Polytiles
Welcome to the Home of Polytiles!
An example octatile
8:2.3.0.1.2.1.0.3,
is an octagon, with 1 concave angle and 2 straight angles. 
A partial
tiling of regular dodecagon structures dodecatiles in the gaps, using
the center of the dodecagons as vertices, and edgetoedge pairs of dodecagons
define edges. 

What is a polytile?

A polytile is an
equilateral
polygon with vertex angles limited to integer multiples of 360/p
degrees for p as am even positive integer. A tetratile (4tile)
has vertex angles as multiples of 90°. A hexatile (6tile) has
angles multiples of 60°. An octatile (8tile) has angles multiples
of 45°. A decatile (10tile) has angles multiples of 36°.
A dodecatile (12tile) 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:a_{1}.a_{2}...a_{m}^n, repeating the sequence
of m angles n times. Each a_{i} represents a
turn angle scaled
as steps on a regular pgon, best limited beween
a_{i}<p/2. A zero turn angle defines 2 colinear edges,
positive turn angles turn counterclockwise, and negative turn angles turn
clockwise. For example, a
square is tetratile,
4:1.1.1.1
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,
p=nΣa_{i.}

What can I do with polytiles?

Polytiles can be used as
prototiles of
tessellations
of edgetoedge polygons. Polytiles can also define star polygons, polygons
whose turn angles sum to multiples of 360°.

How can I use them?

The javascript
applications below (will) allow users to test polytiles by inputing polytile
notation, and building tilings with them.
Papers
Javascript applications
Informational Pages (in progress)
© 20202021 Created by Tom Ruen
(Reset 7/14/21)
