# Manual tiling with 8 dodecadudes

Here are 8 dodecadudes. (Drawn from the very numerous dodecadrafters, made from 12 half equilateral triangles, dodecadudes are a subset of 770 pieces with sharp points and narrow necks excluded). Arrange them into a symmetric dodecagon with sides (1 triangle edge)(2 triangle altitudes) alternating. You may rotate and flip the pieces, no overlaps or gaps. This is at a "somewhat tricky by hand" level, computer help will just spoil it for you.

Here is an example of the target shape made with a different set of dodecadudes.

## 1 Answer

Here’s my solution. As far as I can tell, the crack at the bottom is just a discrepancy in my drawing.

Neater version:

• Spot on, and quicker than I could have done it. Note that if you use a 'standard' polydude solver this solution does not appear. You have to allow 'off grid' AKA 'against the grain' placements. Commented Apr 5, 2021 at 5:56
• @theonetruepath Very nice puzzle. I put it into my solver and it suggests this is the unique solution. I guess that solving it manually isn't too hard since so many pieces are on the boundary of the dodecagon, and have an obvious candidate for a boundary vertex. Commented Apr 5, 2021 at 6:16
• @JaapScherphuis Yes there are 14 sets of 8 pieces (out of the 770 dodecadudes I have on file) that tile the shape 'against the grain' only. There are 313539 sets that tile only 'on grid' and another 14 if you allow 'against the grain'. The majority have a single tiling. Commented Apr 5, 2021 at 7:12