Pentagonal Bipyramid

In geometry, the pentagonal bipyramid (or dipyramid) is third of the infinite set of face-transitive bipyramids.

Each bipyramid is the dual of a uniform prism.

If the faces are equilateral triangles, it is a deltahedron and a Johnson solid (J₁₃). It can be seen as two pentagonal pyramids (J₂) connected by their bases.

Although it is face-transitive, it is not a Platonic solid because some vertices have four faces meeting and others have five faces.

The pentagonal dipyramid is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices. It is one of only four 4-connected simplicial well-covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size. The other three polyhedra with this property are the regular octahedron, the snub disphenoid, and an irregular polyhedron with 12 vertices and 20 triangular faces.