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 whi
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]