Download Divided Spheres: Geodesics and the Orderly Subdivision of by Edward S. Popko PDF

By Edward S. Popko

This well-illustrated book—in colour throughout—presents an intensive creation to the maths of Buckminster Fuller’s invention of the geodesic dome, which prepared the ground for a flood of useful purposes as various as climate forecasting and fish farms. the writer explains the foundations of round layout and the 3 major different types of subdivision in keeping with geometric solids (polyhedra). He illustrates how easy and complicated CAD thoughts observe to round subdivision and covers smooth functions in product layout, engineering, technology, video games, and activities balls.

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Extra info for Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere

Sample text

Its faces can be subdivided into six right triangles; thus, the overall solid could be made from 120 right triangles. The subdivision of any one of them can be replicated over its surface without overlaps or gaps. It is the most used polyhedron for spherical work by far. We discuss the icosahedron in great detail later in the chapter. The cuboctahedron (14 faces, 24 edges, and 12 vertices) is the only polyhedron out of hundreds where every edge is equal in length and this length is the distance between every vertex and the center of the polyhedron.

The earliest example dates to 1922 when Walther Bauersfeld, an engineer for Carl Zeiss optical company, developed the world’s first reinforced concrete dome in Jena, Germany,4 for Zeiss’ planetarium. The dome’s steel reinforcing grid resembles the lattice we associate with today’s geodesic dome. Bauersfeld’s structure was highly innovative at the time. However, unlike Fuller’s domes, Bauersfeld’s dome was never developed into a generalized construction system or used elsewhere. Fuller was the first to establish geodesics in a framework he called energetic synergetic geometry, or synergetics for short.

The cuboctahedron has both square and triangular faces, but can be constructed from just eight tetrahedra. As a result, it is highly stable and rigid. These solids were particularly important in synergetics and would appear and reappear in different combinations in his future inventions. The tetrahedron (4 equilateral triangular faces, 6 edges, and 4 vertices) is the only polyhedron where every vertex is equidistant from every other one. 1. Synergetic building construction. by clustering three equal-diameter spheres into a triangle and nestling a forth on top, as seen in the figure to the left.

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