The Discovery of Irregular Pentagon Tile Number 15

In this quick and nerdy post I would like to share and I suppose also celebrate an interesting shape that I learned about today, that is not only beautiful and dynamic, but can also be tiled without leaving gaps, or overlays.

Its intuitive to understand how the more sides to a shape, the more difficult it is to tile without leaving gaps, or overlays.

Pentagons having one side more than a square are quite difficult shapes to tile, and since 1918 only 15 different irregular shaped variants have been identified.

And only as recently as last week, Casey Mann, Jennifer McLoud and David Von Derau of the University of Washington Bothell announced that they had discovered this 15th irregular variant.

Irregular pentagon tessellations, or tilings should not be mistaken with semi regular variants like the Cairo Tessellation, named after the tiling in the streets of Cairo.

And so far only three types of identical irregular convex hexagons have been discovered that can tile a plane, and no convex heptagons, or octagons.

For more further reading please search for “tessellations” in the search bar on the right side of the page, or check an old post titled Structural Tessellations and Morphologies HERE

You can also download the free and interesting Parametric Patterns Designer for OSX HERE