About Symmetry

Grids and Tessellations

THE EASIEST WAY TO ANALYZE a pattern is to locate points of rotation, and lines of symmetry. Why? Because the rigid motions require centers of rotation and axes of repetition or reflection for symmetry to be present.

WHAT IS AN AXIS? An axis is a visible or implied line that is vertical, horizontal, or diagonal, along which designs are repeated or reflected to form patterns.

WHAT IS A GRID? A grid is a visible or implied series of points, or axes that intersect. Grids underly the structure of all two-dimensional patterns.

square grid

triangular grid

hexagonal grid

rectangular grid

rhomboid grid

oblique grid (square)

Grids are usually based on regular polygons: squares, equilateral triangles, and hexagons. Or they can be based on rectangles, parallelograms and rhomboids.

THE ARRANGEMENT OF POLYGONS that forms a grid is called a tessellation. Other shapes may also tessellate.

WHAT IS A TESSELLATION? A tessellation is a pattern formed by the repetition of a single unit or shape that, when repeated, fills the plane with no gaps and no overlaps. Familiar examples of tessellations are the patterns formed by paving stones or bricks, and cross-sections of beehives.

Tessellations are not typical of Oriental carpets except as visible grid structures. Although they often appear in minor borders, only rarely are tessellations used as field patterns.

[Symmetry] [Asymmetry] [Basic Symmetries] [Border Patterns] [Field Patterns] [Grids]
[About Symmetry and Pattern]
[Title Page]

© 1997-2012 The Textile Museum & The Math Forum @ Drexel
Viewers' Comments || Contact Us