Many of the tiling patterns that I found during my research have been implemented in my viewer applet. On this page are the instructions for how to install and use the applet.
The viewer applet is written in Java, and was originally intended to be run in your web browser. Unfortunately, most modern web browsers no longer allow this due to security concerns. If your browser still allows java applets to run, you can click this link to launch the applet in a new window. It is about 1.6 MB in size, so may take a moment to load.
Unfortunately most modern browsers no longer run applets. In that case you should install the latest version of java, and then download and run the executable jar file from the link on the right (usually double-clicking the saved jar file will start it running).
|The left section of the screen shows a tree structure. Expand any categories in the tree, until you can click on the tiling you want to see.|
|Below the tree is a series of check boxes where you can filter out the tilings based on the symmetries they have.|
|The main centre panel shows the tiling.|
|Below the main tiling are three info panels. The left info panel shows a single tile, with edges and corners labelled.|
|The middle info panel shows the relations that the tile angles and edge lengths must satisfy to be able to form that tiling.|
|The right info panel shows the current angles and edge lengths of the tile.|
|On the right is the control panel where you can change how the chosen tiling is shown.|
|Below the other controls are some sliders. With these you can zoom or rotate the tiling, and change various tiling-dependent parameters that define the shape of the tile.|
Version 1.0: First published online, March 2012, in time for Gathering for Gardner 10.
Version 1.1: 2012/07/22. Added filtering based on symmetry groups.
Version 1.2: 2012/11/04. Added all 2-isohedral non-convex pentagon tilings, and many non-convex hexagon tilings.
Version 1.3: 2013/07/01. Added many 3-isohedral tilings with triangles, and with pentagons.
Version 1.4: 2015/07/30. Added the 15th convex pentagon type (Mann, McLoud, Von Derau)
Version 1.42: 2015/09/29. Added info panel with current angles and side lengths.
Version 1.43: 2015/10/11. Fixed some tilings that showed incorrect angles in the info panel.
Version 1.44: 2015/12/13. Centred unit parallellogram, added missing equation to NC5-14 info.
Version 1.45: 2016/01/13. Fixed N5-8b info, and rearranged pentagon tiling menu to sort by tiling type.
Version 1.46: 2016/09/04. Added two 4-isohedral convex pentagon tilings by Dave Smith.
Version 1.47: 2016/09/05. Added two 6-isohedral convex pentagon tilings by Dave Smith.
Version 1.49: 2017/02/23. Improved Unit Parallelogram - reduce to most rectangular version, and display its stats in info window.
Version 1.491: 2017/07/06. Display more decimals in the info window.
Version 1.495: 2017/07/25. Added the 4-isohedral tiling (N5-1bf2) found in this math.stackexchange post.
Version 1.5: 2017/09/09. Instead of Copy to clipboard (did not work on all platforms), it now saves the tiling image to file in BMP, GIF, PNG, or JPG format.
Version 1.51: 2017/11/24. Subdivided the convex hexagon tilings into types in the selection tree.
Version 1.6: 2017/12/02. Added animation options, and some non-convex tilings.
Version 1.61: 2017/12/07. Small bugfix (ensure sliders are enabled after animation ends unexpectedly)
Written by Jaap Scherphuis, tilings a t jaapsch d o t net.