LIT The cube has 8 vertices, 12 edges, and 6 faces. The dual keeps the 12 edges and exchanges 8 with 6. Both alternating sums are 2.
AMBER Dual is the polyhedral construction named by that swap. This page does not build the geometric octahedron in coordinates beyond the counts.
WALL The swap is not a claim that a second solid is sitting in the galaxy.