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Johnson Folly
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A simple two colour pseudorhombicuboctahedron puzzle with 3x3x3 core and a misleading solve state.

Many twisty puzzles are based on platonic and archimedean solids, but there are several other families of geometric solids worth exploring.
One such family is the Johnson Solids; convex solids where each face is a regular polygon, faces do not need to be identical, but the vertices are not identical (unlike in archimedean solids).

Deep at the heart of every standard 3x3x3 cube is a rhombicuboctahedron, where the faces are only squares or equilateral triangles (rather than including rectangles as in the Diamond Cube), and this is ideal as a simple twisty puzzle because the cuts fall on the edges.

If one layer of the rhombicuboctahedron is rotated by 45 degrees it takes the shape of the pseudorhombicuboctahedron, Johnson solid 37 also known as the elongated square gyrobicupola. Taking a free-moving rhombicuboctahedron and applying a small turn to the right (1/8th R) layer results in a Johnson solid where that right turn has prevented movement of all adjacent layers. As the 3x3x3 edges and centres are the same square shape it can be confusing to work out that a simple reverse of that turn to the right (1/8th R') is needed to release the puzzle from it's 'solved' state. This confusion effect explains the puzzle's name: Johnson Folly.

Edge length: 17 mm
Overall width: 46 mm



Thank you to the following people for their assistance in helping collect the information on this page: Mark Lodge.


This puzzle can be found in collections of these members:

Markube: Mark's Kubes

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