Relationships between Polyhedra
There exist families of
four polyhedra each with interesting internal relationships.
In the following illustrations
the colors of the arrows have a special meaning.
white arrow means: the face centers transform to corners,
gray arrow means: the middle of the edges transform to corners, and
black arrow means: the middle of the edges transform to face centers.
The white arrows appear
in pairs and are pointing in both directions. This reflects the wellknown duality
between to polyhedra.
The transformation from
center of edge to centre of face is achieved by putting planes in each center of edge which
are normal to the vector pointing to the center of the polyhedra. This transformation is equivalent
to a special stellation (star forming) where the pyramids on each face reaches exactly the
height which lets disappear the old edges. (Würfel = cube)
The Cube family
The family of the Dodecahedra
The degenerated family of the Tetrahedra
