I am not a mathematician, only a worker of wood, but for many years, I’ve been intrigued by the study of polyhedra. The geometry and the challenges of construction keep me motivated and I've always enjoyed sharing my assembly techniques. Discovering the website of George Hart many years ago was especially inspirational and acquiring Alan Holden’s book on “orderly tangles” promoted my interest in that area. I have authored, “The Art of Segmented Woodturning” and have produced eight instructional DVDs on the subject of segmented woodturning including the construction of spheres such as the icosahedron.
This assembly of wood-turned components illustrates relationships between three of the Platonic Solids. The maple spindles form an “orderly” tangle of five tetrahedron frames, which surround an internal icosahedron-style sphere. The tangle openings align with the twelve vertices of the inner sphere, which allows for the installation of twelve short spindles. The short spindles provide a uniform mounting location for the dodecahedron-style spheres (the dark wood). Three vertices of the small icosahedron spheres act as connector locations for the tetrahedron edges. There are seventy-five individually “turned” elements comprised of almost 4,000 individual pieces of wood.
This “orderly” tangle is comprised of twelve pentagon-shaped rings. After shaping round rings, they were cut into five sections, inverted, mitered and reassembled into the twelve pentagon star-shaped components. An examination of the assembly reveals twelve openings, surrounded by five vertices, which correspond to the twelve faces of a dodecahedron. The one light-colored ring helps the viewer more clearly see the position of each component. I’ve always enjoyed puzzles and this was certainly a head-scratching puzzle to assemble.
Colin Roberts first explored this shape in 1969 and later, David Springett promoted the shape, calling it a “Ribbon Streptohedron”. The assembly of segmented triangles displays one of the many endless loops within a spherical shape. The final shape was assembled from six half-donut shapes, which were created by turning three full-donut shapes. To achieve the final shape the initial donuts were created with two different diameters and with different orientations of the triangle edges. Each change in direction of 120-degrees aligns with one of the points of a hexagon. There are 5184 individual pieces of wood.