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 edge-to-edge 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 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, 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=n&Sigma;ai.
What can I do with polytiles?
Polytiles can be used as prototiles of tessellations 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?
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)


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