Cubist parquet

Cubism — a nonob­jec­tive school of painting and sculp­ture devel­oped in Paris in the early 20th century, char­ac­ter­ized by the reduc­tion and frag­men­ta­tion of natural forms into abstract, often geometric struc­tures usually rendered as a set of discrete planes.

The Amer­ican Heritage Dictio­nary of the English Language: Fourth Edition. 2000

In how many ways can we cut a card­board cube along the edges so that we can place the resulting parts on a plane. In geometric language, how many nets does a cube have?

It turns out that there are eleven. Think up a proof of the fact that there is no more and we will show you all of them in our cartoon.

It's inter­esting that any of them can be used to parquet your room. In order to do that we have to place planks without over­laps and so that every single point is covered.

Every time we'll prove it in the following way. First we construct an infi­nitely long (in one direc­tion) stripe (some­times with smooth, but gener­ally with uneven border). Then we mention that a copy of the stripe can be placed closely to the first one and repeating this construc­tion we can fill the whole plane.

Other etudes in “Polyhedra’s inner geometry”