Gerard Westendorp on Nostr: This Uniform polyhedron, the Tetrahemihexahedron, is a bit strange. It has Euler ...

This Uniform polyhedron, the Tetrahemihexahedron, is a bit strange. It has Euler characteristic 1, so it kind of has genus (-1/2). It is the only uniform polyhedron with an odd Euler characteristic. Also the only one with an odd number of sides (7). Well OK, apart from the odd prisms. It is non-orientable, like a Klein bottle.
You could see the 4 squares as forming 3 pyramid shape dents. If you consider the polyhedron *composed* of those pyramid dents instead of squares, then the shape is just an ordinary orientable surface with Euler characteristic 2, like the cube. In fact, I folded them like that for easy assembly, the printed side is always on the visible side of the surface.. But when you follow a square as it intersects an other square, you see that it flips orientation.