Polytope of Type {15,6} with group SmallGroup(1800,562)

Overview

Group: SmallGroup(1800,562)
Rank: 3
Schläfli Type: {15,6}
Vertices, edges, …: 150, 450, 60
Order of s₀s₁s₂: 15
Order of s₀s₁s₂s₁: 10
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

3-fold

{5,6}*600

5-fold

{15,6}*360

15-fold

{5,6}*120b

30-fold

{5,3}*60

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=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 3

20 facets

20 of {15}*30

60 vertex figures

45 of {6}*12
15 of {2}*4

P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2> of order 5

12 facets

12 of {15}*30

30 vertex figures

30 of {6}*12

Representations

Permutation Representation (GAP)

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