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Close-packing of equal spheres
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In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement. Carl Friedrich Gauss proved that the highest average density – that is, the
Cannonballs piled on a triangular (front) and rectangular (back) base, both FCC lattices.
Cannonballs piled on a triangular (front) and rectangular (back) base, both FCC lattices.
Figure 2 Thomas Harriot in ca. 1585 first pondered the mathematics of the cannonball arrangement or cannonball stack, which has an FCC lattice. Note h
Figure 2 Thomas Harriot in ca. 1585 first pondered the mathematics of the cannonball arrangement or cannonball stack, which has an FCC lattice. Note how the two balls facing the viewer in the second tier from the top contact the same ball in the tier below. This does not occur in an HCP lattice (the left organization in Figure 1 above, and Figure 4 below).
Figure 3 Shown here is a modified form of the cannonball stack wherein three extra spheres have been added to show all eight spheres in the top three
Figure 3 Shown here is a modified form of the cannonball stack wherein three extra spheres have been added to show all eight spheres in the top three tiers of the FCC lattice diagramed in Figure 1.
Figure 4 Shown here are all eleven spheres of the HCP lattice illustrated in Figure 1. The difference between this stack and the top three tiers of th
Figure 4 Shown here are all eleven spheres of the HCP lattice illustrated in Figure 1. The difference between this stack and the top three tiers of the cannonball stack all occurs in the bottom tier, which is rotated half the pitch diameter of a sphere (60°). Note how the two balls facing the viewer in the second tier from the top do not contact the same ball in the tier below.
Sphere packing in a cylinder
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Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder of specified diameter and length. For cylinders
Close-packing of equal spheres
…Sphere packing Cylinder sphere packing Krishna, P.; Pandey, D. (1981). Close-Packed Structures (PDF). International Union of Crystallography Commission on Crystallographic Teaching Pamphlets…
The berries of the Arum maculatum form a columnar structure (Bushy Park).
The berries of the Arum maculatum form a columnar structure (Bushy Park).
Spherical soap bubbles confined in a cylindrical glass tube.
Spherical soap bubbles confined in a cylindrical glass tube.
An example uniform structure and its corresponding rolled-out contact network. The identical vicinity of each sphere defines a uniform structure.
An example uniform structure and its corresponding rolled-out contact network. The identical vicinity of each sphere defines a uniform structure.
An example line-slip structure and its corresponding rolled-out contact network. A line slip is identified by the loss of contacts.
An example line-slip structure and its corresponding rolled-out contact network. A line slip is identified by the loss of contacts.