Taneli Luotoniemi

Doctoral student of art
Aalto University School of Arts, Design and Architecture
Helsinki, Finland

The geometric concept of the fourth spatial dimension has had a lasting effect on Western culture and science. Kinetic models based on the 4-dimensional regular polychora would be beneficial for understanding these structures, but are difficult to implement because of the distortions resulting from the ‘flattening’ required. Bitruncated versions of the polychora are, however, possible to realize as kinetic models by employing hyperbolic patchwork surfaces composed of cloth hexagons. The 4-dimensional rotations of the polychoron can be visualized as a partial ‘inside-out turning’ of the surface – pulling neighboring cells out through the openings. As a result the object changes its color.

Crooked House II (Bitruncated Hypercube)
Crooked House II (Bitruncated Hypercube)
40 x 40 x 40 cm

The bitruncation of the hypecube results in a polychoron composed of 16 truncated tetrahedra and 8 truncated octahedra. When the square faces are removed, the remaining 64 hexagons form a closed surface. This surface is hyperbolic with 4 hexagons meeting at a vertex. Topologically it is a torus with 17 handles. The 4-dimensional rotations takes us to 8 different cells, each of its own color.