Pentagonal bipyramid
| Pentagonal bipyramid | |
|---|---|
A pentagonal bipyramid with two identical right pyramids attached base-to-base | |
| Type | Bipyramid, Deltahedra Johnson J12 – J13 – J14 Simplicial |
| Faces | 10 triangles |
| Edges | 15 |
| Vertices | 7 |
| Vertex configuration | |
| Symmetry group | |
| Dihedral angle (degrees) | As a Johnson solid:
|
| Dual polyhedron | pentagonal prism |
| Properties | convex, composite (as a Johnson solid), face-transitive |
A pentagonal bipyramid or pentagonal dipyramid is a polyhedron with ten triangular faces. It is constructed by attaching two pentagonal pyramids to each of their bases. If the triangular faces are equilateral, the pentagonal bipyramid is an example of deltahedra, composite polyhedron, and Johnson solid. Regardless of any type of its triangular faces, the pentagonal bipyramid is a simplicial polyhedron like any other bipyramid.
The vertices and edges of a pentagonal bipyramid can give rise to a graph. It is one of the four four-connected simplicial well-covered graphs. It is also one of the six connected graphs in which its neighborhood of every vertex is a cycle of length four or five. Within this structure, the graph forms a topological surface called a Whitney triangulation.
The pentagonal bipyramid has applications in many fields. In chemistry, the pentagonal bipyramidal molecular geometry is a description of an atom cluster resembling a pentagonal bipyramid. In mathematical optimization, the pentagonal bipyramid is a solution for Thomson problem. In mineralogy, it can also be found in decahedral nanoparticles.