Polytope of Type {6,30} with group SmallGroup(1200,941)

Overview

Group: SmallGroup(1200,941)
Rank: 3
Schläfli Type: {6,30}
Vertices, edges, …: 20, 300, 100
Order of s₀s₁s₂: 30
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

5-fold

{6,6}*240a

10-fold

{6,6}*120

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*s2)^2*s1*s0*(s2*s1)^3> of order 2

50 facets

50 of {6}*12

10 vertex figures

10 of {30}*60

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

50 facets

50 of {6}*12

11 vertex figures

9 of {30}*60
2 of {15}*30

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.