How to Make Solid Geometry Puzzles

Subdivide the solids with a saw. Choose cuts that elucidate the nature of sections of the solids. For example, a cylinder cut along its axis shows a rectangular cross section, whereas a diagonal cut provides an oval cross section. Cones cut along the axis have triangular cross sections, parallel with the axis provide hyperbolas, parallel to the diagonal give parabolas and perpendicular to the axis provide circles. Cubes cut diagonally through three vertices have pyramidal sections, whereas cut through four vertices have wedge-shaped sections with rectangular cross sections. Every geometrical solid has special properties, so make multiple cuts on each form to show the characteristics.

Sand the cuts with sandpaper to smooth the surfaces. Do not round, or chamfer, the edges of the cut. Instead, keep a fine edge to express the characteristic shape of the section.

Paint the surfaces of the wood sections, varying the paint color for the interior faces and exterior surfaces of the solids. The difference in paint color highlights the shape of the sections.

Peel the backing from the hook-and-loop fastener dots and apply the two hook-and-loop fastener surfaces to adjoining solid section faces. The hook-and-loop fastener will hold the pieces in place to form the solid, and the sections can be mixed and matched to show formal, spatial possibilities.