Seitenebene

Seitenebene is a term used in geometry to describe the plane that contains a side face of a polyhedron. More precisely, each side face (Seitenfläche) of a polyhedron lies in its own plane, and that plane is called the Seitenebene of that side. The concept is commonly applied to prisms and pyramids, where the solid is bounded by base faces and a set of lateral faces.

In a prism with a base polygon of n sides, there are n Seitenebenen corresponding to the n lateral faces. Each Seitenebene is the plane that supports its associated side face; the planes may be perpendicular to the base plane in right prisms, but their exact orientation depends on whether the prism is right or oblique. For pyramids, the lateral faces each lie in their own Seitenebene that passes through the apex and a base edge.

Properties and use: A Seitenebene is defined by the corresponding side face and its polygonal boundary. These planes form the lateral boundary of the solid, and knowledge of the Seitenebenen allows calculation of lateral surface area by summing the areas of the lateral faces. Dihedral angles between lateral faces and base planes are also described in terms of these planes.

Terminology and context: The term Seitenebene appears primarily in German-language geometry texts. The related term Seitenfläche refers to the side face itself, while the English equivalents are usually “lateral plane” or “plane of a side.”