Editing Cube (section)

=== Construction of polyhedra ===
{{multiple image
 | image1 = CubeAndStel.svg
 | image2 = Tetrakishexahedron.jpg
 | footer = Some of the derived cubes, the [[stellated octahedron]] and [[tetrakis hexahedron]].
 | total_width = 320
}}
The cube can appear in the construction of a polyhedron, and some of its types can be derived differently in the following:
* When [[faceting]] a cube, meaning removing part of the polygonal faces without creating new vertices of a cube, the resulting polyhedron is the [[stellated octahedron]].{{r|inchbald}}
* The cube is [[non-composite polyhedron]], meaning it is a convex polyhedron that cannot be separated into two or more regular polyhedra. The cube can be applied to construct a new convex polyhedron by attaching another.{{r|timofeenko-2010}} Attaching a [[square pyramid]] to each square face of a cube produces its [[Kleetope]], a polyhedron known as the [[tetrakis hexahedron]].{{r|sod}} Suppose one and two equilateral square pyramids are attached to their square faces. In that case, they are the construction of an [[elongated square pyramid]] and [[elongated square bipyramid]] respectively, the [[Johnson solid]]'s examples.{{r|rajwade}}
* Each of the cube's vertices can be [[Truncation (geometry)|truncated]], and the resulting polyhedron is the [[Archimedean solid]], the [[truncated cube]].{{sfnp|Cromwell|1997|pp=[https://books.google.com/books?id=OJowej1QWpoC&pg=PA81 81–82]}} When its edges are truncated, it is a [[rhombicuboctahedron]].{{r|linti}} Relatedly, the rhombicuboctahedron can also be constructed by separating the cube's faces and then spreading away, after which adding other triangular and square faces between them; this is known as the "expanded cube". Similarly, it is constructed by the cube's dual, the regular octahedron.{{r|vxac}}
* The [[barycentric subdivision]] of a cube (or its dual, the regular octahedron) is the [[disdyakis dodecahedron]], a [[Catalan solid]].{{r|ls}}
* The corner region of a cube can also be truncated by a plane (e.g., spanned by the three neighboring vertices), resulting in a [[trirectangular tetrahedron]].{{sfnp|Coxeter|1973|p=[http://books.google.com/books?id=2ee7AQAAQBAJ&pg=PA71 71]}}
* The [[snub cube]] is an Archimedean solid that can be constructed by separating away the cube square's face, and filling their gaps with twisted angle equilateral triangles, a process known as [[Snub (geometry)|snub]].{{r|holme}}
The cube can be constructed with six [[square pyramid]]s, tiling space by attaching their apices. In some cases, this produces the [[rhombic dodecahedron]] circumscribing a cube.{{r|barnes|cundy}}