Thinking about pentagons and dodecahedrons – 7

As within the pentagon itself, the golden mean can be found within the dodecahedron. If you take three intersecting golden rectangles (one standing vertically on one of its shorter edges, one standing vertically on one of its longer edges and running through the center of and perpendicular to the first, and the third lying horizontally and running through the centers of the first two), the center of each face of a dodecahedron will touch one of the twelve corners of those three golden rectangles.
 

The symmetries of the dodecahedron

You can see three symmetries in the dodecahedron. From one angle, it has 2-fold symmetry. In other words, if you were to take one-half of the shape you see and fold it over on top of the other half, the two halves exactly mirror each other.

From another angle, it has 3-fold symmetry. Again, if you take one-third of the shape you see and fold it over on top of another third, they mirror each other.

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