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Plato's Five Gems: Icosahedron Mystery Cache

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firstbass: Behold the Promised Land.

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Hidden : 10/27/2007
Difficulty:
2.5 out of 5
Terrain:
2.5 out of 5

Size: Size:   small (small)

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Geocache Description:



The cache is not at the posted coordinates. The posted coordinates are in the middle of the nearby golf course.

The cache is a small camo-taped lock'n'lock. It contains a gift card for the first to find and also contains several icosahedral dice.

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

The Icosahedron 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.

It may come as a surprise that the Platonic solids were not discovered by Diff'rent Strokes star Dana Plato.

The Icosahedron has twenty faces that are equilateral triangles, with five of the faces arranged around each of the twelve vertices, and 30 edges.

If you lay out the faces of an icosahedron flat, it looks like the picture below (the triangles, not the mugshot).

To solve the puzzle:
1. Print and cut out the diagram.
2. The triangles appear in a row of five, a row of ten, and then a row of five. Label the triangles as follows:
A B C D E
F G H I J K L M N O
P Q R S T
3. After folding up the faces, replace the 20 letters with the numbers 0-19 so that consecutive numbers are on adjacent faces.

The cache is at North HH IH.TPQ West BOG BO.GHQ

You can check your answers for this puzzle on Geochecker.com.

I realize that there is a small number of possible correct answers, but I hope you'll give the geometric puzzle a shot!


Mathematics > Geometry > Platonic Solids > Icosahedron

Additional Hints (No hints available.)