Formalization of Quasilattices

Planes and rows in icosahedral quasilattices

The planar and linear substructures of a threedimensional icosahedral AmmannKramer-Penrose quasilattice have been analysed. Infinitely many families of planes and rows are existing such that each family covers all vertices of the quasilattice. The members of a family of parallel planes are separated by at least three but a finite number of different distances, whose sequence is quasiperiodic an...

Classification of One - dimensional Quasilattices into Mutual Local - Derivability Classes

One-dimensional quasilattices, namely, the geometrical objects to represent quasicrystals, are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. For every MLD class, we can choose a self-similar member as its representative, and a non-self-s...

QUASILATTICES IN IE3 AND THEIR PROJECTION FROM LATTICES IN IEn

Convex polytopes and quasilattices from the symplectic viewpoint

We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold is a space locally modelled on R k modulo the action of a discrete, possibly infinite, group. The way strata are glued to each other also involves the actio...

The formalization of Interpretability