¶ Vector Equilibrium: Great Circles Of (2)
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Index Entry
axes: if we take the 24 mid-edge points and interconnect their diametric opposites, we get 12 axes of spin; when rotated these generate the vector equilibrium’s ‘12 great circles,’ which run from the corners to the opposite mid-edges of the vector equilibrium’s six squares.
"So we now have three axes (from midpoints of the squares); plus four axes (from midpoints of the triangular facets); plus 6 axes (from vertexes); plus 12 axes (from the mid-edges of the squares). 3 + 4 + 6 + 12 = 25, for a total of 25 great circles for the vector equilibrium.
“It is a characteristic of all those great circles that every one of them go through two or more of the 12 vertexes and these 12 vertexes correspond to all the points of tangency of closest packed spheres: four go through six; three go through four; six go through two; and 12 go through two.”
