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Golden Section

44 45 golDen PolyheDra water, ether and the cosmos The Golden Section plays a fundamental role in the structure of 3D space, especially in the icosahedron and its dual, the dodecahedron opposite bottom right, created from the centres of the icosahedrons faces. A rectangle drawn inside an icosahedron has edges in the ratio 1 or 1f see below left and inside a cube opposite top. The rectangles inside a dodecahedron are 21 or 1f2 inside a cube lower opposite. Nested inside an octahedron, the icosahedron cuts its edges in the ratio 1 below centre. The exquisite early drawings by Kepler, DaVinci opposite and Jamnitzer 15081585 opposite page 1 show their fascination with the and root relationships in the 5 Platonic and 13 Archimedean polyhedra. Continuing this theme is the truncated icosahedron opposite upper right, known to us today as the structure of C60, or the common soccer ball the rectangle in this solid has edges in the ratio 31. The icosidodecahedron opposite top left has a radiusedge of 1 and the rhombic triacontrahedron opposite lower left is made of thirty 1 diamonds.
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