I wonder how to name such shape:
It's commonly used by e.g. 3ds max to visualize the bone in animation system. It consist of two pyramids with the exact same square base. It would be a octahedron, but the pyramids have different heights. What's the proper name for such 3d shape? If none exists, how should I call such geometry in my 3d engine (it's not only associated with bones and animation)?
As requested, I am copying my comment as an answer. The shape is an octahedron, just not a regular octahedron.