Quaderformen

Quaderformen are a class of polyhedra in geometry, corresponding to rectangular prisms. They are hexahedra with six faces, where each face is a rectangle and opposite faces are parallel. In standard usage, a quaderform is defined by three perpendicular edge directions, with edge lengths a, b, and c.

The defining properties include that adjacent edges meet at right angles, and the shape is entirely determined by the three side lengths. The volume is calculated as V = a · b · c. The surface area is S = 2(ab + bc + ac). The space diagonal, the line connecting opposite vertices, has length d = sqrt(a^2 + b^2 + c^2). Opposite faces are congruent rectangles, and all interior angles are right angles.

Variants and related shapes: If a, b, and c are equal, the quaderform becomes a cube, a special case with equal edge lengths and equal face squares. If any face deviates from a rectangular shape, or if angles between edges are not right angles, the solid is no longer a quaderform but a different type of polyhedron (for example, a general parallelepiped with non-rectangular faces).

Applications and context: Quaderformen are common in architecture, packaging, and 3D modeling as simple, box-like solids. They provide straightforward formulas for volume and surface area and serve as basic building blocks in both theoretical geometry and practical design.