In geometry, a regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Regular octahedra occur...

geometry, an octahedron (pl.: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid...

stellated octahedron is constructed by a stellation of the regular octahedron. In other words, it extends to form equilateral triangles on each regular octahedron's...

truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices...

Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can...

(earth, air, water, and fire) with a regular solid. Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire...

convex deltahedra: three of the five Platonic solids (regular tetrahedron, regular octahedron, and regular icosahedron) and five of the 92 Johnson solids (triangular...

outermost: regular octahedron, regular icosahedron, regular dodecahedron, regular tetrahedron, and cube. Many antiquity philosophers described the regular dodecahedron...

of them. The regular icosahedron can also be constructed starting from a regular octahedron. All triangular faces of a regular octahedron are breaking...

triangular gyrobicupola. Its construction can be started from a cube or a regular octahedron, marking the midpoints of their edges, and cutting off all the vertices...

attaching two regular square cupolas into the bases of a regular octagonal prism. A rhombicuboctahedron may also be known as an expanded octahedron or expanded...

triangular faces, connected in the same way as a regular octahedron. Unlike the regular octahedron, the Bricard octahedra are all non-convex self-crossing...

cube and the regular octahedron share the same symmetry, as do the regular dodecahedron and regular icosahedron. Two distinct regular polytopes with the...

but that is not always the case. For instance, the surface of a regular octahedron can be re-folded along different creases into a non-convex polyhedron...

In geometry, a hemi-octahedron is an abstract regular polyhedron, containing half the faces of a regular octahedron. It has 4 triangular faces, 6 edges...

with four meeting at each vertex, to form a spherical octahedron. A spherical lune is a regular digon, with two semicircular sides and two equal angles...

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine...

2-dimensional cross-polytope is a square, a 3-dimensional cross-polytope is a regular octahedron, and a 4-dimensional cross-polytope is a 16-cell. Its facets are simplexes...

and regular octahedron. When projected onto a sphere (see right), it can be seen that the edges make up the edges of a cube and regular octahedron arranged...

repositioned to the vertex positions of the regular icosahedron, the Jessen's icosahedron, and the regular octahedron, in accordance with the pyritohedral symmetry...

also be seen in the corner and mid-edge triangulation of the regular cube and octahedron, and rhombic dodecahedron. The edges of a spherical disdyakis...

versa. The regular polyhedra show this duality as follows: The tetrahedron is self-dual, i.e. it pairs with itself. The cube and octahedron are dual to...

In geometry, a triakis octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated...

equal regular tetrahedra and a regular octahedron. Since parallelepipeds can fill space, so can a combination of regular tetrahedra and regular octahedra...

pentagonal bipyramid are Johnson solids, and the regular octahedron is a Platonic solid. The symmetric regular right bipyramids have prismatic symmetry, with...

partition. For instance, K2,2,2 is the complete tripartite graph of a regular octahedron, which can be partitioned into three independent sets each consisting...

define a regular octahedron, which shares the same face-planes as the compound. Thus the compound of two tetrahedra is a stellation of the octahedron, and...

triangle faces, has the same surface geometry as the regular octahedron, and a paper octahedron model can be re-folded into this shape. This form of the...

are: regular tetrahedron, a pyramid with four equilateral triangles, one of which can be considered the base. triangular bipyramid, regular octahedron, and...

polyhedron, it is known as a regular polyhedron. There are nine regular polyhedra: five Platonic solids (cube, octahedron, icosahedron, tetrahedron, and...