Isogonal embeddings of interwoven and self-entangled honeycomb (hcb) nets and related interpenetrating primitive cubic (pcu) nets

Two- and three-periodic vertex-transitive (isogonal) piecewise-linear embeddings of self-entangled and interwoven honeycomb nets are described. The infinite families with trigonal symmetry and edge transitivity (isotoxal) are particularly interesting as they have the Borromean property that no two nets are directly linked. These also lead directly to infinite families of interpenetrating primitive cubic nets (pcu) that are also vertex- and edge-transitive and have embeddings with 90 degrees angles between edges.

Automated summary

This article describes two- and three-periodic vertex-transitive piecewise-linear embeddings of self-entangled and interwoven honeycomb nets. The infinite families with trigonal symmetry and edge transitivity are particularly interesting due to their Borromean property. These findings also directly lead to infinite families of interpenetrating primitive cubic nets with 90 degree angles between edges.