The file QuasicryOcta.pdf shows how eight carbon atoms acting as
triangular panels can form a structurally stable regular octahedral
assembly. The arrangement is quasicrystalline, but identical units can
join to form Simple Cubic and Body Centered Cubic crystalline
structures. Using the same join between the carbon atoms that occurs
in diamond, the octahedral units can form a rhombic dodecahedron in
which the centroid of each unit is at one of the fourteen dodecahedral
vertexes. The file CarbonHedra.pdf shows how four carbon atoms acting
as panels produce the regular tetrahedron which is the crystal forming
unit of diamond, and how twenty carbon atoms produce the regular
icosahedron of a fullerene. The files can be downloaded using the
"Files for sharing" link of the website
http://homepage.mac.com/whitby/