Sodalite Network: Height and Spherical Content (Coordination Sequence)

TL;DR

This paper derives explicit formulas for the height and spherical content functions of the sodalite network, a structure based on Archimedean tilings, aiding understanding of its geometric and combinatorial properties.

Contribution

It introduces explicit expressions for the height and coordination functions of the sodalite network, advancing the analysis of its geometric structure.

Findings

Explicit formulas for height function

Explicit formulas for coordination content

Potential for generalization to other networks

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.