Welcome to the Home of Polytiles!
An example octatile
is an octagon, with 1 concave angle and 2 straight angles.
tiling of regular dodecagon structures dodecatiles in the gaps, using
the center of the dodecagons as vertices, and edge-to-edge pairs of dodecagons
What is a polytile?
A polytile is an
polygon with vertex angles limited to integer multiples of 360/p
degrees for p as an even positive integer. A tetratile (4-tile)
has vertex angles as multiples of 90°. A hexatile (6-tile) has
angles multiples of 60°. An octatile (8-tile) has angles multiples
of 45°. A decatile (10-tile) has angles multiples of 36°.
A dodecatile (12-tile) has angles multiples of 30°. And so on.
How are polytiles defines?
Polytile notation is used to define a polytile.
It has a structure:
p:a1.a2...am^n, repeating the sequence
of m angles n times. Each ai represents a
turn angle scaled
as steps on a regular p-gon, best limited beween
|ai|<p/2. A zero turn angle defines 2 colinear edges,
positive turn angles turn counter-clockwise, and negative turn angles turn
clockwise. For example, a
square is tetratile,
or 4:1^4, as well as
octatile 8:2^4 and dodecatile
12:3^4. If the p: is
not given, is computed as the sum of all the angles,
What can I do with polytiles?
Polytiles can be used as
of edge-to-edge polygons. Polytiles can also define star polygons, polygons
whose turn angles sum to multiples of 360°.
How can I use them?
applications below (will) allow users to test polytiles by inputing polytile
notation, and building tilings with them.
Informational Pages (in progress)
© 2020-2021 Created by Tom Ruen