¶ Icosahedron: Circumferential Closest Packing
Index Entry
Icosahedron: Circumferential Closest Packing:
"…The icosahedron does not accommodate additional closest-packed sphere layers and never develops a nucleus. The icosahedron’s one and only exclusively circumferentially closest packing of omni-intertriangulated uniradius spheres can increase its frequency only as a shell and not as a nucleus.
“If the icosahedron develops a further outward shell it will have to discard its internal shell because the central angles of the icosahedron will not allow of two or more closest-packed omnitriangulated concentric shells to be constructed. Only one closest packed shell is permitted. Considered internally, the icosahedron cannot accommodate even one uniradius, tangentially contiguous interior or nuclear sphere of equal radius to those of its closest packed uniradius outer shell.”
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