Heptahedron

A heptahedron (plural: heptahedra) is a polyhedron having seven sides, or faces.

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

Convex

There are 34 topologically distinct "convex" heptahedra, excluding mirror images. [ [http://home.att.net/~numericana/data/polycount.htm Counting polyhedra] ] (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

References

External links

* [http://www.uwgb.edu/dutchs/symmetry/poly4-7f.htm Polyhedra with 4-7 Faces] by Steven Dutch