Polytope of Type {4,6} with group SmallGroup(1440,5841)

Overview

Group: SmallGroup(1440,5841)
Rank: 3
Schläfli Type: {4,6}
Vertices, edges, …: 120, 360, 180
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

No regular quotients.

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)^2> of order 3

60 facets

60 of {4}*8

42 vertex figures

3 of {2}*4
39 of {6}*12

P/N, where N=<(s1*s2)^2, s0*s1*(s2*s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 9

20 facets

20 of {4}*8

16 vertex figures

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

Representations

Permutation Representation (GAP)

s0 := ( 1, 2)( 3, 5)( 4, 9)( 6, 7)( 8,10);;
s1 := (2,3)(6,7)(8,9);;
s2 := ( 3, 4)( 5, 9)( 6,10)( 7, 8);;
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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

References

None.

to this polytope.