Polytope of Type {12,12} with group SmallGroup(576,8653)

Overview

Group: SmallGroup(576,8653)
Rank: 3
Schläfli Type: {12,12}
Vertices, edges, …: 24, 144, 24
Order of s₀s₁s₂: 3
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Dual

Related Polytopes

Constructions

Facet of

{12,12,2} ·1152

Vertex figure of

{2,12,12} ·1152

Quotients maximal quotients in bold

4-fold

12-fold

24-fold

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

16 facets

8 of {12}*24
8 of {6}*12

12 vertex figures

12 of {12}*24

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

12 facets

12 of {12}*24

16 vertex figures

8 of {12}*24
8 of {6}*12

Representations

Permutation Representation (GAP)

s0 := ( 1, 9)( 2,11)( 3,10)( 4,12)( 5,13)( 6,15)( 7,14)( 8,16);;
s1 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16);;
s2 := ( 1, 4)( 2, 3)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(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*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

References

None.

to this polytope.