Pentachoron (5-Cell)

There are six regular convex polytopes in 4D, which are analogous to the five Platonic solids in 3D. This is the first, the pentachoron or hyperpyramid, in a vertex-first projection. It has 5 tetrahedral cells, and like the tetrahedron is its own dual.

In every dimension there's one polytope like this: all triangles, self-dual, analogous to the tetrahedron. As a group they're called simplexes, so this is the 4-simplex.