Polytope of Type {10,12} with group SmallGroup(1440,4641)

Overview

Group: SmallGroup(1440,4641)
Rank: 3
Schläfli Type: {10,12}
Vertices, edges, …: 60, 360, 72
Order of s₀s₁s₂: 60
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

2-fold

{10,6}*720b

3-fold

{10,12}*480c

4-fold

{10,3}*360

6-fold

{10,6}*240c

12-fold

24-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=<(s0*s1)^2*s2*(s1*s0)^3*s1*s2> of order 3

24 facets

24 of {10}*20

20 vertex figures

20 of {12}*24

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

24 facets

12 of {10}*20
12 of {2}*4

12 vertex figures

12 of {12}*24

Representations

Permutation Representation (GAP)

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