Logical classification of geodesic domes

A geodesic shell is a construction consisting of elements whose connections lie on a grid of intersecting geodesic lines, that is, circles obtained by cutting a sphere with central planes. Research is being carried out in the field of geodesic breakdowns of surfaces, architectural design of geodesic domes, analysis of these structures for strength and stability.
The existing classifications of geodesic shells consider only single-contour lamellar geodesic domes, do not take into account the combined systems, the breakdown algorithms, and clearly do not indicate the shape of the original geometric elements.
To overcome these limitations, a logical classification has been developed, which has the following properties:


1) includes single and double contour geodesic shells;
2) based on the shape of the original geometric elements forming the shell;
3) covers the main combinations of classification features for identifying unrealized classes of geodesic shells.

To build a logical classification of geodesic domes, the following classification features were identified.:

1. Type of polyhedron (icosahedron, octahedron, tetrahedron).
2. Number of contour (single-contour - double-contour).
3. View of the surface of the shell (flat plates - pyramids).
4. Plate shape (triangle, quad, pentagon, hexagon).
5. Pyramid shape (trihedral, tetrahedral, pentahedral, hexagonal).
6. Type of the second contour (internal - external).
7. The configuration of the contours (different - the same).
8. The number of breakdown elements.

We construct the grammar of notation for the classes of geodesic shells..
Grammar G has the form:
S>ABC // The designation of the class of the geodesic shell consists of sections of shell type A, type of element B, and a variant of breakdown C
A>DK // contains shell type D - polyhedron {I - icosahedron, O - octahedron, T - tetrahedron}
B>E|E,PK// contains plate type E {3 - triangle, 4 - quadrilateral, 5 - pentagon, 6 - hexagon}, pyramid type {P3 - trihedral, P4 - tetrahedral, P5 - pentahedral, P6 - hexagon}
C>K // contains the number of elements of the sphere breakdown
D>{IK|OK|TK}
E>{K|K,E}
P>{PK}
K>d|Kd
Terminal character d - digit.

As a result of creating a logical classification, 16 classes of geodesic domes for the icosahedron were identified. A new logical classification of geodesic shells has been developed. It differs from other classifications in that it includes single-contour and double-contour geodesic shells, relies on the shape of the original plates and pyramids that form the shell.

Logical classification of geodesic domes
Logical classification of geodesic domes


Where the following notation is used: DN;{M|PM}, D is a polyhedron type, N is the number of contours, M is the number of sides of the polygon, P is a sign of the presence of a pyramid.

Part 1 D1;N one contour, flat plates.
Part 2 D1;PN one contour, pyramids.
Part 3 D2;N two contours, flat plates and the inner rod contour.
Part 4 D2;PN two contours, pyramids and an external rod contour.

Electronic classification of geodesic domes(ECGEOD) - download ECGEOD program - electronic classification in form of the Visual Basic program with .NET Framework (visualization of Logical classification of geodesic shells and domes).