**Order in Chaos**That's what Taffgoch, the creator of this picture, calls it. It's a computer-generated image, made to look nicely weathered... but it's based on an actual model, made by a monk named Father Magnus Wenninger.

Wenninger's story is interesting. In the 1940s went to the Bahamas to teach at a Benedictine school there. He was asked whether he wanted to teach English or math. He chose math. But not having taken many math courses in college, he struggled at first to stay a few pages ahead of the students! He taught algebra, Euclidean geometry, trig and analytic geometry.

In the 1950's he felt he was getting stale, so he went to Columbia Teachers College in the summer for 4 years. He got interested in the “New Math"... and started studying polyhedra.

In 1966 he wrote a booklet called

*Polyhedron Models for the Classroom*. He wrote to H. S. M. Coxeter, the world's expert on polyhedra and higher-dimensional polytopes, sometimes called the 'king of geometry'. Apparently Coxeter sent Wenninger a copy of his book

*Uniform Polyhedra*.

A

**uniform polyhedron** is one that has regular polygons as faces and is symmetrical enough that there's a symmetry carrying any vertex to any other. There are 75 uniform polyhedra - not counting the infinite list of prisms and 'antiprisms'... and a very weird thing called the 'great disnubdirhombidodecahedron'... which is a topic for another day.

After getting Coxeter's book, Magnus Wenninger spent a lot of time making models of uniform polyhedra. He made 65 of them and put them on display in his classroom. Then he decided to publish a book about them. He had the models photographed and wrote the accompanying text, which he sent to Cambridge University Press.

They said they'd be interested in the book only if Wenninger built all 75 of the uniform polyhedra! And so he did...

It took him 10 years to finish the book,

*Polyhedron Models*, which was published in 1971. Mathematics is full of stories of amazing persistence, and this is one!

The key, which not everyone realizes, is that math is

*immensely fun*. To leave behind this world of woe and lose yourself in a world of beauty and perfection - it's dangerously addictive.

**Puzzle**: this shape is covered with little pentagons, little hexagons and funny-looking nonconvex shapes. How many of each are there?

It only takes a tiny bit of persistence to figure this out... at least compared to Wenninger's persistence.

I got my story from here:

https://en.wikipedia.org/wiki/Magnus_Wenningerand the image from here:

http://taffgoch.deviantart.com/art/Order-in-Chaos-214480976#geometry