A heptahedron (: heptahedra) is a

polyhedron In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal Face (geometry), faces, straight Edge (geometry), edges and sharp corners or Vertex (geometry), vertices. The term "polyhedron" may refer ...

having seven sides, or faces. A heptahedron can take a large number of different basic forms, or topologies. The most familiar are the hexagonal pyramid and the pentagonal prism. Also notable is the tetrahemihexahedron, which can be seen as a tessellation of the real projective plane. No heptahedra are regular.

Topologically distinct heptahedron

Convex

There are 34 topologically distinct ''convex'' heptahedra, excluding mirror images. (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.) An example of each type is depicted below, along with the number of sides on each of the faces. The images are ordered by descending number of six-sided faces (if any), followed by descending number of five-sided faces (if any), and so on.

Concave

One particularly interesting example is the Szilassi polyhedron, a Toroidal polyhedron with 7 non-convex six sided faces.

References

External links

Polyhedra with 4–7 Faces
by Steven Dutch * {{Polyhedra Polyhedra