Dozen

Dozen usually means a group of twelve of the same thing. With the “baker’s” adjective it becomes a group of thirteen. This phrase comes from bakers’ old custom of adding one extra loaf to an order of a 12.

Who would think that the baker’s twelve (really thirteen) is actually a model for the packing of equally sized spheres and atoms in nature?

Buckminster Fuller, in his Synergetics, discusses how 12 spheres of equal size can surround a thirteen sphere of the same size so all spheres are tangent. Above, the thirteenth is the centered red sphere. Fuller invented a formula for calculating how many spheres are in each layer of spheres. The formula becomes: the number of the layer of spheres (N) squared then multiplied by ten, with two added to this product. He applies this to the physics of elements:

Layer one is 1 x 1 x 10 + 2 = 12. In the above picture, the red sphere becomes the central 13th sphere of the group.

Layer two becomes 2 x 2 x 10 +2 = 42

Afterwards, we have layer three as 3 x 3 x 10 + 2 = 92 (note the atomic number of Uranium).

Layer four would be 4 x 4 x 10 + 2 = 162.