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  2. Truncation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Truncation_(geometry)

    Faces are reduced to half as many sides, and square faces degenerate into edges. For example, the tetrahedron is an alternated cube, h{4,3}. Diminishment is a more general term used in reference to Johnson solids for the removal of one or more vertices, edges, or faces of a polytope, without disturbing the other vertices.

  3. Cuboctahedron - Wikipedia

    en.wikipedia.org/wiki/Cuboctahedron

    This process is known as rectification, making the cuboctahedron being named the rectified cube and rectified octahedron. [ 3 ] An alternative construction is by cutting of all of the vertices, known as truncation . can be started from a regular tetrahedron , cutting off the vertices and beveling the edges.

  4. List of uniform polyhedra by vertex figure - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra...

    The relations can be made apparent by examining the vertex figures obtained by listing the faces adjacent to each vertex (remember that for uniform polyhedra all vertices are the same, that is vertex-transitive). For example, the cube has vertex figure 4.4.4, which is to say, three adjacent square faces. The possible faces are 3 - equilateral ...

  5. Face (geometry) - Wikipedia

    en.wikipedia.org/wiki/Face_(geometry)

    where V is the number of vertices, E is the number of edges, and F is the number of faces. This equation is known as Euler's polyhedron formula. Thus the number of faces is 2 more than the excess of the number of edges over the number of vertices. For example, a cube has 12 edges and 8 vertices, and hence 6 faces.

  6. Truncated cube - Wikipedia

    en.wikipedia.org/wiki/Truncated_cube

    3D model of a truncated cube. 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.

  7. Cube - Wikipedia

    en.wikipedia.org/wiki/Cube

    As mentioned above, the cube has eight vertices, twelve edges, and six faces; each element in a matrix's diagonal is denoted as 8, 12, and 6. The first column of the middle row indicates that there are two vertices in (i.e., at the extremes of) each edge, denoted as 2; the middle column of the first row indicates that three edges meet at each ...

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  9. Chamfer (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chamfer_(geometry)

    The chamfered cube is constructed as a chamfer of a cube: the squares are reduced in size and new faces, hexagons, are added in place of all the original edges. The cC is a convex polyhedron with 32 vertices, 48 edges, and 18 faces: 6 congruent (and regular) squares, and 12 congruent flattened hexagons.

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