A heptahedron is a polyhedron with seven faces. Through duality, the 34 polyhedral 7-vertex graphs correspond to the 34 topologically distinct convex heptahedra.
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There are three semiregular heptahedra: the pentagonal prism and pentagrammic prism (illustrated above), and a faceted version of the octahedron (Holden 1991).
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The elongated triangular pyramid (Johnson solid 
; left figure) is a convex heptahedron, and the Szilassi
polyhedron (right figure) is a concave heptahedron that contains a hole.
There is a single "regular" heptahedron, consisting of a one-sided surface made from four triangles and three quadrilaterals. It is topologically equivalent to the Roman surface (Wells 1991). While all of the faces are regular and vertices equivalent, the heptahedron is self-intersecting and is therefore not considered an Archimedean solid.
