Patrick Honner’s Pi Day exercise in 4d day 4: The Hyperdiamond

This is the 4th (of 5) in series of 4 dimensional explorations inspired by Patrick Honner’s Pi Day exercise:

The first three parts in the series are here:

Playing with 4 dimensional shapes using Zometool

Introducing Patrick Honner’s Pi day idea in 4 dimensions

Patrick Honner’s Pi day exercise in 4d: part 3

Also, since I didn’t want to really dive into the “surface volume” and “hyper volume” calculations, this website was critical for today’s project:

Regular Convex Four-Dimensional Polytopes

Today we looked at the 24 cell – aka the Hyperdiamond. We’ve looked at the shape previously after seeing this great video from Matt Parker:

Using Matt Parker’s Platonic Solid video with kids

Unfortunately my older son didn’t remember the previous exercise – ha! Oh well, luckily we started with a quick review of the hyperdiamond and the rhombic dodecahedron:

After that quick talk about the 24-cell we returned to our whiteboard to talk about the value of “$\latex \pi$” for this shape. The “surface volume” and the “hyper volume” for the 24-cell turn out to be fairly simple numbers, and that but of luck gives us an easy value of “\pi for this shape!

So, one last project tomorrow. We’ll look at the 120-cell and the 600-cell. Can’t wait!

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