Polytope of Type {5,10} with group SmallGroup(1200,944)

Overview

Group: SmallGroup(1200,944)
Rank: 3
Schläfli Type: {5,10}
Vertices, edges, …: 60, 300, 120
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 30
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{5,5}*600

5-fold

{5,10}*240

10-fold

20-fold

{5,5}*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=<s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 2

60 facets

60 of {5}*10

30 vertex figures

30 of {10}*20

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

60 facets

60 of {5}*10

30 vertex figures

30 of {10}*20

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

24 facets

24 of {5}*10

12 vertex figures

12 of {10}*20

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.