Chalice: Concave Girih Polyhedra with Decagons and Pentagons

These girih polyhedra have 32 faces. They include 2 decagon and 10 pentagon faces, as well as triangles. The decagon and pentagon are decorated with the girih tile pattern. A similar pattern continues across the triangles. The triangles are equilateral.

These polyhedra are related to an icosidodecahedron and pentagonal orthobirotunda. You can split an icosidodecahedron in half (making two pentagonal rotunda) and reattached the halves at pentagons to create the chalice.

Chalice Wireframe Girih Pattern