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Fascinating mathematical model? Ingenious puzzle? Extraordinary toy?

Yes! all three!

Kaleidoscope is a flexagon, a marvellous mathematical discovery with astounding properties. By squeezing certain of its surfaces together, it can be re-opened to display new surfaces which were previously hidden. This version is a hexahexaflexagon - a hexagon which can be flexed to exhibit 6 faces. Due to the ingenious distribution of its coloured wooden triangles, the 6 sides can furthermore be made to display a total of 15 different patterns.
The animation shows Kaleidoscope being flexed 12 times to bring 9 of the possible 15 colours to the centre. The other 6 colours appear on the reverse side. This sequence of flexing is called a Tuckerman Traverse, after the mathematician who discovered that this is the most efficient method of bringing each of the 6 faces to the outside.
At the bottom of this page is an animated demonstration of Kaleidoscope being folded from a strip into the hexagonal shape. Do not look at it if you intend to try and puzzle this stage out for yourself.
Kaleidoscope has been constructed by heat-bonding 90 wood veneer triangles to a length of nylon ribbon, which makes it immensely durable. A further enhancement over the traditional paper flexagon is the addition of magnetic plates at each end (instead of permanently gluing the ends together), so Kaleidoscope has to be assembled before the flexing fun begins. If you choose to try and assemble Kaleidoscope without using the supplied instructions, you will find it quite a puzzle.

Strongly constructed from 90 wooden triangles and 2 magnets on a nylon ribbon. 26 inches/65 mm long when unfolded. Instruction leaflet and separate solution are included.

Price: £12.00
(U.K. Pounds Sterling)

At the bottom of this page is an animated demonstration of how to fold Kaleidoscope from a strip into a hexagon. If you intend to treat Kaleidoscope as a puzzle and work out this stage without help from the instructions, proceed no further.

Loading Page Puzzle: There is a barrel with no lid and some wine in it. "This barrel of wine is more than half full," said Curly. "No it's not," says Mo. "It's less than half full." Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?

Solution: Tilt the barrel until the wine barely touches the lip of the barrel. If the bottom of the barrel is visible then it is less than half full. If the barrel bottom is still completly coverd by the wine, then it is more than half full.