There are six regular convex polytopes in 4D, which are analogous to
the five Platonic solids in 3D. This one is the odd polytope out, the one without a 3D counterpart.
It has 24 octahedral cells, all shown in this Schlegel diagram. Like the pentachoron it's self-dual -- the only self-dual solid in any dimension > 2 that is not a simplex. And if that wasn't enough, it's also the only regular convex polytope in any dimension > 2 that tiles its space and is not a hypercube.
It has 24 octahedral cells, all shown in this Schlegel diagram. Like the pentachoron it's self-dual -- the only self-dual solid in any dimension > 2 that is not a simplex. And if that wasn't enough, it's also the only regular convex polytope in any dimension > 2 that tiles its space and is not a hypercube.
cm:
5.482 w x
5.486 d x
5.484 h
in:
2.158 w x
2.16 d x
2.159 h
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