An ideal mathematical line has zero thickness. For rendering lines on two-dimensional computer displays, simple standard algorithms have been developed which produce lines one pixel in thickness, to be as close as possible to the mathematical ideal, yet clearly visible. For producing lines in three-dimensional space, other techniques are necessary. Leonardo da Vinci invented a solid segment representation of polyhedra for the illustrations to Luca Pacioli's 1509 book, De Divine Proportione. Prior to this, polyhedra were illustrated as either opaque solids or transparent line drawings.
Opaque representations have the disadvantage of hiding the rear structure.
In Leonardo's new form of representation, thick segments and open faces show the front and back structure, avoiding both problems. Many styles for solid-segment models are possible. Consider, for example, molecular models used by chemists, with cylindrical struts and spheres at each vertex. This makes for a very lucid presentation of convex polyhedra, but it does not generalize to an arbitrary network of vertices and segments, in which the structure need not determine planes tangent to the surface of a sphere. In the design of geometric sculpture, I faced the problem of connecting a set of points in space with faceted struts of some form, and needing an algorithmic procedure to design interesting struts.