Seven Origins of Cubic Close(st) Packing (CCP)
There can be seven origins defined in CCP, where n = {1, 2, 3, …}:
- Origin 1: offset 0,0,0, radius sqrt(2n)
- Origin 2: offset 1/2,1/2,0, radius sqrt(2+4n)/2
- Origin 3: offset 1/3,1/3,2/3, radius sqrt(6(n+1))/3
- Origin 3*: offset 1/3,1/3,1/3, radius sqrt(3+6n)/3
- Origin 4: offset 1/2,1/2,1/2, radius sqrt(3+8(n-1))/2
- Origin 5: offset 0,0,1/2, radius sqrt(1+4n)/2
- Origin 6: offset 1,0,0, radius sqrt(1+2(n-1))
Depending on the origin of the sweeping, a different shape and resulting polyhedron are obtained.
Read more about this topic: Waterman Polyhedron
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