Polytope of Type {6,35} with group SmallGroup(1680,931)

Overview

Group: SmallGroup(1680,931)
Rank: 3
Schläfli Type: {6,35}
Vertices, edges, …: 24, 420, 140
Order of s₀s₁s₂: 70
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{6,35}*840

7-fold

{6,5}*240b

14-fold

28-fold

{3,5}*60

60-fold

{2,7}*28

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

70 facets

70 of {6}*12

12 vertex figures

12 of {35}*70

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.