutation Representation (GAP)

s0 := (2,3)(4,5)(7,9);;
s1 := (1,2)(3,4)(8,9);;
s2 := (2,5)(3,4)(6,8)(7,9);;
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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(9)!(2,3)(4,5)(7,9);
s1 := Sym(9)!(1,2)(3,4)(8,9);
s2 := Sym(9)!(2,5)(3,4)(6,8)(7,9);
poly := sub<Sym(9)|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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.