RobertLovesPi.net

Polyhedra, tessellations, and more.

Three-Color Arrangement for the Dodecahedron

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Three-Color Arrangement for the Dodecahedron

There are well-known symmetrical 4- and 6-color arrangements for the dodecahedron, and the rhombic dodecahedron has such arrangements in 3, 4, and 6 colors. What’s different about the (Platonic) dodecahedron that the 3-color arrangement you see here doesn’t make the cut, yet there is one for the rhombic dodecahedron?

The answer: in the other arrangements mentioned, faces of the same color do not share edges. Here, they do, so this one is usually not listed with the others.

Software credit: please visit http://www.software3d.com/Stella.php and try the free download of Stella 4d available there. It’s the program I used to make this image. And, as for the color arrangements mentioned above, they’re pre-loaded into the Stella interface as easy-to-find options.

James Randi, on the Limited Effectiveness of Belief

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James Randi, On the Effectiveness of Belief

One of the high points of my life was the day I got to have several conversations with James Randi. I enjoyed them. Some others who were there, though, not so much.

An example of how one of the question-and-answer sessions went:

Question: What happens to us after we die?
Randi’s answer: What happens to a computer after you turn off the power?

Apparently the questioner was rather upset by this reply, but I didn’t figure that out myself, even though I was present. I learned about it later, from others. Randi’s response simply made sense to me.