Talking about the 2d projection of a 5d cube with my younger son

Last week I saw this really neat tweet from Tom Ruen:

The projections are closely related to quasicrystals as well. The Penrose tilings come from projections of a 5-cube (which stack infinitely in 5D like cubes in 3D).
This shows all the rhombic dissections of a decagon.https://t.co/hmk3Vt0fHnhttps://t.co/knff5ywvn9 pic.twitter.com/PRClCio2Hu

— Tom Ruen (@Tom_Ruen) January 31, 2020

Yesterday my younger son and I talked through the decagons after building them from our Zometool set. Today we talked about the projection of the 5d cube.

Here are his initial thoughts:

My son was interested in comparing this 5d cube shape to a shape that we’d built previously. So we got that shape and continued the comparison. We also talked a bit about where else the number 5 appeared in the 5d cube and in our shape:

I’m so happy to have seen the conversation that Nalini Joshi got started on Twitter last week. We’ve had two super fun projects so far inspired by it!