http://teamikaria.com/wiki/Icositetrachoron
I've noticed a few flaws on this page.
A pyramid is self-dual iff it's base is self dual. (the page doesn't specify which type of polytopes are self-dual)
Also the "Hexadecachoron" can tesselate (this tesselation is the dual to the Icositetrachoron tesselation)
And the "hypercube tesselation is self-dual
In terms of 3D equivelants it can have a few more than the ones mentioned:
cube (three ortheplexes round a peak)(square is also 2-ortheplex)
augmented cube (the shape can be made by augmenting a tesseract)