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Barlow's law, or the crystallographic restriction
A law of crystallography that states that a crystal may have only rotational symmetries that are twofold, threefold, fourfold, or sixfold.
Centrosymmetric
Symmetric by 180 degrees rotation around its center.
Convex
A geometric figure is convex if for any two points on the figure (including its boundary), all the points on the line segment joining them also belong to the figure (including its boundary).
Conway criterion
A criterion for determining whether a shape can tile by means of translations and half-turns.
Edge-to-edge tiling
A tiling in which adjacent tiles meet only along full edges of each tile.
Equilateral triangle
A triangle with all three sides equal.
Exterior angle
The angle outside a polygon formed by one side and the extension of an adjacent side.
Fundamental region
A tile or group of adjacent tiles that can tile by translation.
Interior angle
The angle inside a polygon formed by two adjacent sides.
Monohedral tiling
A tiling with only one size and shape of tile (the tile is allowed to occur also in "turned-over," or mirror-image, form).
n-gon
A polygon with n sides.
Nonperiodic tiling
A tiling in which there is no repetition of the pattern by translation.
Parallelogram
A convex quadrilateral whose opposite sides are equal and parallel.
Par-hexagon
A hexagon whose opposite sides are equal and parallel.
Periodic tiling
A tiling that repeats at fixed intervals in two different directions, possibly horizontal and vertical.
Quadrilateral
A polygon with four sides.
Regular polygon
A polygon all of whose sides and angles are equal.
Regular tiling
A tiling by regular polygons, all of which have the same number of sides and are the same size; also, at each vertex, the same kinds of polygons must meet in the same order.
Rhombus
A parallelogram all of whose sides are equal.
Scalene triangle
A triangle no two sides of which are equal.
Semiregular tiling
A tiling by regular polygons; all polygons with the same number of sides must be the same size.
Tiling
A covering of the plane without gaps or overlaps.
Translation
A rigid motion that moves everything a certain distance in one direction.
Vertex figure
The pattern of polygons surrounding a vertex in a tiling.