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The truncated cube, or truncated hexahedron, is an Archimedean solid
Archimedean solid

In geometry an Archimedean solid is a highly symmetric, semi-regular convex set polyhedron composed of two or more types of regular polygons meeting in identical vertex ....
. It has 6 regular octagon
Octagon

In geometry, an octagon is a polygon that has 8 sides. A regular octagon is represented by the Schl?fli symbol ....
al faces, 8 regular triangular faces, 24 vertices and 36 edges.








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The truncated cube, or truncated hexahedron, is an Archimedean solid
Archimedean solid

In geometry an Archimedean solid is a highly symmetric, semi-regular convex set polyhedron composed of two or more types of regular polygons meeting in identical vertex ....
. It has 6 regular octagon
Octagon

In geometry, an octagon is a polygon that has 8 sides. A regular octagon is represented by the Schl?fli symbol ....
al faces, 8 regular triangular faces, 24 vertices and 36 edges.

Area and volume

The area A and the volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 V of a truncated cube of edge length a are:

Cartesian coordinates

The following Cartesian coordinates define the vertices of a truncated
Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new Facet in place of each vertex....
 hexahedron
Hexahedron

A hexahedron is a polyhedron with six faces. A Regular polyhedron hexahedron, with all its faces Square , is a cube.There are many kinds of hexahedra, some topologically similar to the cube and some not....
 centered at the origin with edge length 2?:
(±?, ±1, ±1),
(±1, ±?, ±1),
(±1, ±1, ±?)
where ? =

Related polyhedra


Compare:
Uniform Polyhedron 43 T0

Cube
Cube

A cube is a three-dimensional space solid object bounded by six square faces, facets or sides, with three meeting at each wikt:vertex. The cube can also be called a Regular polyhedron hexahedron and is one of the five Platonic solids....
Uniform Polyhedron 43 T01

Truncated cube
Truncated cube

The truncated cube, or truncated hexahedron, is an Archimedean solid. It has 6 regular octagonal faces, 8 regular triangle faces, 24 vertices and 36 edges....
Uniform Polyhedron 43 T1

cuboctahedron
Cuboctahedron

In geometry, a cuboctahedron is a polyhedron with eight triangular faces and six square faces. A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each, and 24 identical edges, each separating a triangle from a square....
Uniform Polyhedron 43 T12

Truncated octahedron
Truncated octahedron

The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces, 6 Square faces, 24 vertices and 36 edges. Since each of its faces has point symmetry the truncated octahedron is a zonohedron....
Uniform Polyhedron 43 T2

Octahedron
Octahedron

An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each wikt:vertex....


It shares the vertex arrangement
Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....
 with three uniform star polyhedrons:
Great Rhombihexahedron

(4.8/3.4/3.8/5)
Great rhombihexahedron

In geometry, the great rhombihexahedron is a nonconvex uniform polyhedron, indexed as U21.It shares the vertex arrangement with the convex truncated cube....
Great Cubicuboctahedron

(8/3.3.8/3.4)
Great cubicuboctahedron

In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14.It shares the vertex arrangement with the convex truncated cube....
Uniform Great Rhombicuboctahedron

(4.3/2.4.4)
Uniform great rhombicuboctahedron

In geometry, the Uniform great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17.It shares the vertex arrangement with the convex truncated cube....


See also

  • Spinning truncated cube
  • Cube-connected cycles
    Cube-connected cycles

    In graph theory, the cube-connected cycles is an undirected graph cubic graph, formed by replacing each vertex of a hypercube graph by a cycle graph....
    , a family of graphs that includes the skeleton of the truncated cube


External links

  • The Encyclopedia of Polyhedra
  • www.georgehart.com: The Encyclopedia of Polyhedra
    • VRML
      VRML

      VRML is a standard file format for representing 3-D computer graphics interactive vector graphics, designed particularly with the World Wide Web in mind....
       
    • Try: "tC"