Regular octahedron
In geometry, a regular octahedron is an eight-sided polyhedron with equilateral triangles as its faces. Known for its highly symmetrical form, the regular octahedron is a Platonic solid, and more generally, a regular polyhedron. If the faces are isosceles triangles, the regular octahedron becomes a square bipyramid. The regular octahedron is an example of many classifications as deltahedron and simplicial polyhedron.
Regular octahedra occur in nature and science, such as the crystal structures and in stereochemistry as a resemblance of a chemical molecule known as octahedral molecular geometry. Other appearances are in popular culture and music theory. It can be the core of polyhedra construction, and it can tile with different polyhedra to create a honeycomb.
The vertices and edges of a regular octahedron give rise to a graph, a discrete structure drawn in a plane. The name is octahedral graph. The octahedral graph is an example of a four-connected simplicial well-covered graph. It is also one of the six connected graphs in which the 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.