You know how something can be 'over-engineered'? Well, I think some things are over-mathematicianed.
This bouncy ball, on sale for a couple of quid next to the tills at Mothercare, is a fine example. It's made of six rubber threads, woven together to make a shape with dodecahedral symmetry, such that each face has five different colours. Why six threads? So it can embody the outer automorphism group of \(S_6\)!
It was invented by Dick Esterle. This is my daughter's one; my dog has a bigger one.
I bought a couple more of these, because I reckon they'll be good juggling balls. The tag says they're called "Tangle Ball" and has the address www.keycraft.eu on it.
That page contains this rather stark message:
"The Science of Impulse
How can you turn low value into high profit?
Keycraft's Science of Impulse explains how. Click the link to find out more."
Like, they were next to the till, so I get that's what they're for, but imagine working in that industry! How soul-crushing!
I suppose I just admire the chutzpah of putting that address on something consumers see.
Imagine if you bought a book and on the last page it said
YOU ARE A CLASSIC CHUMP
This book cost us pennies to print.