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In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular ), 36 edges, and 24 vertices. If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and δ S +1 , where δ S is the silver ratio, √ 2 +1.
A hexahedron (pl.: hexahedra or hexahedrons) or sexahedron (pl.: sexahedra or sexahedrons) is any polyhedron with six faces. A cube, for example, is a regular hexahedron with all its faces square, and three squares around each vertex. There are seven topologically distinct convex hexahedra, [1] one of which exists in two mirror image forms ...
A cuboid, a topological cube, has 8 vertices, 12 edges, and 6 quadrilateral faces, making it a type of hexahedron. In the context of meshes, a cuboid is often called a hexahedron, hex, or brick. [1] For the same cell amount, the accuracy of solutions in hexahedral meshes is the highest.
The middle image is the uniform truncated cube; it is represented by a Schläfli symbol t{p,q,...}. A bitruncation is a deeper truncation, removing all the original edges, but leaving an interior part of the original faces. Example: a truncated octahedron is a bitruncated cube: t{3,4} = 2t{4,3}.
The cube can be represented as the cell, and examples of a honeycomb are cubic honeycomb, order-5 cubic honeycomb, order-6 cubic honeycomb, and order-7 cubic honeycomb. [47] The cube can be constructed with six square pyramids, tiling space by attaching their apices. [48] Polycube is a polyhedron in which the faces of many cubes are attached.
Etymologically, "cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. [1] [2] General cuboids have many different types.
Like the cube, it can tessellate (or "pack") 3-dimensional space, as a permutohedron. The truncated octahedron was called the "mecon" by Buckminster Fuller. [1] Its dual polyhedron is the tetrakis hexahedron. If the original truncated octahedron has unit edge length, its dual tetrakis hexahedron has edge lengths 9 / 8 √ 2 and 3 / ...
In geometry, a rhombohedron (also called a rhombic hexahedron [1] [2] or, inaccurately, a rhomboid [a]) is a special case of a parallelepiped in which all six faces are congruent rhombi. [3] It can be used to define the rhombohedral lattice system , a honeycomb with rhombohedral cells.