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  2. Cuboid - Wikipedia

    en.wikipedia.org/wiki/Cuboid

    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. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles. [1] [3] Along with the rectangular cuboids ...

  3. 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 ...

  4. Polyhedral combinatorics - Wikipedia

    en.wikipedia.org/wiki/Polyhedral_combinatorics

    The dimension of a face is the dimension of this hull. The 0-dimensional faces are the vertices themselves, and the 1-dimensional faces (called edges) are line segments connecting pairs of vertices. Note that this definition also includes as faces the empty set and the whole polytope P.

  5. Rectangular cuboid - Wikipedia

    en.wikipedia.org/wiki/Rectangular_cuboid

    A rectangular cuboid is a convex polyhedron with six rectangle faces. These are often called "cuboids", without qualifying them as being rectangular, but a cuboid can also refer to a more general class of polyhedra, with six quadrilateral faces. [1] The dihedral angles of a rectangular cuboid are all right angles, and its opposite faces are ...

  6. Conway polyhedron notation - Wikipedia

    en.wikipedia.org/wiki/Conway_polyhedron_notation

    Meta adds vertices at the center and along the edges, while bevel adds faces at the center, seed vertices, and along the edges. The index is how many vertices or faces are added along the edges. Meta (in its non-indexed form) is also called cantitruncation or omnitruncation. Note that 0 here does not mean the same as for augmentation operations ...

  7. Euler characteristic - Wikipedia

    en.wikipedia.org/wiki/Euler_characteristic

    Vertex, edge and face of a cube. The Euler characteristic χ was classically defined for the surfaces of polyhedra, according to the formula = + where V, E, and F are respectively the numbers of vertices (corners), edges and faces in the given polyhedron.

  8. 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.

  9. Cube - Wikipedia

    en.wikipedia.org/wiki/Cube

    Like other cuboids, every face of a cube has four vertices, each of which connects with three congruent lines. These edges form square faces, making the dihedral angle of a cube between every two adjacent squares being the interior angle of a square, 90°. Hence, the cube has six faces, twelve edges, and eight vertices.

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