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Sacred Geometry

36 SimPLe tiLingS repeating patterns over an infinite sur face There are three regular tilings or tessellations of the plane below and eight semiregular opposite. The top left and right grids opposite are a left and righthanded pair, an early example of chirality. All these can be drawn easily with ruler and compasses. Regular tilings are those where only one regular polygon is used to fill the plane, whereas semiregular tilings allow for more than one type of polygon but insist that each meetingplace, point or vertex is the same. For instance, in the central pattern opposite every vertex is a meeting of two hexagons and two triangles. Some designs can be filled in further as we saw on page 11, dodecagons are just made of hexagons, triangles and squares, and hexagons can be reduced to triangles. Triangles and squares can go on to do the most amazing things together next page. Octagons only tile with squares opposite top centre. Pentagons do not fit together easily on the plane, preferring the third dimension see pages 1213. Heptagons and enneagons stand aloof. 37
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