SSO - Brief Summary on Tetrahedron / Cube / Octahedron

On Symmetric Structures within Symmetric Solid Objects

Section XIII - Brief Summary on the Tetrahedron / Cube / Octahedron

In this Section , we shall briefly summarize our observations so far on the Tetrahedron / Cube / Octahedron .

The Tetrahedron has four (4) faces :
- [ 4 ] = [ 2 ] x [ 2 ] .
It is only natural that the possibility of [ bi-symmetry ] might exist within the Tetrahedron .
The Cube has six (6) faces :
- [ 6 ] = [ 2 ] x [ 3 ] .
It is only natural that the possibility of [ bi-symmetry ] and [ tri-symmetry ] might exist within the Cube .
The Octahedron has eight (8) faces :
- [ 8 ] = [ 2 ] x [ 4 ] .
It is only natural that the possibility of [ bi-symmetry ] and [ quad-symmetry ] might exist within the Octahedron .

the Dodecahedron has twelve (12) faces :
- [ 12 ] = [ 2 ] x [ 6 ] = [ 3 ] x [ 4 ] .
We shall be looking for [ bi-symmetry ] , [ tri-symmetry ] , [ quad-symmetry ] and [ hexa-symmetry ] here .
the Icosahedron has twenty (20) faces :
- [ 20 ] = [ 2 ] x [ 10 ] = [ 4 ] x [ 5 ] .
We shall be looking for [ bi-symmetry ] , [ quad-symmetry ] , [ penta-symmetry ] and [ deci-symmetry ] here .

Let us now also identify the two (2) Tetrahedra hidden within the Cube :

This information here will become rather useful when we look at [ quad-symmetry ] in the Icosahedron at a later stage :
- So , readers beware !