Editing Truncated octahedron (section)

{{Short description|Archimedean solid}}
{{CS1 config|mode=cs1}}
{{infobox polyhedron
 | name = Truncated octahedron
 | image = Truncatedoctahedron.jpg
 | type = [[Archimedean solid]],<br>[[Parallelohedron]],<br>[[Permutohedron]],<br>[[Plesiohedron]],<br>[[Zonohedron]]
 | faces = 14
 | edges = 36
 | vertices = 24
 | symmetry = [[octahedral symmetry]] <math> \mathrm{O}_\mathrm{h} </math>
 | dual = [[tetrakis hexahedron]]
 | net = Polyhedron truncated 8 net.svg
 | vertex_figure = Polyhedron truncated 8 vertfig.svg
}}
In [[geometry]], the '''truncated octahedron''' is the [[Archimedean solid]] that arises from a regular [[octahedron]] by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular [[hexagon|hexagons]] and 6 [[Square (geometry)|squares]]), 36 edges, and 24 vertices. Since each of its faces has [[point symmetry]] the truncated octahedron is a '''6'''-[[zonohedron]]. It is also the [[Goldberg polyhedron]] G<sub>IV</sub>(1,1), containing square and hexagonal faces. Like the cube, it can tessellate (or "pack") 3-dimensional space, as a [[permutohedron]].

The truncated octahedron was called the "mecon" by [[Buckminster Fuller]].<ref>{{mathworld|id=TruncatedOctahedron |title=Truncated Octahedron}}</ref>

Its [[dual polyhedron]] is the [[tetrakis hexahedron]]. If the original truncated octahedron has unit edge length, its dual tetrakis hexahedron has edge lengths {{sfrac|9|8}}{{sqrt|2}} and {{sfrac|3|2}}{{sqrt|2}}.