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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).

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Define "serious." –  Mike Wierzbicki 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
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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
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17 Answers

up vote 9 down vote accepted

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.

enter image description here

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

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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."

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His book the Cuckoo's Egg is a lot of fun, too. –  Ross Millikan Jan 18 '12 at 6:20
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The Rubik cube. ${}{}{}{}{}{}{}$

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

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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.

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@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
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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.

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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.

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I love the Spirograph; +1 of course. –  J. M. Jan 26 '12 at 12:12
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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.

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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".

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Also the Towers of Hanoi. –  JeffE May 14 '12 at 7:21
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Sudoku and all other logic trainers would also fit.

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Love zometool [1]

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

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Check Montessori mathematical materials like the binomial cube just google it

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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.

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