Glossary

Polygon: the key structural element of a tesselation. Difficult to see in the finished product as the edges are obscured. The edges of the polygons define the center-lines of fans and the turning-points of twists. The interior of a polygon is either a clockwise or counterclockwise spiral. The commonly used polygons are triangles, quadrilaterals, pentagons, and hexagons.

Wing: a group of lines of common color within a polygon that appear to be connected. Together, two wings in adjacent polygons form a plane. The “bottom” of a wing is the point at which it converges; the “top” is the opposite. The “height” of the wing is the length of the edge of the polygon that is the root of the wing; the “wingspan” is the length of the spiral.

Plane: also known as a surface. A group of lines of common color within two adjacent polygons that appear to be connected into a single surface, creating the key optical illusion of the tesselation. The two major plane structures are fans and twists.

Spiral: the center of a polygon where a number of wings twist together. In low-N polygons the wings tend to appear to quickly slide past each other; for each higher N they tend to “swirl” for longer, with longer wingspans and shorter heights.

Fan: the basic plane structure caused by two adjacent polygons, one spiraling clockwise and one counterclockwise.

Twist: the basic plane structure caused by two adjacent polygons that are spiraling in the same rotational direction.

Top Angle: the angle of a polygon at the “top” of a wing, which is the opposite side of the wing from its convergence point. The top angle has significant influence on the character of the wing.

Seagull: a special case of a fan that is usually to be avoided. Caused by the top angles of the fan’s wings adding up to more than 180 degrees.

Triangle: a polygon that’s rarely the center of attention. Useful for detail and chaos. Great for small spaces and to break up straight lines. In a triangle the surfaces appear to slide past each other rather than spiraling into infinity. This is less dramatic and appears “tidy”. The wings of a triangle tend to have very short wingspan and can appear heart-shaped.

Quadrilateral: the most common polygon in most tesselations; quadrilaterals are the easiest to draw and produce well-balanced results. Quadrilaterals are also the most flexible polygon, with much potential for varying line lengths and angles. Can appear repetitive if not broken up by other polygons.

Pentagon: the second-most-used polygon; similar to a quadrilaterial but slightly more difficult. The wings of a pentagon tend to be longer than those of quadrilaterials, and the spirals deeper.

Hexagon: the largest and most dramatic commonly used polygon. Overuse of hexagons is not recommended as their deep and powerful spirals tend to be centers of attention.

Nested Split: an experimental technique in which the remaining empty space in a partially-filled polygon is split into two polygons. This produces a twist that appears embedded in the larger polygon and not directly connected to anything else. At present only a single split has been achieved; a double split was tried with poor results.