The Caltech Snub Cube

It is not that common to encounter Archimedean solids “in the wild”, especially the two chiral ones (meaning having a left-hand or right-hand orientation). But then the California Institute of Technology is not exactly “the wild” when it comes to anything related to STEM. It turns out that this fountain was designed by two scientists.

The fountain was clearly under repair when I saw it on June 8, 2024.

The courtyard surrounding the fountain belongs to the Beckman Institute, a multi-disciplinary research center for chemistry and biology. The architect of the building asked for fountain design ideas from the future occupants of the building, and they came up with the snub cube. The reason for their choice is described on the plaque below.

The text is a bit hard to read, so here is what it says


The polyhedron in the fountain is a snub cube, an Archimedean semi-regular solid derived from a cube, with all its edges of equal length. This shape was chosen for the central fountain in the Beckman Institute because it mimics the symmetry of the iron storage protein ferritin, which has 24 ferritin protein subunits arranged in 432 symmetry about a core of perhaps 4500 iron atoms in the form of hydrated ferric phosphate. The snub cube has 38 faces and 24 vertices, the vertices then representing the subunits of ferritin.”

For an interesting account of how the fountain came into being, have a look at this article in the Caltech Magazine. More details about the designers’ thought process can be found in this piece in the Chemical Intelligencer. A fun fact I gathered from it is that the snub cube was one of Linus Pauling‘s favorite solids (the other one being an icosahedron). Eventually word about the Caltech snub cube got out about to the math community, which mentioned it in the College Mathematics Journal.

I was on the Caltech campus for a meeting, and thought it might be fun to build a snub cube with Geometiles and photograph it next to the fountain. This is what you see in the main image of this blog post. In addition, I wanted to use the Geometiles snub cube to illustrate the symmetry that is the crux of why the snub cube was chosen for the fountain: the 432 symmetry. The 4, 3, and 2 in this case represent rotational symmetry of the respective orders.

Here is a video illustrating this

The final note is on the chirality, or handedness of the snub cube. I have addressed it in a previous blog, using extremely appropriate models!

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