A heptahedron can take a surprising number of different basic forms, or topologies. Probably most familiar are the hexagonal pyramid and the pentagonal prism. Also notable is the Tetrahemihexahedron, whose seven equilateral triangle faces form a rudimentary projective plane.
Topologically distinct heptahedra
ConvexThere 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.
- Polyhedra with 4-7 Faces by Steven Dutch
heptahedron in Esperanto: Sepedro
heptahedron in Thai: ทรงเจ็ดหน้า