A 130×130-square solution to the Knight’s Tour problem.

## Phonetic Word Wheel

The “Phonetic Word Wheel”, which appears to create combinatorial words (here are some more rudimentary word wheels). Via the book “Reinventing the Wheel”, via an excellent post on similar rotating devices from Brain Pickings.

## Zonohedrified Crossed Heptagrammic Cupolaic Blend

“Zonohedrified Crossed Heptagrammic Cupolaic Blend”, a mathematical sculpture in plywood by Roland Gagneux.

## Recursive Rotation Error

## How Voronoi Diagrams Work

Lots of time thinking about Voronoi Diagrams this week; click image for full-size or here for a high-res PDF.

## Algorithms for Self-Assembly

An interesting article on finding algorithms for self-assembling, nano-scale polyhedra. Related to some things I’m thinking about in the studio at the moment, the process seems quite interesting/complicated. Researchers “determined the best 2-D arrangements, called planar nets, to create self-folding polyhedra with dimensions of a few hundred microns, the size of a small dust particle. The strength of the analysis lies in the combination of theory and experiment… There have been some successes with simple 3-D shapes such as cubes, but the list of possible starting points that could yield the ideal self-assembly for more complex geometric configurations gets long fast. For example, while there are 11 2-D arrangements for a cube, there are 43,380 for a dodecahedron (12 equal pentagonal faces). Creating a truncated octahedron (14 total faces — six squares and eight hexagons) has 2.3 million possibilities.”

Also of interest is the ideation process for this work, where “…the students got acquainted with their assignment by playing with a set of children’s toys in various geometric shapes. They progressed quickly into more serious analysis”.

Via: Science Daily (via: Philip Torrone on Make Blog)