What shaped hole would you need for an octahedron to get through a shape sorter?

Answer 1

That's a really good question. It has several answers.

You can put an octahedron through a square hole - just look at the octahedron point on.

You can put an octahedron through a hole that's a regular hexagon - lay the octahedron down on a table on one of its triangles and look down on it and that's what you'll see.

You can put an octahedron through a rhombus - to see that, look at it edge on. (This was the first answer posted to the question.)

If you don't have a real octahedron to play with you can find one to rotate about with your mouse by visiting http://mathworld.wolfram.com/Octahedron.html