Tetragonaldipyramidal

Tetragonaldipyramidal describes a specific geometric shape, referring to a polyhedron that is composed of two square pyramids joined at their bases. This creates a total of eight triangular faces and one square base shared between the two pyramids. The term itself breaks down to "tetra" meaning four (referring to the four sides of the square base), "gonal" meaning angle or shape, and "dipyramidal" indicating it is made of two pyramids.

The resulting shape is a type of bipyramid. A bipyramid is a polyhedron formed by joining two pyramids base-to-base. In the case of the tetragonaldipyramidal shape, the base of each pyramid is a square. This means the bipyramid has a square cross-section through its center. It possesses eight vertices: four at the shared square base and one apex for each of the two pyramids. The symmetry of this shape is quite high.

The tetragonaldipyramidal shape can be thought of as a square antiprism if the edges of the square base are not considered as a single entity, but rather as four separate edges. However, when referring to the classical bipyramid structure, the square base is a single shared face. This geometric form is sometimes encountered in crystallography, where certain mineral structures can exhibit this arrangement of atoms. It's a relatively simple yet distinct polyhedron in geometry.