The geodesic dome was popularised by Buckminster Fuller in the 1940s. The dome is most commonly a variant of an icosohedron, or twenty-sided polyhedron, constructed of subdivided regular pentagons and hexagons. The form is roughly the geometry of a traditional soccer ball divided in half, and the area of the geodesic dome roof is a little more than a hemisphere, which is calculated as half the product of four, Pi and the hemisphere radius squared. To re-roof a geodesic dome, you will need to find the exact area and edges of each dome face. This can be accomplished easily with a measuring tape and some geometry.
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Things you need
- Measuring tape
Break the geodesic dome into its constituent regular pentagons and hexagons. A spherical geodesic dome has up to 12 regular pentagons and 20 regular hexagons, and the construction of the pentagons and hexagons is equal in size and structural members. So, when you know how many of each form you have, you can measure one example of each pentagon and hexagon and multiply by the number of polygons.
Count the number of regular triangular faces in the pentagonal and hexagonal sections. A simple icosohedron will have five canted, regular triangles in a pentagon and six regular triangles in a hexagon, but the geometry of a geodesic dome can be complicated enough to have scores of regular triangles in each polygon. The triangular subdivisions should be equivalent in size across the pentagonal sections and across the hexagonal sections. Furthermore, the economy of construction usually dictates that the triangular subdivisions should be equivalent in size across the pentagonal and hexagonal sections. Therefore, you will only need to measure one or two triangular faces and multiply times the number of faces per polygonal section and times the number of each section geometry.
Measure the side and bisecting length dimensions of the regular triangular subdivision for a pentagonal section and a hexagonal section. For roofing that will be placed over the geodesic structure, measure from the centre line of structural members and nodes, or vertices. For roofing panels that go between the geodesic structure, measure from the inside of the member and node widths.
Calculate the regular triangle area by multiplying half the side dimension by the bisecting length dimension. This product is the area of the face, or panel, of the geodesic dome.
Multiply your calculated area by the number of regular triangles in a pentagonal section, as well as the number of regular triangles in a hexagonal section. Then, multiply this number by the total number of each of the two polygonal sections, and add the results. You now have the total area of the geodesic dome roof and the dimensions of the constituent faces and members of the roof.
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