Okay, the patio tile box is practically finished. Lessons learnt: next time use an electric saw, because using a handsaw on such small planks leads to very rough cuts. Not that there's anything wrong with rough cuts, but it looks bad.
The box was designed for a double honey frame, and I don't have such a frame with me, so that explains the frame in the images would appear rather short for the box. I also haven't added frame rest strips (strips of plastic or wood that the frames will rest on, so that they are lifted up from the frame rest plank, and so that the box gets bottom bee-space instead of top bee-space).
Here's the finished product:
The frame rest consists of a piece of polystyreen covered with milk carton cardboard, and on top of the polystyreen is a plank, where the frames rest on. This setup allows me to adjust the frame rest after the box is built, to tweak the distance between the wall and the frame. I used the milk carton cardboard because I hope the bees won't eat it, and it's watertight.
At some points the wood looks a little rough, but there are no sharp or splitery edges where it matters.
In the above photo is looks like there is a plank underneath the frame, but that is because I've pushed the frame all the way to the edge. Also it looks like the frame ears sit very deep in the hive, but that is because the frame rests haven't been adjusted to the correct height yet.
The image below shows the underside of the box.
The box is lovely light-weight...