GC9D653 Dual (Unknown Cache) in Washington, United States created by PYC

This cache has been archived.

PYC: Cutting down on our maintenance time by archiving a few of our caches. Container and log sheet have been retrieved.

GC9D653 ▼

A cache by PYC Message this owner

Hidden : 6/24/2021

Difficulty:

Terrain:

Size: Size: small (small)

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Geocache Description:

The dual of every Platonic solid is another Platonic solid.

In the drawing below, on the left,
the red regular hexagon (cube) and
the green regular octahedron form a dual pair,
where the vertices of one correspond to the faces of the other.

This is also true of the figures on the right.
The red regular octahedron and
the green regular hexagon (cube) also make a dual pair.

--------The Puzzle-------

To solve this mystery you will need to determine the missing lengths
of the sides of the dual Platonic figures described below.
All numbers should be rounded to 4 decimal places.
If a number is less than 1, then it should be written like this: 0.xxxx
Note: The vertices of the internal figures meet the faces of the external figures.

1. Using the image on the left, if the length of each side of the red external cube is equal to 1, then what is the length of a side of the green internal octahedron.
(Answer looks like this x.xxxx)

2. Using the image on the left, if the length of each side of the green internal octahedron is equal to 1, then what is the length of a side of the red external cube.
(Answer looks like this x.xxxx)

3. Using the image on the right, if the length of each side of the red external octahedron is equal to 1, then what is the length of a side of the green internal cube.
(Answer looks like this x.xxxx)

4. Using the image on the right, if the length of each side of the green internal cube is equal to 1, then what is the length of a side of the red external octahedron.
(Answer looks like this x.xxxx)

--------The Checker-------

Enter your answers, in order, as a single string
(no spaces, no units), into the Certitude checker below.
Your solution will take this form: x.xxxxx.xxxxx.xxxxx.xxxx
A correct solution will give you the final coordinates.

You can validate your "keyword" solution with certitude.

--------The Platonic Series-------

Here are links to this cache and the other two caches
in this Platonic polyhedra series:

1. Straw, String, Soap, Shape - GC9A398

2. Schlegel - GC9AWZ6

--------Prize-------

If you are the next geocacher to solve, find and log this cache,
then you can claim this variation of a Tensegrity Sphere (tensional integrity sphere).

The unique design of this structure
1. balances the forces of compression and tension
without any of the struts touching.
2. forms 6 floating pentagons (of different colors).
3. suspends each of the 30 colored sticks from two other sticks.

This 8" diameter ornament makes a great mistletoe holder or a Xmas tree topper,
one that you can spray paint whatever color fits your decor.