In geometry, a regular octahedron is a highly symmetrical type of octahedron (eight-sided polyhedron) with eight equilateral triangles as its faces, four of which meet at each vertex. It is a type of square bipyramid or triangular antiprism with equal-length edges. Regular octahedra occur in nature as crystal structures. Other types of octahedra also exist, with various amounts of symmetry.
A regular octahedron is the three-dimensional case of the more general concept of a cross-polytope.
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra: a tetrahedron (four faces), a cube (six faces), an octahedron (eight faces), a dodecahedron (twelve faces), and an icosahedron (twenty faces).
Geometers have studied the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato, who hypothesized in one of his dialogues, the Timaeus, that the classical elements were made of these regular solids.
In geometry, an octahedron (pl.: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Many types of irregular octahedra also exist, including both convex and non-convex shapes.
A deltahedron is a polyhedron whose faces are all equilateral triangles. The deltahedron was named by Martyn Cundy, after the Greek capital letter delta resembling a triangular shape Ξ.
Deltahedra can be categorized by the property of convexity. The simplest convex deltahedron is the regular tetrahedron, a pyramid with four equilateral triangles. There are eight convex deltahedra, which can be used in the applications of chemistry as in the polyhedral skeletal electron pair theory and chemical compounds. There are infinitely many concave deltahedra.