The cell bases of honeybee combs

Pirk et al. [Naturwissenschaften 91, 350–353 (2004)] posited that beeswax is a thermoplastic medium that softens with increasing temperature and literally flows among an array of close-packed cylinders, which are actually the self-heated building bees and so hexagonal cells arise quite passively. But, it was further argued that the three apparent rhomboids of the cell base arise as optical artefacts. A re-examination of the cell bases of freshly drawn comb, old comb, and the silk residues of wax-extracted old combs prepared from a silicone-based moulding rubber preparation showed that three perfect rhomboids are seen to form the trihedral pyramid in the cell base (Fig. 1), those of old combs show hemispheres inside the cell bases (Fig. 2). Longitudinal sections of old combs clearly show the parabolic curvature of the inside of the cell base; but the edges of rhomboids are clearly visible on the outside of the cell base (Fig. 3). The silken cell “ghosts” exhibit rhomboids on the outside of the cells (Fig. 4) but a hemispherical base on the inside of the “ghost cell” (Fig. 3). Three rhomboids would be expected as a product of thermodynamic equilibrium in precisely the same way that soap bubbles form angular, not hemispherical, contact faces because the wax moves to a more probable state resulting in rhomboids, or a trihedral pyramid, which forms the cell base. Thus, the underlying geometry of the cell walls and bases are in keeping with mathematical laws on surface minima.