Acrylic, 17 cm x 15 cm x 17 cm, 2007.
The regular tiling of the dodecahedron requires a different approach than the other Platonic solids, as five-fold symmetry is not possible in the 17 plane pattern classes. As a consequence of the duality expressed by the Platonic solids, the icosahedron may be inscribed into the dodecahedron, so that the vertices of the icosahedron correspond with the centre of the faces of the dodecahedron. A pattern may then be projected outwards from the icosahedron onto the faces of the dodecahedron with only minor distortion. This projection method can be applied to other polyhedra and is dependent on the inter-relationships between solids. Hall of the Ambassadors 3, results from the projection of a p6mm pattern from the surface of the icosahedron.
Briony Thomas, Lecturer in Design Theory, School of Design, University of Leeds, UK
"An understanding of the symmetry characteristics of patterns and polyhedra can help provide a means by which patterns may be applied to polyhedra in a systematic and complete way, avoiding gaps or overlaps. Research has recently been undertaken to discover which of the 17 pattern classes can regularly repeat around the Platonic solids, applying only the restriction that the unit cell must repeat across the solid in exactly the same way that it does in the plane pattern. The study focused on the application of areas of the unit cell to act as a tile when applied to the faces of the polyhedra. Emphasis was placed on the pattern's underlying lattice structure and the inherent symmetry operations. The results of this enquiry have given rise to the creation of a series of remarkable mathematical solids. Tiling designs were inspired by geometric patterns at the Alhambra Palace in Granada, Spain and created through the use of routing and laser-cutting techniques."
Other works by the artist