Similarly to the octahedral antithesis, it was imagined last autumn during the same transatlantic flight from South America to Europe.
Description
As the name suggests, this solid is a derivation of an earlier creation named tangential cohesion. While its frame consists of the same 24 curved edges (12 convex + 12 concave), it lacks the straight ones. Concomitantly, instead of 24, it’s made up by 12 identical minimal surfaces, each bordered by 2 convex and 2 concave arcs.
Taking the rhombic dodecahedral skeleton out of its structure, it looses the tessellation (honeycomb) property of its predecessor. The general aspect of the solid is more delicate, “flower-like”, with both very thin and very sharp parts. The thin ones are 6 in number and are associated with the convex constituents, while the 4 needle-like spurs are formed around the concave joints.
Regarding the 12 hyperbolic “pseudo-rhombic” faces it has more similarity with the octahedral antithesis, but while there the convex and concave arc triplets are distributed in separate parcels related to the symmetry of a reference octahedron, here the arcs are fluidly intertwined, forming waves in complementary pairs.
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