heptadecahedron

A heptadecahedron is a polyhedron with 17 faces. The term itself is derived from Greek words: "hepta" meaning seven, "deca" meaning ten, and "hedra" meaning face. Therefore, a heptadecahedron literally translates to a "seventeen-faced" solid.

Like any polyhedron, a heptadecahedron has faces, edges, and vertices. The number of faces is fixed at 17. However, the shape of these faces and the arrangement of edges and vertices can vary greatly. This means there isn't a single, unique heptadecahedron in the way there is a unique cube or tetrahedron. Many different geometric configurations can result in a solid with 17 faces.

Examples of heptadecahedra can be constructed by modifying simpler polyhedra. For instance, one could take a prism with a particular base and then truncate some of its vertices or edges, leading to a new polyhedron with 17 faces. The specific type of heptadecahedron is often further described by the shapes of its constituent faces, such as if they are all triangles, quadrilaterals, or a mix of different polygons. The study of polyhedra with a specific number of faces, like the heptadecahedron, falls within the broader field of geometry and polyhedral combinatorics.