But does it fit in the square hole?

Made me think of these toys.

Nah man, real folks know to go through Cliff Stoll and get one of them babys for the house. I finally got mine this year after hearing his talk at DEFCON. Look how happy this legend is!

In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of “clockwise” and “anticlockwise”. It generalizes the concept of curve orientation, which for a plane simple closed curve is defined based on whether the curve interior is to the left or to the right of the curve. A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if “clockwise” is changed into “counterclockwise” after running through some loops in it, and coming back to the starting point. This means that a geometric shape that moves continuously along such a loop is changed into its own mirror image.

Well yeah, it’s a 3d projection of a 4d shape. Maybe you can orient it in 4d, I haven’t checked