Introducing the Pentagon Patterns

Deke's Techniques by Deke McClelland

In this week’s free episode of Deke’s Techniques, Deke begins a deep dive into tessellating irregular convex pentagons. Because, you know, if there’s anything Deke can get totally obsessed with, it’s math meets art, with a side of pattern-making. It’s a recipe for a dekeDive.

He begins with a discussion of a simple, regular pentagon in which all the angles and side lengths are the same.

A regular pentagon

Which, makes for a cool pattern, but it does not tessellate on its own. (Not without the addition of some filler diamond shapes.)

Attempt to tesselate a regular pentagon

Meanwhile, an irregular non-convex pentagon (i.e., in which one of the angles indents), like this:

An irregular pentagon with one concave angle

...creates an interesting pattern, about which Deke manages to avoid going down a tangential rabbit hole. But here it is anyway.

Irregular non-convex pentagon tesselation

And finally, we have one—of fifteen, apparently, so far, maybe forever—irregular convex pentagonal shapes, like this one for instance:

One of the tesselating irregular convex pentagons.

Which yields this intriguing and beautiful tessellation:

A tesselating pattern from an irregular convex pentagon.

In the next few weeks, you’re bound to find out all about which irregular pentagons actually yield which results. (Like the one at the top of this post, Number 12, discovered in 1977 by Marjorie Rice, a mom and amateur mathematician who would smoke the rest of us in the art of pattern-making.)

Oh, and speaking of recipes (were we?), in case you missed it over on Deke’s Instagram thing: Here is how I put Deke’s special gradient-making talents to work for a cocktail party we were hosting. I give you the Deconstructed Gradient Caprese Salad. Deke’s pretty handy to have around sometimes.

Gradient deconstructed caprese a la Deke

Deke’s Techniques, where math and art and geekery and tomatoes converge!

Next entry:Tessellating Pentagons Types 1–5: Karl Reinhardt, 1918

Previous entry:Illustrator Puppet Warp Tips and Tricks


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