# The Hex

by Kevin J. Lin

There are many solid shapes which, from a certain perspective, could yield the appearance of the impossible hex. Shown above is such an object, rotating to illustrate the perspective illusion.

Our eyes are trained to receive "cues" from the environment telling us what we are looking at. In the case of the impossible hex, an illusion generated by the interlacing of two impossible triangles, the lighting, grain of the wood, and the apparent intersections, all seem to clearly show the intersection of two wooden beams at right angles at each vertex. However, our knowlege of spatial relations tells us that no object built with such angles could exist. Any two points on either triangle do not point to paradox, but all three at once? The mind rejects it. And correctly so- no triangles to date have been discovered in Euclidean space with three right angles.

But neither object really is a triangle. They are, in fact, three beams of wood joined together each with a unique axis perpendicular to the other two. A slight "cut" in the wood causes it to seem to blend in with its far end, but only from a certain angle. As it turns out, the "right angles" we see at the top left and lower right of the image are not right angles at all, but tricks of perspective.