7 6 5

7 6 5

You can't tile the plane with regular heptagons, hexagons, and pentagons.

But you can tile the plane with figures that are close to regular heptagons, hexagons, and pentagons.

Suppose that we want to put a bunch of those figures together.

Let's assume that all the side lengths are the same.

We assume that our heptagons, hexagons, and pentagons have unit side length.

Now the radius of a pentagon with unit side length is five sixths.

The radius of a hexagon with unit side length is six sixths.

And the radius of a heptagon with unit side length is seven sixths.

Really?

No.

But they're almost five sixths and seven sixths.

So if when we make our figures, if we measure six centimeters or six inches or six cubits, whatever your preference is, we can get a decent approximation with radii on figures that are easy to measure.