Tetrahemihexahedron

youmagine

This is a model of a tetrahemihexahedron, the only non-convex uniform polyhedron with seven faces. What makes this polyhedron different from the ones we're used to seeing, where faces only touch along their edges, is that three of the faces pass through each other. The seven faces are four equilateral triangles and three large squares that intersect in the center. Smaller right triangles visible on the model are actually sections (one quarter each) of the squares; they don't end at the center but pass through to the other side. This is analogous to the way a Klein surface, another non-orientable object, must pass through itself in order to be represented in three dimensions. It's easier to see with a model that has each square a different color. To make a printable version of the tetrahemihexahedron, we have to resort to an approximation. Neither OpenSCAD nor the 3D printer can handle a model with intersecting but continuous faces, so this model has small fillets along those intersections to make it manifold and printable. The fillets are small enough that they don't show up in the finished print. Choose whether you would like to print the model with a solid face or a hollow face on the printbed; there are STLs for both, and you can also make the choice by editing the OpenSCAD code. Both versions work fine on our printers, but one may work better than the other for you; when printing with the hollow face down I added a brim to make sure it stuck to the bed. OpenSCAD can also be used to change the size of the print; the STLs are 50 mm along each edge.