See link above. It is recomended reading, as it explains a lot of the results below. Thus all edges are equal in length and face corners equal in angle. Duals are also all Plationic Solids. All faces are regular polygons but not of same shape.
All edges are equal in length.
The cuboctahedron if produced if the truncation of the cube and octahedron continues in sequence. Simularly for the icosi-dodecahedron for the dodecahedron and icosahedron. The snub cube has a left and right-handed version Truncation is the term commonly used but as true truncation can produce rectangular edges, the correct term is rombic, where the rectanges are modified to more regular squares. Pyramids becom very pointy. A quad-dipyramid is an octahedron.