Octahedral number
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In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The nth octahedral number O n can be obtained by th
146 magnetic balls, packed in the form of an octahedron
Square pyramidal number
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In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes an
Octahedral number
…underneath the other, by splitting it along a square cross-section. Therefore, the n th octahedral number O n can be obtained by adding two consecutive square pyramidal numbers together: If O n is the n th octahedral number and T n is the n th tetrahedral number then…
A square pyramid of cannonballs at Rye Castle in England