These are structures that I call Hyperspheres. They're based on 3-D shapes known mathematically as the Platonic Solids. I've adapted these shapes to the art of woodturning to create these fascinating structures.  

I've been fascinated by the symmetry and elegance of the three-dimensional shapes know as the Platonic Solids for most of my life. These are multi-faceted shapes such as the tetrahedron, octahedron, dodecahedron, etc. Mathematically they are distinguished by having each of the faces of the object being identical, and each of these faces having identical length edges and identical angles. The most common of these is the cube - a 6 faced solid where each face is a square (identical sides, identical angles).

  To adapt these shapes to the art of woodturning, I've replaced each side of the original solid with a turned disk.   So, for example, using a cube as a starting point, I replace each of the 6 square faces of the cube with a circular disk. The disks are joined to a smaller central cube by short wooden struts. The outer surface of each of the disks is curved so that the entire structure is round. The effect is that of an open sphere projecting outward from a central 'core'.  Some have likened the structure to an exploding star, others to a stylized dandelion seed, still others to a soccer ball.

  There are 5 basic shapes in the set of Platonic Solids - the 4-faced tetrahedron (4 triangles), the 6-sided cube (6 squares), the 8-sided octahedron (8 triangles), the 12-sided dodecahedron (12 pentagons), and the 20-sided icosahedron (20 triangles). I have created hyperspheres for each of these. I have also created a 32-sided figure (mathematically known as a truncated icosahedron).  This is a shape made famous by Buckminster Fuller's work on geodesic domes - the shape of the 'bucky ball'.