A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson
solid 
),
bislit cube, Dürer
solid, elongated gyrobifastigium,
gyrobifastigium (Johnson
solid 
),
heptagonal pyramid, hexagonal
prism, regular octahedron, square
dipyramid, triangular cupola (Johnson
solid 
),
tridiminished icosahedron (Johnson
solid 
),
tritetrahedron, and truncated
tetrahedron.
There are 257 convex octahedra, corresponding to the duals of the octahedral graphs. The convex octahedra consisting of regular polygonal faces of equal edge
lengths are summarized in the following table. They all have 
, as required by the polyhedral
formula.
| polyhedron | degree sequence |  |  |
| truncated tetrahedron | 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 | 12 | 18 |
| heptagonal pyramid | 3, 3, 3, 3, 3, 3, 3, 7 | 8 | 14 |
| triangular cupola | 3, 3, 3, 3, 3, 3, 4, 4, 4 | 9 | 15 |
| tridiminished icosahedron | 3, 3, 3, 3, 3, 3, 4, 4, 4 | 9 | 15 |
| gyrobifastigium | 3, 3, 3, 3, 4, 4, 4, 4 | 8 | 14 |
| augmented triangular prism | 3, 3, 4, 4, 4, 4, 4 | 7 | 13 |
| octahedron | 4, 4, 4, 4, 4, 4 | 6 | 12 |
The regular octahedron, often simply called "the" octahedron, is the Platonic solid 
with six polyhedron
vertices, 12 polyhedron edges, and eight equivalent
equilateral triangular faces, denoted 
. It is also uniform
polyhedron 
and Wenninger model 
.
It is given by the Schläfli symbol 
and Wythoff
symbol 
.
The octahedron of unit side length is the antiprism
of 
sides with height 
. The octahedron is also a square
dipyramid with equal edge lengths.
