[An expanded, corrected and illustrated update of this article appears in The Lost Inventions of Buckminster Fuller.]
The television program LOST (first broadcast on the United States channel ABC between 2004-2010) includes geodesic domes. I do not intend to say much here about the show other than I have enjoyed it tremendously. The sixth and final season of LOST begins in February 2010. This essay will discuss the geodesic domes appearing in LOST.
To date the dome has been seen in three forms. The first version of the dome is the dome itself, seen in the episode ‘Man of Science, Man of Faith’ on 21 September 2005. This dome is a full-sized set, while the other two are models. It is implied that this dome is a 5/8th-sphere made up of panels with one or more entryways. The second version of the dome is a model of the completed dome, seen in the episode ‘Orientation’ on 5 October 2005. This dome is a cutaway model made of panels of a 5/8th-sphere. The second version of the dome is a model of the dome under construction, seen in the episode ‘Namaste’ on 18 March 2009. This dome is an in-progress 5/8th-sphere made of struts. The ‘Man of Science’ dome and another dome appear in the computer game LOST: Via Domus. All of the geodesic domes appearing in LOST are class one, four-frequency, 5/8ths truncated spheres.
The word geodesic is made up of the root words geo (Earth) and desic (divide). A geodesic sphere is a sphere divided by lines. The equator around the Earth is a geodesic line, dividing the Earth into a Northern and Southern hemisphere (partial sphere). The equator and the Prime Meridian line divide the Earth into four sections. A longitude line 90-degrees from the Equator and from the Prime Meridian would divide the Earth into eight sections. Were the points where these lines cross connected within the Earth, the connections would form an octahedron. If the triangular faces of that octagon were subdivided into smaller triangles each, and if these triangles were projected out from a central point onto the surface of the earth, it would form the coordinates for a geodesic sphere. Geodesic spheres can also be ‘projected out’ from an imagined icosahedron inside a sphere. If the triangular faces of an icosahedron are subdivided into smaller triangles and these smaller triangles are projected out from a central point onto the surface of a sphere, the familiar pattern of a geodesic sphere is seen.
The first patent for a geodesic dome shelter was awarded to Walter Bauersfeld in 1925 (see The Lost Inventions of Buckminster Fuller by Trevor Blake). Buckminster Fuller popularized the use of the geodesic dome. He also conducted and inspired a great deal of original research into the use of geodesic domes as shelters. Fuller first referred to ‘alternative’ and ‘regular’ domes, but the terms class one and class two have become standardized terms.
Class one and class two domes are differentiated by how the faces of a polyhedron (in this case, the triangular faces of an icosahedron) are subdivided before being projected out from a central point onto the surface of a sphere . A class one dome divides the faces of a polygon more or less parallel to the edges of the polygon. A class two dome divides the faces of a polygon more or less perpendicular to the edges of the polygon. To see the difference, draw two triangles. Place a mark in the center of each edge of each triangle. On the first triangle, draw a line connecting the marks. On the second triangle, draw a line connecting the mark to the opposite corner. The first triangle will be subdivided into four smaller triangles, one in the center and one in each corner. The second triangle will be subdivided into six smaller right-angle triangles, each one touching a center point. The first triangle is how the face of an icosahedron is subdivided in a class one geodesic sphere. The second triangle is how the face of an icosahedron is subdivided in a class two geodesic sphere. The LOST domes are class one domes.
The frequency of a geodesic sphere is how many times a projected polygon face is subdivided. An icosahedron has a frequency of one (or 1v), as its faces are not subdivided. The first triangle mentioned in the previous paragraph, the subdivided triangular faces found in a class one geodesic sphere, are two frequency (or 2v). Triangular faces on an icosahedron can be divided into any number of frequencies. Low frequency geodesic spheres have the advantage of a uniformity of components. High frequency geodesic spheres have the advantage of a closer approximation to a sphere. Most of the triangles on a geodesic sphere can be seen as part of a hexagon. Some triangles, however, are also part of pentagons. The edges of the triangles making up pentagons on geodesic spheres radiate from a central point to another pentagon on the sphere. Counting the number of edges from pentagon to pentagon (including edges in a pentagon) reveals the frequency of a geodesic sphere. The LOST domes have a pentagon at the highest point.
The LOST domes are not geodesic spheres, but are instead geodesic domes. A single pentagon of five triangles on a 4 frequency geodesic sphere is a 1/8th truncated sphere. Adding the band of triangles around that pentagon makes a 1/4th truncated sphere. The LOST domes are 5/8ths truncated spheres. Geodesic spheres truncated into domes are a collision point between mathematical purity and architectural integrity. The truncation lines of a geodesic sphere are nearly flush with a surface to sit on, but not exactly flush. Readers are encouraged to join many generation of amateur geometric dome model builders. Desert Domes offers an online calculator for finding component measurements of a 4 frequency geodesic sphere and 1/2 truncated sphere. The audience of LOST is an audience ready for figuring out the rest.
The narrative of LOST places the construction of these geodesic domes in the mid-1970s. In the mid-1970s Buckminster Fuller was at the height of his popularity and influence. The use of domes in LOST helps establish when the story is taking place and the sympathies of the characters that constructed them.
– Trevor Blake
Trevor Blake is the author of the Buckminster Fuller Bibliography, available at synchronofile.com