Much is said about symmetry, but little about the divide between symmetry and satisfaction. We need a little chaos in our lives to appreciate perfect circles and dodecahedrons.
That having been said, I was mesmerized yesterday when I stumbled across an assertion that a tetrated dodecahedron is a near-miss Johnson solid—one with full tetrahedral symmetry—that has 28 vertices, 28 faces, and 54 edges. That explanation provided all the chaos my mind needed.
