## GEODESIC DOMES – THE GEOMETRY

### DOMES ARE PARTS OF SPHERES

Geodesic domes are fractional parts of complete geodesic spheres. Actual structures range from less than 5% to 100% (a full sphere). The Spaceship Earth Pavilion constructed by Tishman Construction for AT&T at Disney’s Epcot is the best-known example of a full sphere.

### DOMES HAVE VARIOUS FREQUENCIES

Geodesic spheres and domes come in various frequencies. The frequency of a dome relates to the number of smaller triangles into which it is subdivided. A high frequency dome has more triangular components and is more smoothly curved and sphere-like. If your web browser is Java-enabled, you can interact with the exhibit on Frequency above.

### DOMES RELATE TO SPHERE PACKING

5-frequency

9-frequency

Fuller realized that spheres packed around a nuclear sphere in successive layers give a cuboctahedral shape, which may be distorted into an icosahedron or octahedron via what he called the jitterbug transformation.

animated GIF by Richard HawkinsThe network of rods between adjacent spheres in a hollow icosahedral packing gives the framework for the classic geodesic sphere. Geodesic domes may also be based on other polyhedra, such as the octahedron and tetrahedron.

### DOMES COME IN CLASSES

Class I

The classic geodesic sphere is composed of 20 curved triangles, each of which corresponds to one facet of the icosahedron, a 20-faceted polyhedron. Each of the 20 triangles is curved because it is subdivided into smaller triangles, the corners of which are all pushed out to a constant distance from the sphere’s center. The pattern used for this subdividing into smaller triangles is used to classify domes into classes I, II and III.