At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.
This shape is a “spherical pseudo-cuboctahedron”, prompted by a request from Jim Propp on the math-fun mailing list.
It has 24 vertices, 12 edges and 14 faces. That doesn’t satisfy Euler’s formula $V – E + F = 2$, so it can’t be a proper polyhedron – hence “pseudo-cuboctahedron”.
However, if you push all the vertices onto the surface of a sphere, all the edges are spherical arcs, it sort of works.
While designing this object, I got fed up with OpenSCAD‘s awkward control syntax, and switched to Python. I wrote Python code to produce the coordinates of points along the edges, which the SolidPython library turned into something that OpenSCAD can cut out of a sphere.
You can download all the files needed to print your own spherical pseudo-cuboctahedron from Thingiverse.