Octahedral-hexagonal tiling honeycomb Octahedral-hexagonal tiling honeycomb In the geometry of hyperbolic 3-space, the octahedron-hexagonal tiling honeycomb is a paracompact uniform honeycomb, constructed from octahedron, hexagonal tiling, and trihexagonal tiling cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. A lower symmetry form, index 6, of this honeycomb can be constructed with [(6,3,4,3)] symmetry, represented by a trigonal trapezohedron fundamental domain, and a Coxeter diagram . The cyclotruncated octahedral-hexagonal tiling honeycomb is a compact uniform honeycomb, constructed from hexagonal tiling, cube, and truncated octahedron cells, in a triangular antiprism vertex figure. It
Honeycomb structure as far as we can see, is absolutely perfect in economizing labour and wax”. The first paper honeycomb structures might have been made by the Chinese 2000 years ago for ornaments, but no reference for this has been found. Paper honeycombs and the expansion production process has been invented in Halle/Saale in Germany by Hans Heilbrun in 1901 for decorative applications. First honeycomb structures from corrugated metal sheets had been proposed for bee keeping in 1890. For the same purpose, as foundation sheets to harvest more honey, a honeycomb moulding process using a paper paste glue mixture had been patented