Honeycomb one part per 2850) more efficient. This difference is too minute to measure on an actual honeycomb, and irrelevant to the hive economy in terms of efficient use of wax, considering wild comb varies considerably from any mathematical notion of "ideal" geometry. Bees used their antennae, mandibles and legs to manipulate the wax during comb construction, while actively warming the wax. During the construction of hexagonal cells, wax temperature is between 33.6 and 37.6°C, well below the 40°C temperature at which wax is assumed to be liquid for initiating new comb construction. The body temperature of bees is a factor
Order-5 dodecahedral honeycomb pentagonal prism vertex figure. There are four rectified compact regular honeycombs: The truncated order-5 dodecahedral honeycomb, , has icosahedron and truncated dodecahedron cells, with a pentagonal pyramid vertex figure. The bitruncated order-5 dodecahedral honeycomb, , has truncated icosahedron cells, with a disphenoid vertex figure. The cantellated order-5 dodecahedral honeycomb, , has alternating rhombicosidodecahedron and icosidodecahedron cells, with a triangular prism vertex figure. The cantitruncated order-5 dodecahedral honeycomb, , has truncated icosidodecahedron, icosidodecahedron, and pentagonal prism cells, with a mirrored sphenoid vertex figure. The runcinated order-5 dodecahedral honeycomb, , has dodecahedron and pentagonal prism cells, with a triangular antiprism vertex figure.