Polytope of Type {42,6} with group SmallGroup(1680,927)

Overview

Group: SmallGroup(1680,927)
Rank: 3
Schläfli Type: {42,6}
Vertices, edges, …: 140, 420, 20
Order of s₀s₁s₂: 42
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Quotients maximal quotients in bold

7-fold

{6,6}*240b

14-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)^3*s2*(s1*s0)^2*s1*s2> of order 2

10 facets

10 of {42}*84

70 vertex figures

70 of {6}*12

P/N, where N=<s0*s2*(s1*s0)^2*s2*(s1*s0)^3*s2*s1*s0*s1*s2> of order 2

11 facets

2 of {21}*42
9 of {42}*84

70 vertex figures

70 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.