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.
5 w x
5 d x
1.969 w x
1.969 d x