The shape is essentially a dodecahedron with a five-sided pointy pyramid on top of each face. There are 10 groups each consisting of 5 triangles which are coplanar.
Mathematically however, it is actually composed of twelve intersecting pentagrammic faces. At each outer vertex five faces meet. The inner vertices are not true vertices at all in the sense that they are points where edges end and meet.
Top view of the great stellated dodecahedron along 5-fold symmetry axis:
Top view of the great stellated dodecahedron along 3-fold symmetry axis: