**Mathematical Zoo** is a mix of real and fictional creatures that hold at least some interest for recreational mathematicians. Gardner imagines an actual zoo split up into the two sections, with a newsletter named *ZOONOOZ* (with permission from the Zoological Society of San Diego, which already uses this name) for announcing new arrivals.

(All rights belong to their owners. Images used here for review purposes only. Radiolaria skeletons from Ernst Haekel’s **Monograph of the Challenger Radiolaria**.)

One of the first entries would be visible only through a microscope – the radiolaria that live in the sea and were documented by Ernst Haekel from the Challenger expedition of 1872-76. Not only are these creatures spherical, but their claw protrusions mark the corners of regular octahedrons (8 faces), icosahedrons (20 faces) and dodecahedrons (12 faces). Martin spends some time talking about the five Platonic solids, two of which have faces that are equilateral triangles, adding that there is an infinite number of semi-regular solids that are also composed of equilateral triangles, called deltahedra since their faces look like the Greek letter delta. Eight of the deltahedra are convex, and have 4, 6, 8, 10, 12, 16 and 20 faces. Note that radiolaria #4 above is a deltahedra.

The Aulonia hexagona is accompanied by a question: Can you cover a sphere with a regular map of hexagons, three edges at each vertex? Euler proved that the answer is “no,” but many observers thought that Aulonia showed he was wrong until they looked closer and discovered that some of the cells on the thing’s surface have fewer than 6 sides.

Other real, small, creatures would include viruses that crystallize into macromolecules shaped like regular icosahedra (eg. – the measles virus), while the mumps virus is helical. For other helical structures, we’d have the cochlea of the human ear, the DNA molecule, the horns of various sheep and goats, and the devil’s corkscrews. Fish are good examples of bilateral symmetry, but animals that violate this symmetry would include the crossbill, a small red bird with a crossed beak for prying open evergreen cones; and the wrybill plover (which has a beak that curves to the right for turning over stones to find food).

For knots, we’d have the hagfish, which can tie itself into a knot, the filament-like leucothrix mucor that reproduces by tying itself into a knot, and humans that can cross their arms. Other specimens would include the four-eyed stargazer and the spiral-toothed narwhal. There are many other creatures as well, but it would be easier to scan in the pages than to type them all up.

For imaginary animals, we’d have Frank L. Baum’s Duo, Woozy, Wheeler and Ork, the curl-ups by M. C. Escher, and the Ta-Ta of Sidney Sime (Sidney is best known for illustrating the books of Lord Dunsany, but he did write one book of his own, titled **Bogey Beasts**). The Ta-Ta can turn itself inside-out.

“**The Ta-Ta**

There is a cozy kitchen inside of his roomy head

Also a tiny bedroom in which he goes to bed.

So when his walk is ended and he no more would roam

Inside out he turns himself to find himself at Home.

He cleared away his brain stuff, got pots and pans galore!

Sofa, chairs and tables, and carpets for the floor.

He found his brains were useless, as many others would,

If they but tried to use them a great unlikelihood.

He pays no rent, no taxes, no use has he for pelf

Infested not with servants, he plays with work himself.

And when his chores are ended and he would walk about,

Outside in he turns himself to get himself turned out.”

In the addendum, Martin says that readers informed him about the wheel spider, which escapes predators by extending its legs, flipping on its side and rolling away. And, of the pangolin, mammals that have keratin scales on their skin. Pangolins will curl themselves up into balls to roll down hills to avoid enemies.

**Challenge:** Find a pangolin backpack and give it to Alice Otterloop.