Reversible cardboard cube

Made of coloured cardboard. 7 x 7 x 7 cm. The model makes the varied movement of the cube tangible.

The invertible cube was discovered in the first half of the 20th century by Paul Schatz as a result of his intensive observation of movement. He developed a theory of movement from this, which he called inversion kinematics. By observing the path of spatial diagonals when inverting the tretrahedral cube elements, Paul Schatz discovered the geometric shape of the oloid.

The oloid is a fascinating geometric body: it was discovered in 1929 by Paul Schatz, a Swiss sculptor and mechanical engineer from Constance. The oloid is the only geometric body that can roll over its entire surface. The base is formed by two circles of equal size. To illustrate this, you can imagine two round beer mats of the same size: If you cut one beer mat along its radius to the centre and then stick it vertically onto the radius of the second beer mat so that right angles are formed between the surfaces, you can approximate the shape. The oloid forms a kind of envelope around the two circles. For Paul Schatz, the shape resulted from the inversion of a cube. Due to its special properties, the oloid is used, for example, as part of an oloid agitator in circulation technology.