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This other picture probably taken from the restaurant in the upper sphere is interesting because it shows a strange departure from the precise regularity of the famous skin layout of the Atomium spheres which is an open book for all to see on the 'duality of polyhedra'. It represents, projected onto a sphere, the beginning of the morphing, by filing (chamfering) the edges, between the disdyakis dodecahedron, a Catalan with 48 triangular faces, and its dual, the truncated cuboctahedron, an Archimedean with 12 squares, 8 hexagons and 6 octagons. The chamfering produces the 9 large 40cm wide 'belts' surrounding the spheres (carrying at night the 'moving' lights as metaphors of the electrons circling around the iron atoms of the element of the centered cubic crystal lattice the Atomium represents) and dividing the spheres in 48 spherical triangles, while crossing each other 2 by 2, 3 by 3, and 4 by 4 on the corners of the triangles, and so forming on each sphere 40cm-sided spherical intersection polygons : 12 squares, 8 hexagons and 6 octagons, some of the last two kinds being hidden by the connecting pipes of the Atomium (which interestingly means, by the way, that if those small polygons were leaving their 18m diameter sphere, migrating towards the center, they'd assemble in a truncated dodecahedron about 1.5 meter in diameter, something that would have justified to save the small original vintage plates, most of them now unfortunately lost... ) and here now comes the interest of the photograph which shows, when looked at very carefully, that the 'belts', close to the top, are no longer 40cm wide, leading to largely irregular polygons, no longer a square and a hexagon... This, in my opinion, constitue the Atomium's 'beauty spots ' ! (Samuel Verbiese)

## samve47's conversations

Thanks! And thanks for the info, I didn't know all those things :-)

This other picture probably taken from the restaurant in the upper sphere is interesting because it shows a strange departure from the precise regularity of the famous skin layout of the Atomium spheres which is an open book for all to see on the 'duality of polyhedra'. It represents, projected onto a sphere, the beginning of the morphing, by filing (chamfering) the edges, between the disdyakis dodecahedron, a Catalan with 48 triangular faces, and its dual, the truncated cuboctahedron, an Archimedean with 12 squares, 8 hexagons and 6 octagons. The chamfering produces the 9 large 40cm wide 'belts' surrounding the spheres (carrying at night the 'moving' lights as metaphors of the electrons circling around the iron atoms of the element of the centered cubic crystal lattice the Atomium represents) and dividing the spheres in 48 spherical triangles, while crossing each other 2 by 2, 3 by 3, and 4 by 4 on the corners of the triangles, and so forming on each sphere 40cm-sided spherical intersection polygons : 12 squares, 8 hexagons and 6 octagons, some of the last two kinds being hidden by the connecting pipes of the Atomium (which interestingly means, by the way, that if those small polygons were leaving their 18m diameter sphere, migrating towards the center, they'd assemble in a truncated dodecahedron about 1.5 meter in diameter, something that would have justified to save the small original vintage plates, most of them now unfortunately lost... ) and here now comes the interest of the photograph which shows, when looked at very carefully, that the 'belts', close to the top, are no longer 40cm wide, leading to largely irregular polygons, no longer a square and a hexagon... This, in my opinion, constitue the Atomium's 'beauty spots ' ! (Samuel Verbiese)