What I call a 543 model is correctly called a rhombicosidodecahedron. It is often abbreviated as RID.
As prior to thinking about this I had taught the students of Vigyan Ashram how to build a big lantern based on only squares and equilateral triangles, it was logical to call this shape based on pentagons, squares and equilateral triangles as 543 reflecting the number of sides of the shapes inside it. The previous shape is then called 43. Here are two pictures.