Sat, 17 Nov 2018
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:
Then you erect spikes onto four of the octahedron's faces; this produces a regular tetrahedron:
Then you erect spikes onto the other four of the octahedron's faces. Now you have a stella octangula.
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.