TITLE: What is the name of this 3D shape with 12 outer vertices?
QUESTION [18 upvotes]: Faces: 48
Outside vertices: 12
Other vertices: 14 (I believe)

REPLY [28 votes]: The object is the first stellation of the rhombic dodecahedron.

This is sometimes known as Escher's solid, for its use in a study for his Stars, though the final picture uses a compound of three regular octahedra rather than the squashed ones of this question's solid.