File:2 cubes linked to a Platonic dodecahedron in 6 projections.svg

Each pair of views:  faced and from above,  shows the same three concentric Platonic solids.  On the first pair of views,  on the left,  no segment represents a whole face.  On this first front view,  the Platonic dodecahedron hides ten of its thirty edges,  including two red edges in dashed lines,  red because laying each on a face of the largest cube,  in dashed lines because hidden.  That outline is made up of ten edges of dodecahedron,  whereas its outline seen from above is a dodecagon.

From the first pair of views to the second one,  either the 3D figure or the observer rotates around a vertical axis through the center,  so that each cube is projected onto a square of the front view.  No more dashed lines in this second front view,  where the blue segments of the outline of dodecahedron are four projections of its twelve faces,  a red point of the outline is a projection of a red edge,  and the sides of each colored pentagon are each the projection of two edges,  one of them being hidden at rear of the solid,  except one or the other red segment of outline which is the projection of only one edge laying on a face of the greatest cube.

The 3D figure has a center of symmetry:  its center C.  The horizontal axis through C,  projected onto the symmetry point of the second and third front views,  is a rotational axis of the 3D figure.  By a rotation around this axis,  two opposite faces of dodecahedron become horizontal on the third pair of views,  superior and inferior faces not distorted seen from above,  like the two horizontal cross sections through five vertices of the outline of the last top view,  vertices of two regular pentagons symmetric of one another with respect to C,  two regular cross sections not on the drawing,  but we can imagine thm.  Therefore this last outline is a regular decagon,  as written on the image bottom.

A convex regular pentagon with sides of length ${\displaystyle \,a\,}$ has five diagonals of length ${\displaystyle \;{\text{φ times }}\,a,}$  written ${\displaystyle \;{\text{φ}}\,a\;}$ on the image,  ${\displaystyle {\text{φ being}}}$ the golden ratio.  ${\displaystyle {\text{φ is }}}$ also the ratio of the homothety of center C that transforms the smallest cube into the largest one,  the dimension of which is the distance between two opposite edges of the dodecahedron.