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The regular heptahedron is 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. There are three semiregular heptahedra: the pentagonal and pentagrammic Prisms, and a Faceted Octahedron (Holden 1991).


Holden, A. Shapes, Space, and Symmetry. New York: Dover, p. 95, 1991.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. New York: Viking Penguin, p. 98, 1992.

© 1996-9 Eric W. Weisstein