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  2. 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 ...

  3. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry.

  4. Cuboctahedron - Wikipedia

    en.wikipedia.org/wiki/Cuboctahedron

    A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square.

  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. 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 ...

  7. Edge (geometry) - Wikipedia

    en.wikipedia.org/wiki/Edge_(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 edges is 2 less than the sum of the numbers of vertices and faces. For example, a cube has 8 vertices and 6 faces, and hence 12 edges.

  8. List of Johnson solids - Wikipedia

    en.wikipedia.org/wiki/List_of_Johnson_solids

    None of its faces are coplanar—they do not share the same plane and do not "lie flat". None of its edges are colinear—they are not segments of the same line. A convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors exclude uniform polyhedra from the definition.

  9. Archimedean solid - Wikipedia

    en.wikipedia.org/wiki/Archimedean_solid

    An example is the rhombicuboctahedron, constructed by separating the cube or octahedron's faces from the centroid and filling them with squares. [8] Snub is a construction process of polyhedra by separating the polyhedron faces, twisting their faces in certain angles, and filling them up with equilateral triangles.