Key ideas to the proofs of many properties of Penrose tilings are the processes of composition, and its opposite, decomposition.
Other useful tools are deflation, a composition
followed by a decrease in tile size, and inflation, a decomposition
followed by a decrease in tile size. Below is the standard decomposition
for the kite and dart. Note that the intermediate step turns them into
rhombs. Decomposition for: kites
and darts rhombs
Composition: for kites and darts rhombs
