Tilings

The gyroelongated triangular prismatic tiling has the same vertex figure as one of the plain prismatic tilings; the two may be derived from the gyrated and plain triangular prismatic tilings, respectively, by inserting layers of cubes.

Examples include: *Tilings or tessellations of the plane.

His tilings of the plane underlie the newly discovered quasi-crystals.

It thus suffices to prove Stokes' theorem for sufficiently fine tilings (or, equivalently, simplices ), which usually is not difficult.

Or, in other words: : Animated GIF file showing successive tilings of the plane, and a graph of approximations to the Golden Ratio calculated by dividing successive pairs of Fibonacci numbers, one by the other.

Such tilings or tessellations are infinite and do not bound a "4D" volume, and are examples of infinite 4-polytopes.

The elongated and gyroelongated alternated cubic tilings have the same vertex figure, but are not alike.

The regular icosahedron, seen as a snub tetrahedron, is a member of a sequence of snubbed polyhedra and tilings with vertex figure (3.3.3.3.

These are the same methods that produce aperiodic tilings with the additional constraint for the diffractive property.

The Socolar-Taylor tile forms two-dimensional aperiodic tilings, but is defined by combinatorial matching conditions rather than purely by its shape.

With orbifold notation symmetry of *n32 all of these tilings are Wythoff constructions within a fundamental domain of symmetry, with generator points at the right angle corner of the domain.

With orbifold notation symmetry of *n32 all of these tilings are wythoff construction within a fundamental domain of symmetry, with generator points at the right angle corner of the domain.