Earlier in the week – on March 14th, in fact! – we were playing around with Patrick Honner’s Pi Day Project:

Here’s a link to that project:

Patrick Honner’s Pi Day Exercise

When we finished, my older son wondered what a similar exercise would look like in the 4th dimension:

I played with it a little, and the idea was a bit more difficult than I expected. Here’s what I was able to write down while my younger son was at a little enrichment math program he does on Monday evenings:

Patrick Honner’s Pi Day Exercise in 4d

We have also – thanks to a great video from Matt Parker – looked a bit a some fairly complicated 4 dimensional shapes before:

Using Matt Parker’s Platonic Solid Video with Kids

So, with that all as background, last night and this morning I spent some time with each of the kids looking a the “smallest” 4d platonic solid – the 5-cell. It is fascinating to hear kids describe the shape.

Here’s my older son:

and here’s my younger son:

I love that my younger son remembered that we’d seen these shapes in our soap bubble project:

Zometool and Minimal Surfaces

It even turned out that our friend Paula drew the 5-cell after seeing our project !!

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