A FAMILY OF 3D-SPACEFILLERS NOT PERMITTING ANY PERIODIC OR QUASIPERIODIC TILING

摘要

A prototile T (homeomorphic to the unit ball) is called a 1-tile (an "Einstein"), if the species So := S({T},lmro) is aperiodic2 (i.e. does not contain any tiling permitting any proper translation). In general by S^, lmr) we denote the species of all tilings of the whole of space, where every tile is congruent to a member of the protosetF, and satisfying the JocaJ matching ruJelmr. lmro stands for "face-to-face, no other requirements".