Tetrahemihexahedron

A seven-sided non-convex non-orientable uniform polyhedron.

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Description

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 the
faces only touch along their edges, is that three of the faces pass
through each other. The seven faces are the four equilateral triangles
and three large squares that intersect in the center. The smaller right
triangles that can be seen 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.

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