About
In geometry, the 5-cell (sometimes known as a Pentachoron, or a 4-simplex) is a four-dimensional object bounded by 5 tetrahedral cells. It is also a tetrahedral hyperpyramid. It is a 4-simplex, the simplest possible convex regular 4-polytope (four-dimensional analogue of a polyhedron), the 5-cell is also analogous to the tetrahedron in three dimensions and the triangle in two dimensions. It has 5 vertices, 10 edges, 10 faces, and 5 cells, making it self-dual.
Formula
- Hypervolume: (sqrt(5))/96 x a4
- Surface Volume: (5sqrt(2))/12 x a3
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