The Rome de Lisle problem

Acta Crystallogr A Found Adv. 2017 Nov 1;73(Pt 6):480-484. doi: 10.1107/S2053273317011834. Epub 2017 Sep 13.

Abstract

The `Rome de Lisle problem' on the vertex and edge truncations has been formulated and solved for all crystal closed simple forms (two, eight, five and 15 for orthorhombic, trigonal + hexagonal, tetragonal and cubic syngonies, respectively). The collections of simple forms obtained are enumerated and considered as special combinations of simple forms in symmetry classes.

Keywords: Rome de Lisle problem; crystal closed simple forms; crystalline polyhedra; symmetry classes; vertex and edge truncations.