RThorm – Antherwyck Blog

This past weekend, there was an interesting article I came across with a really interesting graphic.  The article was about a group of mathematicians who discovered a new kind of pentagon that will tile the plane.  Gamers are well acquainted with grids of regular polygons that tile the plane, squares and hexes being familiar to us all.

According to the article, there are now 15 different pentagonal tilings that can completely cover a plane.  (There are also Penrose tiles, something else that I am very intrigued by, but there are some differences with those.  The most fascinating thing is that it is an irregular tiling of the plane.  But also, it takes two different tiles, “kites” and “darts” (two different parallelograms) for the tiling, although interestingly, the patterns that are created in Penrose tiles are also pentagonally-based, with lots of 72 degree angles in the field.  But I digress.)

Some of these tilings are more suited to be a hatch pattern than a grid.  But others, like the one I’ve used, have a cell that is large enough to make a decent grid network, and it seemed worth exploring whether or not a dungeon could be drawn using one of those tilings as the grid.  And one of these patterns (top row, middle) is actually a hexagonal tiling, with each hex divided into three matching pentagons.

To my mind, the experiment was a success.  There’s an irregular, organic quality to this map, but it is all straight lines (almost all the same length; 4 of the 5 sides of the pentagon in this tiling are equal) and a handful of repeated angles.

There’s also a version where I filled the dungeon floor with a light gray.  (I thought it might help increase the readability of the map, but it may not be everyone’s preference.

I’m not sure how it would play out to use this as the dungeon map for a game (but if you give it a try, I would love to hear about it).  You could certianly overlay a conventional grid over the top of this, and use it much like you’d use any other map with irregular walls that don’t conform to the grid.  But I think it would be even better to try it out with the pentagonal grid as the game grid.  (For facing, you could have one front facing side of the pentagon, two flanking sides, left and right, and then just two rear sides.)  Certainly some things might get awkward in places, but I think it would be a lot of fun.  You could use this as a map of a dungeon withing some powerful magical vortex, or on an alternate plane, where Euclidian geometry doesn’t work, and everything the players (and the characters) know is not quite what they thought it was.

I’ve got larger, high resolution versions of both of these; those will be Patreon offerings.

These maps are posted here to share, and as is typical for these, you can use it for any personal use, but please only share them with attribution {CC-BY-NC 2015 by Rodger Thorm}  If you have a project in mind that you’d like to use this (or one of my other maps) for, drop me a line.

[image credit for pentagonal tilings: Ed Pegg Jr/Wikimedia Commons via NPR]