rhombicuboctahedron
The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. (Note that six of the squares only share vertices with the triangles while the other twelve share an edge.)
The Schlegel diagram of a rhombicuboctahedron gives a clear view on the configuration of the verticles and edges.