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In graph theory, the hypercube graph Q n is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q 3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Q n has 2 n vertices, 2 n – 1 n edges, and is a regular graph with n edges touching each vertex.
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.
A face of a convex polytope P may be defined as the intersection of P and a closed halfspace H such that the boundary of H contains no interior point of P. 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 ...
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.
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.
There is no fullerene with = but these graphs are realizable for any other value of ; [4] see for instance, the 26-fullerene graph, with =. A hexagon bisects the cube into two copies of a simple polyhedron with one hexagonal face, three isosceles right triangle faces, and three irregular pentagonal faces.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. [1] In a polygon, an edge is a line segment on the boundary, [2] and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides ...
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.