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Plato's Five Gems: Dodecahedron Mystery Cache

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firstbass: Behold the Promised Land.

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Hidden : 2/7/2008
Difficulty:
3 out of 5
Terrain:
2 out of 5

Size: Size:   regular (regular)

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Geocache Description:



It's a 2x6 Picture Sudoku!

Just kidding. The pictures above have nothing to do with the puzzle. (Or do they?) I salute Twin Cities puzzlers!


The cache is not at the posted coordinates.

The cache is a lock'n'lock container on the large side of small. It contains several dodecahedral dice.

The cache also contains a clue to the final coordinates for Plato's Five Gems: Bunganator's Grand Slam.

The Dodecahedron is one of the five Platonic Solids. A Platonic solid is a convex polyhedron that has identical regular polygons for faces and has the same number of faces arranged around each vertex. See my blog for a proof that there are only five Platonic solids.

The Dodecahedron has twelve faces that are pentagons, with three of the faces arranged around each of the 20 vertices, and 30 edges.

To find the final coordinates of the cache:

  1. Construct the two differently-labeled dodecahedra that are attached.
  2. Imagine that they are spinning, one inside the other, on an axis that passes through the N faces on top and the W faces on the bottom.
  3. Spin the dodecahedra until the 10 pairs of middle faces match up -- there are five different ways to do that; you have to find the correct way.
  4. Make new labels for a dodecahedron consisting of the sums of the numbers on matching faces (ignore the tens digits).
  5. The minutes of the north coordinates can be read around the N face, and the minutes of the west coordinates can be read around the W face -- there are 10 different ways to take the N reading and 10 different ways to take the W reading.

That produces 500 possible sets of coordinates. Very few of them are in the general vicinity of Highland Park, Saint Paul.

Finally, apply to the puzzle solution the rickrich Puzzle Offset™: subtract from north .010 and add to west .013.

You can check your answers for this puzzle (before the rickrich Puzzle Offset™) on Geochecker.com.

Additional Hints (No hints available.)