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Description :
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Octahedra have their faces attached above the triangles of one
orientation and below the triangles of the other orientation. The
transformation of the triangle tiling transforms the octahedra in
their layers. At the maximum expansion the empty space forms
cuboctahedra, and these cuboctahedra close down to form a pair of
tetrahedra at the minimum expansion.
The following animations show a 3x3x3 lattice of octahedra.
view animation with fixed plane (7Mb)
view animation with fixed triangle (7Mb)
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