Red: edges of dodecahedron
Green: edges of icosahedron
Blue: edges of rhombic triacontahedron
32 vertices, 60 edges (all the same length), 30 rhombic faces.
The center of each rhombic face is the intersection point of
the edges of a dodecahedron and icosahedron. (See red and green line
intersections). Alternatively, the
edges of the dodecahedron and icosahedron form
the diagonals of the rhombic faces.
The ratio of the long diagonal of the rhombic faces to the
short diagonal is the golden ratio, (1 + sqrt(5)) / 2. (Ratio
of the length of the green lines to red lines)
The vertices are at two distances from the center, the
vertices with three connected edges are at one distance and
the vertices with 5 connecting edges are at a greater distance.