Ethan Bolker
I've built mathematical models ever since I read Hugo Steinhaus's
"Mathematical Snapshots" more than 65 years ago. Over time I
graduated
from crude cardboard platonic polyhedra and soma cubes to
constructions in wood and paper that friends have graciously called
art.
3d printing is a new medium for me.
Let v=(a,b,c,d) be a vector of positive integers and N = a+b+c+d. Slice the unit tesseract by the parallel hyperplanes ax+by+cz+dw = n for n between 1 and N-1 and project those three dimensional slices onto the orthogonal complement of v.
The blue model shows all 7 slices for (2,2,2,2). The middle slice is an octahedron. The filled triangles and hexagons typify the faces of the slices.
The red model shows (2,2,3,3). The filled faces sample the triangles, trapezoids, pentagons and hexagons
The green model illustrates (2,2,2,5). The yellow one encodes the first four primes.
All were printed from stl files written by an openscad program written by a python program written by Catalin Zara.
See animations at the link above.