Cubic-octahedral honeycomb Cubic-octahedral honeycomb In the geometry of hyperbolic 3-space, the cube-octahedron honeycomb is a compact uniform honeycomb, constructed from cube, octahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. Wide-angle perspective views: It contains a subgroup H2 tiling, the alternated order-4 hexagonal tiling, , with vertex figure (3.4). A lower symmetry form, index 6, of this honeycomb can be constructed with [(4,3,4,3)] symmetry, represented by a trigonal trapezohedron fundamental domain, and Coxeter diagram . This lower symmetry can be extended by restoring one mirror as .
Wax foundation Wax foundation Wax foundation or honeycomb base is a plate made of wax with the base of the honeycomb. It is used in beekeeping to give the bees a foundation on which they can build the honeycomb. Wax foundation is considered one of the most important inventions in modern beekeeping. Wax foundation was invented by German Johannes Mehring in 1857, a few years after Langstroth designed and patented the Langstroth hive on October 5, 1852. Mehring's wax foundation had only the bottom of the cells, and today's base with the foundation of the cells was invented by US beekeeper Samuel