Sodalite Network: Height and Spherical Content (Coordination Sequence)

Abstract

The `sodalite' network is the edge-skeleton of the uniform tiling in Euclidean 3-dimensional space by Archimedean tetrakaidecahedra (truncated octahedra). We develop explicit expressions for its `height' (minimum network path length from some fixed to given vertex) and `coordination' (content of network sphere of given height) functions. The final discussion should to some extent assist in motivating and signposting our proof strategy, in the course of ruminating on its potential generalisation.