An Impossible Figure

Dodecahedron on Grid

It makes me sad that it’s not mathematically possible for hexagons to form a polyhedron on their own. Images like these come up labelled as ” 3D hexagon.” At least it reminds me of Tarski’s World.

Tarski's WorldIf you truncate a polyhedron (which I assume means to use a mix of polygons, thus making it irregular) you can get some pretty cool looking solids with hexagons.

Truncated Octahedron

Truncated Octahedron 

Truncated Icosahedron

Truncated Icosahedron

In discovering this, I stumbled across Catalan solids and some of them are just beautiful. The pentagonal hexecontahedron is mesmerizing. Definitely improving my opinion of pentagons.

HexBoard0013

Hexagons are so captivating for games because they increase the number of options a player has by just enough. I can see that the designers of a game like Settlers were going for that sweet spot of options for the player because it shows up in the cards too. Having 5 resources seems to be the perfect number for a players processing, providing just the right amount of complexity. If there were too few resources, there wouldn’t be enough contingencies for the player to think about while others took their turn and trades would be too simple. But if there were too many resources, then the amount of complexity would be overwhelming and Settlers would only come off the shelf about as often as Risk.

This guy has done a little of the math on the suitability of hexagons.

Civilization V

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