¶ Stable & Unstable Structures
← Stable & Unstable | Stable Systems and Unstable Systems →
Index Entry
Tetrahedral, octahedral, and icosahedral necklace structures are all stable. Necklace cubes, rhombic dodecahedra, pentadodecahedra, vector equilibria and tetrakaidecahedra are all unstable. Only necklace-omnitriangulated, multifrequency geodesic spheres are stable structures, because they are based entirely on omnitriangulated tetra-, octa-, and icosahedral systems.
The number of vertexes of the omnitriangulated spherical tetra-, octa-, or icosahedral structures of multifrequency geodesic spheres corresponds exactly with the number of external layer spheres of closest-packed, unit radius spherical agglomeration of tetrahedra, octahedra, or icosahedra:
Tetrahedra 2 F^2 +2
Octahedra 4 F^2 +2
Icosahedra 10 F^2 +2
Only tetrahedral, octahedral, and icosahedral structural systems are stable, i.e., complete, nonredundant, self-stabilizing.
