  For an arbitrary polygon consider a new one by joining the centres of
consecutive edges. Iteration of this procedure leads to a shape which is affine
equivalent to a regular polygon. This regularisation effect is usually ascribed
to Count Buffon (1707-1788). We discuss a natural analogue of this procedure
for 3-dimensional polyhedra, which leads to a new notion of affine $B$-regular
polyhedra. The main result is the proof of existence of star-shaped affine
$B$-regular polyhedra with prescribed combinatorial structure, under partial
symmetry and simpliciality assumptions. The proof is based on deep results from
spectral graph theory due to Colin de Verdiere and Lovasz.
