The arrangement of pentagons shown in the background here is called the Cairo tiling, because it is said to form the street pavements in parts of that city.  That Islamic art has made use of this tiling (and many others) is well documented, but I’ve never heard or read an account from anyone who claimed personally to have seen it used as a paving in Cairo.  I’d be grateful if anyone who could verify the story would use the e-mail link at the bottom of the page to give me particulars.

The object of these four puzzles is to divide each of the figures shown below (without dividing any of the pentagons that make them up) into four congruent pieces, each piece containing one of the four spots.

Dissecting a lattice with restrictions is a familiar puzzle type, but I’ve only seen it done with square grids.  The earliest example I know of is by Henry Ernest Dudeny, a puzzlist who worked early this century, reprinted as #344 in 536 Curious Problems & Puzzles (ed. Martin Gardner).

I’ve also invented some (untested) board games based on the Cairo tiling:  Alhambra, Cairo and Cairo Bead Game.

(Click on the puzzle below to see the solution.)