Plastic Polyhedroid

Geometry Level pending

I have 3 cuboids, each of which has precisely one linear dimension of length 1.

The volumes of these cuboids are 0.105441752, 0.3247179568 and 0.5698402912.

If I were to fit these 3 cuboids together to form a polyhedron, whose perimeter and surface area are integer values \(A\) and \(B\), respectively, find \(A+B\).

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