The Universe of Disco


Sat, 17 Nov 2018

How do you make a stella octangula?

Yesterday Katara asked me out of nowhere “When you make a stella octangula, do you build it up from an octahedron or a tetrahedron?” Stella octangula was her favorite polyhedron eight years ago.

“Uh,” I said. “Both?”

Then she had to make one to see what I meant. You can start with a regular octahedron:

a regular octahedron made of six steel
ball bearings and twelve blue and green magnetic struts

Then you erect spikes onto four of the octahedron's faces; this produces a regular tetrahedron:

A very similar octahedron, this time
with an orange tripod attached to four of its eight faces, forming an
orange tetrahedron with a blue and green octahedron embedded in it

Then you erect spikes onto the other four of the octahedron's faces. Now you have a stella octangula.

The octahedron from before, but with
red tripods attached to its other four faces, making eight tripods in
all.  The final result looks like interpenetrating red and orange
tetrahedra, with the original octahedron in their intersection

So yeah, both. Or instead of starting with a unit octahedron and erecting eight spikes of size 1, you can start with a unit tetrahedron and erect four spikes of size ½. It's both at once.


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