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

Overview

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

{6,10}*720b

3-fold

{12,10}*480d

4-fold

{3,10}*360

6-fold

{6,10}*240e

12-fold

24-fold

{3,5}*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*(s2*s1)^2*s0*(s1*s2)^4> of order 3

20 facets

20 of {12}*24

24 vertex figures

24 of {10}*20

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

12 facets

12 of {12}*24

24 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.