72cell

The 72-cell is a uniform 4-dimensional polytope, also known as a 4-orthoplex or 4-cube. It is one of the six convex regular 4-polytopes, and can be constructed by projecting a 5-cell (4-simplex) orthogonally onto a hyperplane. The 72-cell has 72 faces, each of which is an octahedron. It has 36 edges and 12 vertices. The 72-cell is self-dual, meaning that its dual polytope is isomorphic to itself. It is also a member of the family of hypercube-related polytopes, which includes the 5-cell, 16-cell, 24-cell, 120-cell, and 600-cell. The 72-cell can be visualized using various techniques, such as parallel projection or stereographic projection, to represent its 4-dimensional structure in 3-dimensional space.