By Defense Meteorological Satellite Program (U.S.); National Geophysical Data Center

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This work starts with the equilateral triangle and ends with the construction of the icosahedron. The five so-called Platonic solids form the first and simplest group of polyhedra. They have regular faces, all of which touch one another, and the lines which make up any of the vertices form a regular polygon. Further variations of the regular polyhedra, unknown in ancient times, are the Kepler-Poinsot star polyhedra. In all four cases the vertex figures spring from pentagrams. These polyhedra can be formed from the regular dodecahedron and icosahedron.

It is a criminal offence to carry out any work without consent. No application fees are required. See also p. 54. Conservation Areas Consent is needed to demolish any building in a Conservation Area with a volume of more than 115 m3 or a gate or fence more than 1 m high where abutting a highway, or more than 2 m high elsewhere. No application fees are required. National Parks, Areas of Outstanding Natural Beauty and the Broads, World Heritage Sites Generally permissions to carry out building work in these areas are more limited, so check with the appropriate body first.

This is implicated in the mathematics of growth as demonstrated in the Fibonacci series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 . . where each number is the sum of the preceding two. This ratio of successive numbers increasingly approaches that of the golden rectangle. 22 Architect’s Pocket Book The Fibonacci spiral is a curve that increases constantly in size without changing its basic shape. e. 1, 2, 3, 5, from the diagram of which can be seen three nearly golden rectangles. 1170–1230) was an Italian mathematician who introduced arabic numerals to Christian Europe.

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