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In five-dimensional geometry, a 5-cube (or penteract) is 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}, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge.
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}.It is also known as the C600, hexacosichoron, hexacosihedroid and hypericosahedron.It is also called a tetraplex (abbreviated from "tetrahedral complex") and a polytetrahedron, being bounded by tetrahedral cells.
The 600-cell's boundary is composed of 600 tetrahedral cells with 20 meeting at each vertex.Together they form 1200 triangular faces, 720 edges, and 120 vertices.It is the 4-dimensional analogue of the icosahedron, since it has five tetrahedra meeting at every edge, just as the icosahedron has five triangles meeting at every vertex.Its dual polytope is the 120-cell.
View the full Wikipedia page for 600-cellIn geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss mathematician Ludwig Schläfli before 1853.
The two-dimensional analogue of a 4-polytope is a polygon, and the three-dimensional analogue is a polyhedron.
View the full Wikipedia page for 4-polytope