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In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces. It is represented by Schläfli symbol {4,3,3,3} or {4,3 3 }, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge .
It has the same number of vertices and edges as the cube, twelve vertices and eight edges. [ 29 ] The cubical graph is a special case of hypercube graph or n {\displaystyle n} - cube—denoted as Q n {\displaystyle Q_{n}} —because it can be constructed by using the operation known as the Cartesian product of graphs .
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.
The edge-first parallel projection of the tesseract into three-dimensional space has an envelope in the shape of a hexagonal prism. Six cells project onto rhombic prisms, which are laid out in the hexagonal prism in a way analogous to how the faces of the 3D cube project onto six rhombs in a hexagonal envelope under vertex-first projection.
Infinite number of uniform tilings in ... The regular hexahedron is a cube. Table of polyhedra ... 5 / 3 (3) 5 / 2 have some faces occurring as ...
regular 5-polytope 5-dimensional cross-polytope; 5-dimensional hypercube; 5-dimensional simplex; Five-dimensional space, 5-polytope and uniform 5-polytope. 5-simplex, Rectified 5-simplex, Truncated 5-simplex, Cantellated 5-simplex, Runcinated 5-simplex, Stericated 5-simplex; 5-demicube, Truncated 5-demicube, Cantellated 5-demicube, Runcinated 5 ...
The number of vertices of a hypercube of dimension is (a usual, -dimensional cube has = vertices, for instance). [ 5 ] The number of the m {\displaystyle m} -dimensional hypercubes (just referred to as m {\displaystyle m} -cubes from here on) contained in the boundary of an n {\displaystyle n} -cube is
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.