Symmetrical intersections of cylinders

There are four regular cylindrical solids, comprising the symmetrical intersections of three, four, six and ten cylinders of equal radius; two quasi-regular solids, six and 15; and their duals, seven and 16 cylinders respectively. There are further solids with cubic crystal symmetry formed by the intersection of six, 12 or 24 cylinders with axes along (hkl) directions; as well as combinations of forms. Their volumes are independent of π and are equal to ⅓ × surface area × radius. Possible applications to the geometry of laser fusion and to crystal dissolution morphology are briefly considered.