# Dodek Duo

The Dodek Duo is dodecahedron built up from twelve pentagonal pyramids, held together by magnets. Each pentagonal face is split into 5 triangles of different colours. Five colours occur on every face, but their order differs so that the faces are unique. The aim is to assemble the puzzle so that at every edge two triangles of the same colour meet. There are also shapes cut out of the triangles at each edge. The three shapes (semicircle, triangle, rectangle) occur once or twice on every face, but in different orders or amounts so that every face is unique. A second and much more difficult puzzle is to assemble the puzzle so that at every edge identical shapes meet.

It is not possible to have matching colours and matching shapes at the same time. There is only one solution with matching colours, and it does not have matching shapes. There are 47 solutions to the matching shapes puzzle, but this is nevertheless much more difficult than matching the colours.

The puzzle was designed and patented by Jerry Langin-Hooper, WO 2010/005635, published 14 January 2010.

## The number of positions:

The 12 pyramids can be assembled in 11!·511 = 1,949,062,500,000,000 ways. This is not a realistic measure of difficulty since you would never continue assembly after the first mismatch.

## Solution:

Here is the solution with matching colours.

Here are the 47 solutions with matching shapes.