This kind of solid was idealized by Douglas R. Hofstadter to illustrate the cover of his book Gödel, Escher, Bach: An Eternal Golden Braid.

Are there objects whose projections include more than 3 letters? The answer is yes! In fact, there is a theorem from the fractal theory that guarantees the following: if you choose a collection of plane pictures (not necessarily letters), there is an object whose projections include the pictures you've specified (except for a set of measure zero).

This theorem is the starting point for the concept of a digital sundial, that is, a clock which displays the time in numbers using only shadows and the light from the sun. Like the conventional sundial, the device contains no moving parts and it does not use electricity. The digits change as the sun moves across the sky.

The idea started in the late 80s (with the mathematician Kenneth Falconer) and, in 1991, it was presented by Ian Stewart in the Scientific American magazine (August edition). A few years later, in 1994, three Germans, Hans Scharstein, Daniel Scharstein and Werner Krotz-Vogel, built the model shown below. The patent may be found here. A portable version of this digital sundial is being commercialized by the company Digital Sundial.

The object below has three holes in the form of a square, a circle and a triangle. The circle's diameter and the square's side have the same length. The triangle is isosceles and its base and height have lengths equal to the length of the square's side. Is it possible to build a three dimensional solid that can stopper tape these three holes? Click/touch on the image below to see an answer!