Review Vocabulary

Barlow’s law (crystallographic restriction) A law of crystallography stating that a crystal can have only rotational symmetries that are twofold, threefold, fourfold, or sixfold. (p. 853)

Centrosymmetric Symmetric by 180° of rotation around its center. (p. 840)

Convex A tile (including its boundary) is convex if for any two points on it, all the points on the line segment joining them also belong to the tile. (p. 834)

Conway Criterion A criterion for determining whether a shape can tile by means of translations and half-turns. (p. 841)

Edge-to-edge tiling A tiling is edge-to-edge if for every tile, each edge coincides with the entire edge of a bordering tile. (p. 830)

Equilateral triangle A triangle with all three sides equal. (p. 828)

Exterior angle The angle outside a polygon formed by one side and the extension of an adjacent side. (p. 829)

Fundamental region A tile or group of adjacent tiles that can tile by translations, rotations, mirror reflections, and/ or glide reflections. (p. 845)

Interior angle The angle inside a polygon formed by two adjacent sides. (p. 830)

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.) (p. 828)

Musical sequence A sequence of intervals between Ammann bars. (p. 852)

-gon A polygon with sides. (p. 828)

Nonperiodic tiling A tiling that cannot be made to coincide with itself by any translation. (p. 845)

Parallelogram A convex quadrilateral whose opposite sides are equal and parallel. (p. 833)

Par-hexagon A hexagon whose opposite sides are equal and parallel. (p. 840)

Periodic tiling A tiling that repeats by translations in two different directions, possibly horizontal and vertical. (p. 844)

Quadrilateral A polygon with four sides. (p. 833)

Quasiperiodic A tiling that exhibits local periodicity under some transformations: It can be translated or rotated so that a finite number of tiles coincide perfectly, yet the entire tiling will not. (p. 850)

Regular polygon A polygon whose sides and angles are all equal. (p. 828)

Regular tiling An edge-to-edge tiling that uses only one kind of regular polygon. (p. 830)

Rhombus A parallelogram whose sides are all equal—four equal sides and equal opposite interior angles. (p. 847)

Scalene triangle A triangle with no sides equal. (p. 833)

Semiregular tiling An edge-to-edge tiling that uses a mix of regular polygons with different numbers of sides but in which all vertex types are alike—the same polygons in the same order, clockwise or counterclockwise. (p. 832)

Tiling (tessellation) A covering of the entire infinite plane by nonoverlapping regions, called tiles. (p. 828)

Translation A rigid motion that moves everything a certain distance in one direction. (p. 838)

Vertex type The pattern of polygons surrounding a vertex in a tiling. (p. 832)