Tetrahedral-octahedral honeycomb

Imagine we have a bunch of bubbles, all stacked together in a nice and orderly way. But these aren't regular bubbles, these are shaped like little pyramids, like a tent. Each bubble has four sides that come together to form a point at the top.

Now imagine we take these little pyramidal bubbles and stack them together in a big grid, like a checkerboard. But instead of just placing them side-by-side, we're going to stack them so that the points of one bubble fit into the little pockets between the bubbles on the level above.

If we keep doing this, we end up with a really cool shape called a tetrahedral-octahedral honeycomb. It's like a three-dimensional checkerboard made up of these little pyramidal bubbles.

But wait, there's more! If we add some more bubbles that are shaped like hexagons and put them in the gaps where the pyramidal bubbles meet, we end up with an even cooler shape called a rhombic dodecahedral honeycomb. But that's a story for another day.