Triangular tiling honeycomb infinite cells or vertex figures. There are nine uniform honeycombs in the [3,6,3] Coxeter group family, including this regular form as well as the bitruncated form, t{3,6,3}, with all truncated hexagonal tiling facets. The rectified triangular tiling honeycomb, , has alternating trihexagonal tiling and hexagonal tiling cells, with a triangular prism vertex figure. A lower symmetry of this honeycomb can be constructed as a "cantic order-6 hexagonal tiling honeycomb", ↔ . A second lower construction, index is ↔ . The truncated triangular tiling honeycomb, is the same as the hexagonal tiling honeycomb, . The bitruncated triangular tiling honeycomb, , has
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