If the triangular faces are equilateral, the pentagonal bipyramid is an example of deltahedra, composite polyhedron, and Johnson solid.

This polyhedron may be used in the chemical compound as the description of an atom cluster known as pentagonal bipyramidal molecular geometry, as a solution in Thomson problem, as well as in decahedral nanoparticles.

[1] These pyramids cover their pentagonal base, such that the resulting polyhedron has ten triangles as its faces, fifteen edges, and seven vertices.

[2] The pentagonal bipyramid is said to be right if the pyramids are symmetrically regular and both of their apices are on the line passing through the base's center; otherwise, it is oblique.

of order twenty: the appearance is symmetrical by rotating around the axis of symmetry that passing through apices and base's center vertically, and it has mirror symmetry relative to any bisector of the base; it is also symmetrical by reflecting it across a horizontal plane.

It is one of only four four-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.

More generally, the dual polyhedron of every bipyramid is the prism, and the vice versa is true.

[8] If the pyramids are regular, all edges of the triangular bipyramid are equal in length, making up the faces equilateral triangles.

The pentagonal bipyramid with the regular faces is among the numbered Johnson solids as

[10] It is an example of a composite polyhedron because it is constructed by attaching two regular pentagonal pyramids.

[13] The Thomson problem concerns the minimum-energy configuration of charged particles on a sphere.

[14] Pentagonal bipyramids and related five-fold shapes are found in decahedral nanoparticles, which can also be macroscopic in size when they are also called fiveling cyclic twins in mineralogy.