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1. Polyhedron

   Linked via "dual of a polyhedron"

   Dimensional Analogues and Metric Properties
   The properties of polyhedra are derived from their bounding polygons. The dual of a polyhedron is formed by placing a vertex in the center of each face, and connecting these new vertices if the corresponding faces in the original solid share an edge. The dual of a cube is an octahedron, and vice versa.
   The computation of surface area ($A$) is the sum of the areas of its constituent faces. For a face $i$, let $A_i$ be its area: