Truncated Octahedron
 |
An Archimedean Solid, also known as the Mecon, whose Dual Polyhedron is the TetrakisHexahedron. 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 originalOctahedron. From the above diagram, the height and base area of the Square Pyramid are
 |  |  | (1) |
 | |  | (2) |
The Volume of the truncated octahedron is then given by the Volume of the Octahedron
 | (3) |
 | (4) |
The truncated octahedron is a Space-Filling Polyhedron. The Inradius, Midradius, andCircumradius for 
are
 | |  | (5) |
 | |  | (6) |
 | |  | (7) |
See also Octahedron, Square Pyramid, Truncation
References
Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, pp. 29-30 and 257, 1973.
- Secant
- Secant Line
- Secant Method
- Secant Number
- Sech
- Second
- Second Curvature
- Second Derivative Test
- Second Fundamental Tensor
- Sectional Curvature
- Section (Graph)
- Section (Pencil)
- Section (Tangent Bundle)
- Sector
- Sectorial Harmonic
- Secular Equation
- Seed
- Seed of Life
- Seek Time
- Segment
- Segmented Number
- Segner's Recurrence Formula
- Segre's Theorem
- Seiberg-Witten Equations
- Seiberg-Witten Invariants