An Archimedean Solid, also known as the Mecon, whose Dual Polyhedron is the Tetrakis Hexahedron. It is also Uniform Polyhedron and has Schläfli Symbol t and Wythoff Symbol . The faces of the truncated octahedron are . The truncated octahedron has the Octahedral Group of symmetries.
The solid can be formed from an Octahedron via Truncation by removing six Square Pyramids, each with edge slant height and height , where is the side length of the original
Octahedron. From the above diagram, the height and base area of the Square Pyramid are
The truncated octahedron is a Space-Filling Polyhedron. The Inradius, Midradius, and
Circumradius for are
See also Octahedron, Square Pyramid, Truncation
Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, pp. 29-30 and 257, 1973.
© 1996-9 Eric W. Weisstein