Tonal study of Platonic solids

I've had these lying around courtesy of A&I magazine for a few months as an accessory to a tonal painting exercise. As I couldn't otherwise put my hands immediately on "simple shapes" I thought that these would get me started on the exercise.

I drew the double pyramid (octahedron) first, and used a lot of blended shading. As is obvious, I used more cross-hatching in the other dodecahedron. I had set them up on a white card base with a table lamp to give directional lighting to the right-hand side, and it was surprising to discover how much of a double shadow was created by having the light source so close. Not having much knowledge of what these shape's properties were they proved quite challenging to draw- I moved the dodecahedron from its original position in order to relate it to the double pyramid shadow as I found I couldn't get a sense of scale without this. After that I learned quite a lot about the relative measurements sighting various measurements with my pencil at arm's lenght, especially the common measurements which proved to be not (too) far out in the final accounting.

Later that evening I made myself use a drawing pen (and my glasses) to develop the required tonal range in cross-hatching- I haven't done it yet but will do the cross-hatched Platonics yet!