This pictorial shows the Geometrical determination of the relative spacing between nodes of the elements. It also shows the geometrical derivation of the radius of a Hex-Pent if its' pentagon edge distances were unity. This page was updated 5/13/97.
The following gif shows the geometric derivation of the Tri-Pent-Rect Geodesic from the Hex-Pent Geodesic. It also shows the derivation of the Tri-Hex-Pent structure from the Hex-Pent Geodesic. The Tri-Pent-Rect Geodesic can be used as a universal connecting node for the construction of the differing elements and their compounds.
The following gif shows a relative of the Tri-Pent-Rect Geodesic arrived at by means of geometric reduction. This geodesic will be referred to as Reduction I. Further reductions can be used for larger structures.
If one were to compare this type of structure with the present Buckminster Fuller type of Geodesic, it would be like comparing an Isocahedron based system to a discipline which is a composite of both the isocahedron and dodacahedron, but which leans more toward the dodacahedron in overall attributes. It's underlying structural compound being the Tri-Pent Geodesic. The principal advantage of this system, other than greater versatility from having more possible configurations, is that it is a derived system which can be converted into a compound geodesic with ease, offering greater strength to the system. A compound system would concentrate compression forces on the comparatively stronger short members and tension on the relatively weaker long members. Other geodesic and structural domes can be derived from this type of discipline.
The following gif shows a full Reduction I Geodesic and six different possible arrays of components. This configuration is well suited for use in designing an intermediate sized structural dome. Its' drawback is that there are 6 different shaped panels involved in constructing a partial dome. Four different shaped panels required for a full dome.
The following graphic is of an 80 panel 2/5 50' diameter reduction I dome.
