Shower Towel Rack Shelf

For a pretty long time (at least the 50's through the 80's), it was popular for showers and bathtubs to include a distinctive towel rack on the wall opposite the spigot, with a square towel rod. I've never found them particularly useful, so I designed a shelf to mount to them instead.

In the showers in my house, the distance between the ceramic mounts (where they attach to the wall) is exactly 47cm, so that's how wide I made the shelf. I'm not sure how standard that distance is, so I've also