Artists
Henry Segerman
Professor of Mathematics
Oklahoma State University
Stillwater, Oklahoma, USA
Statement
I am a professor in the department of mathematics at Oklahoma State University. My research interests are in three-dimensional geometry and topology, and in mathematical art and visualization. In visualization I work in 3D printing, spherical video, and virtual reality. I wrote the book "Visualizing Mathematics with 3D Printing".
Artworks
This is a cubical chunk of a mechanical three-dimensional network that can change size. The underlying geometry is based on the NbO network, which is named after the crystal structure of niobium monoxide. The various racks and gears ensure that the mechanism has a single degree of freedom as it expands or contracts.
Two ways to transform a cube into an octahedron
20.0 x 40.0 x 20.0 cm
3D printed plastic, laser cut MDF, M3 nuts and bolts
2026
These are two solutions to the problem of creating a mechanism that transforms between a cube and its dual octahedron shape. The first mechanism, independently discovered by Liao, Kiper, and Krishnan, is a jitterbug-like linkage that represents each edge with two links that rotate in opposite directions to implement the transformation. Unfortunately, the configuration space has five endpoints, only two of which are the cube and the octahedron. To fix this, the second mechanism uses a geared core to enforce the same rotation angle for all edges. The edge midpoints do not move, which means that the edges of the octahedron must be longer than those of the cube. Rack and pinion mechanisms are used to achieve this required increase in length.