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Sacred Geometry

55 54 PentagonaL PoSSibiLitieS those phantastic phizzy phives Although the regular pentagon does not tile on the plane, it does do various other things which no good book on sacred geometry should omit to mention. One of these, taken from Keplers studies, is shown opposite, where a seed pattern can be grown from the centre. The gray pentagons leave spaces which are bits of pentagrams and vice versa. The design is riddled with examples of the golden section. Other seeds are shown. The mathematician Roger Penrose recently discovered the tiling shown lower opposite. Two shapes tile to fill the plane with pentagonal elements which half repeat and half dont at all scales. These patterns have recently been found to underly the nature of most liquids. They are, for instance, crosssections through water. Shown below are the fourteen types of irregular convex pentagon which tile the plane. Keplers early 17th century infinite pentagonal system and below, Penroses 20th century pair of tiles which fill the plane
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