A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation
to a sphere (or hemisphere).
The th order geodesation operation replaces
each polygon of the polyhedron by the projection onto the circumsphere
of the order-
regular tessellation of that polygon.

The first geodesic dome was built in Jena, Germany in 1922 on top of the Zeiss optics company as a projection surface for their planetarium projector. R. Buckminster
Fuller subsequently popularized so-called geodesic domes, and explored them far more
thoroughly. Fuller's original dome was constructed from an icosahedron
by adding isosceles triangles about each polyhedron vertex and slightly repositioning the
polyhedron vertices. In such domes, neither
the polyhedron vertices nor the centers of faces
necessarily lie at exactly the same distances from the center. However, these conditions
are approximately satisfied.

In the geodesic domes discussed by Kniffen (1994), the sum of polyhedron vertex angles is chosen to be a constant. Given a Platonic
solid, let
be the number of edges,
the number of vertices,

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Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 81, 1989.Wells,
D. The
Penguin Dictionary of Curious and Interesting Geometry. London: Penguin,
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