A 3D projection of the 8-cell (Hypercube), one of the 6 regular polytopes in four dimensions.
4D Polytopes (or polychora) are the 4-dimensional analogous of the 2D polygons and 3D polyhedra.
Regular polychora are composed of a finite set of cells (polyhedra), all regular and alike, surrounding each edge in an identical way.
We cannot see a 4D polytope, but we can project it in 3D (in the same way as we make a flat drawing of a polyhedron).
The 8-cell is composed of 8 cubes.
This is a parallel projection of the polytope, in which no edges intersect each other, but some cells do (for example the two regular cubes). The edges are all the same length.
2.666 w x
2.666 d x
1.05 w x
1.05 d x