The other three polyhedra with this property are the pentagonal dipyramid, the snub disphenoid, and an irregular polyhedron with 12 vertices and 20 triangular faces. 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 octahedron is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices. If the edge length of a regular octahedron is a, the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is It is also a triangular antiprism in any of four orientations.Īn octahedron is the three-dimensional case of the more general concept of a cross polytope.Ī regular octahedron is a 3-ball in the Manhattan ( ℓ 1) metric. It is a square bipyramid in any of three orthogonal orientations. Each of the faces of the octahedron meets three other faces. These figures have the shape of a double square pyramid. An octahedron has 8 triangular faces, 12 edges, and 6 vertices. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.Ī regular octahedron is the dual polyhedron of a cube. The octahedron is a Platonic solid, which has all its faces with a triangular shape. ![]() ![]() In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces.
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