Mathematical toys?

Anybody know of "serious" mathematical ornaments or toys like the Gömböc, etc?

Already have a rubix and abacus (that's more of a tool though).

• Define "serious." – user13888 Jan 18 '12 at 4:29
• I was being lack there, perhaps I should define what I do want by what I don't want; placing the correct shape in the hole, children games and so on. – Adam Jan 18 '12 at 4:32
• You probably mean "lax" in the above comment (somewhat Ironic since in your question statement it probably should be "Rubik's" cube). – Willie Wong Jan 18 '12 at 10:37

On Shapeways, you can find a variety of mathematical ornaments.

My favorites are the differential geometric surfaces designed by Bachman. I also like Bathsheba's designs as well.

(Sorry the image is so large. Is there a way to reduce the size?)

For when the Möbius strip is too pedestrian, the good people at Acme Co. claim their Klein bottles are the "finest closed, non-orientable, boundary-free manifolds sold anywhere in our three spatial dimensions."

• His book the Cuckoo's Egg is a lot of fun, too. – Ross Millikan Jan 18 '12 at 6:20

I have a Rattleback at my desk. Fun to fiddle with while thinking.

The Rubik cube. ${}{}{}{}{}{}{}$

• Oh yeah obviously I have one of those - I have some with more than 6 faces also, though in the end it's a tougher algorithm. Very nice puzzles though. – Adam Jan 18 '12 at 4:33

Spirograph from Hasbro. You can make lots of famous mathematical curves with its pieces: epicycloids, hypocycloids, etc. MathWorld has an article on some of these curves.

Zometool is a construction kit which has 2-, 3-, and 5-fold symmetry, which is great for building (3D projections of) the 120-cell, or just for playing around.

• @Adam: Seeing this, I thought of K'nex. Their website doesn't have any info on what symmetries are supported on the home page. I grew up with tinker toys. – Ross Millikan Jan 18 '12 at 6:17

Wikipedia has a section on mechanical puzzle.

As for myself, my fascination with algebraic topology began with metal link puzzles or hanayama.

Of course, Tower of Hanoi is a classic.

Of interest may be the reference: Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys by David Joyner. Book description in Amazon.

While it may be a 'children's toy', the Switch Pitch works remarkably well as an object of mathematical sculpture; it's fundamentally based on the fact that the vertices of a regular cube are also the vertices of two (interlocked) regular tetrahedra (if your cube is $\{0,1\}^3$, take the vertices with $i+j+k$ respectively odd or even). It helps that people can't help but fiddle with it; it's been a perfect hand-fidgetting toy for me.

The Oloid is fun to touch, to watch and understand.

Maybe a Tippe Top.

Love zometool [1]

[1]: http://www.zometool.com/ for geometry, platonic and archimedean solids, among others/

I think there are 2 different toy devices that mimic a Gray code. One can be seen at http://mypuzzlecollection.blogspot.com/2011/12/brain.html. The other is named "Spin Out".

• Also the Towers of Hanoi. – JeffE May 14 '12 at 7:21

Sudoku and all other logic trainers would also fit.

Check Montessori mathematical materials like the binomial cube just google it

Origami to fold shapes to find surface area of 3 dimensional shapes. Wooden blocks. The Game of 24. Math Jeopardy. Bucky balls. Sudoku. Computer games with rotations and other types of transformations.

In a blatant reference to my own creative work, I submit for your consideration the mathematical artwork presented on my Shapeways Shop at this address: https://www.shapeways.com/shops/Feingold_Math_Art But there are a huge number of other artists whose work can also be found in other shops there.