Pentakis dodecahedron

In geometry, a pentakis dodecahedron or kisdodecahedron is a dodecahedron with a pentagonal pyramid covering each face; that is, it is the Kleetope of the dodecahedron. This interpretation is expressed in its name.^[1] There are in fact several topologically equivalent but geometrically distinct kinds of pentakis dodecahedron, depending on the height of the pentagonal pyramids. These include:

• The usual Catalan pentakis dodecahedron, a convex hexecontahedron with sixty isosceles triangular faces illustrated in the sidebar figure. It is a Catalan solid, dual to the truncated icosahedron, an Archimedean solid.
• As the heights of the pentagonal pyramids are raised, at a certain point adjoining pairs of triangular faces merge to become rhombi, and the shape becomes a rhombic triacontahedron.
• As the height is raised further, the shape becomes non-convex. In particular, an equilateral or deltahedron version of the pentakis dodecahedron, which has sixty equilateral triangular faces as shown in the adjoining figure, is slightly non-convex due to its taller pyramids (note, for example, the negative dihedral angle at the upper left of the figure).

https://en.wikipedia.org/wiki/Pentakis_dodecahedron