Simplex
Triangles and Tetrahedra Taken to the Nth Dimension
The last one you can see
An \(N\)-Simplex lives in \(n\)-dimensional space. It is made of \(N+1\) vertices, each pair the same distance apart.
Imagine a hypersphere of plastic encasing all of the points. If you shrunk it down and pulled it taut, the result would be an \(N\)-simplex.
The vertices are 0-simplexes. The edges are 1-simplexes. The faces are 2-simplexes. There isn't a common word for higher dimensional faces, so we call them 3-faces, 4-faces, etc.
Five Ancient Shapes