A tessellation covers a surface without gaps or overlaps.
Work with one repeating tile, then change colour and orientation to discover how a simple rule becomes a surprisingly
lively field.
FORM STUDY / TESSELLATIONA STUDY IN FORM
Three things to learn
THE ESSENTIAL PRACTICE
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Angles make the fit
At every interior meeting point, the angles of the surrounding tiles must add to a full turn of 360 degrees. Six
equilateral triangles meet because each contributes 60 degrees. Four squares contribute 90 degrees each, and three
regular hexagons contribute 120 degrees each. These are the three regular tilings made from a single kind of regular
polygon. A regular pentagon leaves an awkward remainder at a vertex, so identical regular pentagons cannot fill the
plane alone. Draw a cluster around one point before filling a whole sheet. That tiny test tells you far more than a
large, almost-fitting arrangement.
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Read the movements
Translation slides a shape without turning it. Rotation turns it around a point, while reflection produces its
mirror image. Look for these movements in a repeated pattern before thinking about colour. A motif may repeat every
tile, every second tile or over a larger group. Mark a possible repeat unit with a light outline, then imagine moving
that unit across the page. If the boundaries match in both directions, you have found a useful repeat. Colour can hide
or reveal the underlying structure, so first draw your pattern in one colour. Add a second colour only after the
geometry is settled.
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Invent a friendly motif
Begin with a square cut from thin card. Draw a small shape along one edge, cut it away, and attach that exact piece
to the opposite edge without rotating it. Repeat on the other pair of edges if you want a more elaborate tile. The
matching boundaries will still translate neatly across a sheet. Trace several copies before decorating them, checking
that corners stay aligned. Turn the outline into a leaf, creature or abstract mark using interior lines that do not
change the boundary. Keep your first cuts shallow; a dramatic outline can be harder to trace accurately than it
looks.
THE WORKING DESK
Build a repeating field
Choose a regular tile and a colour rhythm. Compare the
vertices and edges as you change tile shapes. Count how many corners meet, then connect that observation to the angle
guide above. It is a small preview of an unbounded tiling: shapes cut by the border continue beyond the viewing
window. Change the motif colour to compare visual balance.
KEEP BESIDE YOUR WORK
A few useful notes.
Try the builder in square, triangle and hexagon mode. The geometry changes, while the two-colour rule remains
visible.
Compare a checker rhythm with a stripe rhythm. Both can use the same tile but suggest a different
direction of movement.
Use a fine pencil for construction and a wider marker for the final repeat unit.
Separate the rule from the decoration.
For a classroom display, label the angle at one vertex and count the
tiles meeting there. Let the diagram explain the fit.