Polytope of Type {8,4} with group SmallGroup(1344,11289)

Overview

Group: SmallGroup(1344,11289)
Rank: 3
Schläfli Type: {8,4}
Vertices, edges, …: 168, 336, 84
Order of s₀s₁s₂: 28
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{8,4}*672d

4-fold

{8,4}*336b

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

44 facets

40 of {8}*16
4 of {4}*8

84 vertex figures

84 of {4}*8

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

24 facets

18 of {8}*16
6 of {4}*8

42 vertex figures

42 of {4}*8

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

22 facets

20 of {8}*16
2 of {4}*8

42 vertex figures

42 of {4}*8

P/N, where N=<(s0*s2*s1)^4> of order 7

12 facets

12 of {8}*16

24 vertex figures

24 of {4}*8

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.