Florate Polyhedra

These models of regular and semi-regular polyhedra bear some resemblance to flower heads, so florate seems to describe them. But behind them there is a set of basic geometric principles. If the vertices of any of the polyhedra are joined to their centres by straight lines, a set of pyramids appears. The pyramids are based on equilateral triangles, squares, regular pentagons, hexagons, and decagons. If these radii are extended outwards to infinity, we can visualise Euclidean space divided into four regions by the tetrahedron, six by the cube, eight by the octahedron, and so on. The ratios of the sides of the isosceles triangles which form the sloping slides of the pyramids are remarkably simple. Once the method of using straight-edge and compasses to make simple surd lengths has been understood, the nets based on these ratios lend themselves to construction. The nets for all thirteen models in this book may be constructed using the ratios given in the table, and may be scaled up or down to make attractive decorations, perhaps for a Christmas tree.