|There's a tetrahedron inside every cube (and in two possible orientations.) (Image quoted from http://burrtools.sourceforge.net/gui-doc/Spacegrids.html )|
In this way a vox solid (voxel-based solid) can be converted into a deltahedron (a solid faceted exclusively with equilateral triangles) that lies entirely within the original vox solid.
A structural problem arises with this technique. For example, a rigid stack of voxels becomes a flexible chain of tetrahedra.
|The tetrahedra that lie inside a rigid stack of cubes form a flexible chain. (Image quoted from http://www.kaleidocycles.de )|
A solution to this structural problem is to divide each voxel into eight sub-voxels, and replace those sub-voxels by tetrahedra. Here again there is a parity choice, one that makes these eight tetrahedra either a stella octangula or a "cumulated cuboctahedron."
|A "cumulated cuboctahedron" (shown in red) inserted between the two halves of a stella octangula (gray.) (Image quoted from http://the-arc-ddeden.blogspot.com )|
|If stella octangula voxels are used, the corners are prominent. Using cumulated cuboctahedra (which can be imagined by slicing a half-voxel margin off this object) results in bevelled corners.|