Polytope of Type {7,4} with group SmallGroup(672,1254)

Overview

Group: SmallGroup(672,1254)
Rank: 3
Schläfli Type: {7,4}
Vertices, edges, …: 84, 168, 48
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{7,4}*336

Covers minimal covers in bold

2-fold

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

24 facets

24 of {7}*14

44 vertex figures

40 of {4}*8
4 of {2}*4

P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2, s0*(s1*s0*s2)^3*s1*s2> of order 4

12 facets

12 of {7}*14

24 vertex figures

18 of {4}*8
6 of {2}*4

Representations

Permutation Representation (GAP)

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