Phasons in these objects relax via the atomic rearrangement of structures called "worms".The cut-and-project method of constructing these objects models them as three-dimensional cross-sections of simpler functions on higher-dimensional hyperplanes, and as a result, the reciprocal lattice for the mass density of these objects cannot be spanned by fewer than 4 basis vectors.
Phasons in these objects relax via the atomic rearrangement of structures called "worms".The cut-and-project method of constructing these objects models them as three-dimensional cross-sections of simpler functions on higher-dimensional hyperplanes, and as a result, the reciprocal lattice for the mass density of these objects cannot be spanned by fewer than 4 basis vectors. Most of these substances are aluminum-rich, including the only natural one known, icosahedrite, which has a crystallographically forbidden five-fold symmetry. Since they can be represented by Penrose tilings, they lack translational symmetry. FTP, name these structures which exhibit long-range order but are aperiodic.
Phasons in these objects relax via the atomic rearrangement of structures called "worms".The cut-and-project method of constructing these objects models them as three-dimensional cross-sections of simpler functions on higher-dimensional hyperplanes, and as a result, the reciprocal lattice for the mass density of these objects cannot be spanned by fewer than 4 basis vectors.
quasicrystals [or quasiperiodic crystals; prompt on "aperiodic tilings" or "quasiperiodic tilings" before Penrose is mentioned]