Pentagonal Tiling...

I was reading Julie Rehmeyer's current column (I like Julie's writing and have been following MathTrek for more than almost a year now) at Science News, which is on quasicrystals.

But this column I think she said something other than what she intended... I'd have commented there but you have to register, which I'm not going to do just to leave one small comment, and anyway, posting it here gives me a change to prattle on and point at pictures and such.

To quote:
"That's why you've never seen a bathroom tiled with pentagons - it'd be impossible to cover the whole surface with no gaps."

Now the problem is, this statement is wrong... in fact, here's a counterexample I knocked up in a few seconds (it's a bit rough, but you can see what's going on easily enough).



This is called the Cairo pentagonal tiling. It's one of fourteen known tilings of pentagons (it's probably not obvious, but "Type 4" on that page is the same type of tiling). Another favourite of mine is the the Floret pentagonal tiling. (Go take a look at those two named ones, they're pretty.)

What Julie meant was "...tiled with regular pentagons". Cos, yeah, that doesn't work.

Anyway, aside from that hiccup, it's a good article; worth a read.