In our three-dimensional world there are really no two-or four things, nothing is absolutely flat, even the most carefully polished mirror. From an early age a person draws on these "plane", but is not absurd – draw a few lines on paper and say: 'This House'? " – Maurits Esher. This is true, but still, if you count photo paper, two-dimensional surface of a mirror, objects, and a thin wire, a line on paper – one-dimensional, then, with equal rights for a four-dimensional objects exist – the simplest of which – the hypercube (four-dimensional cube) and the hypersphere (four-dimensional sphere). Reconnaissance in force! First, get acquainted with the inhabitants of the fourth measurements. The four-dimensional cube. To visualize the four-dimensional cube, it is useful to first look at the usual – a three-dimensional – a cube, as well as the "two-dimensional cube" (square) and "one-dimensional cube" (segment) look at the transformation of one of Other: If the point of "drag" on the paper, you get a line. The line, in turn, "sweeps" the plane – get a square.
Elongated square of the plane – it would make a cube. This is the third dimension. But what to do with cube to turn it into a four-body? And imagine it? And what are we doing to depict on a flat piece of paper three-dimensional cube? We project it onto the plane. Obtained two squares one inside the other, connected vertices. Since project the same four-dimensional cube! We get a similar two cubes, one inside the other, and once again the top pairs are connected.