In geometry, an **8-orthoplex** or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells *4-faces*, 1792 *5-faces*, 1024 *6-faces*, and 256 *7-faces*.

It has two constructive forms, the first being regular with Schläfli symbol {3^{6},4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol {3,3,3,3,3,3^{1,1}} or Coxeter symbol **5**_{11}.

It is a part of an infinite family of polytopes, called cross-polytopes or *orthoplexes*. The dual polytope is an 8-hypercube, or octeract.

**Octacross**, derived from combining the family name *cross polytope* with *oct* for eight (dimensions) in Greek
**Diacosipentacontahexazetton** as a 256-facetted 8-polytope (polyzetton)
There are two Coxeter groups associated with the 8-cube, one regular, dual of the octeract with the C_{8} or [4,3,3,3,3,3,3] symmetry group, and a half symmetry with two copies of 7-simplex facets, alternating, with the D_{8} or [3^{5,1,1}] symmetry group.A lowest symmetry construction is based on a dual of an 8-orthotope, called an **8-fusil**.

Cartesian coordinates for the vertices of an 8-cube, centered at the origin are

(±1,0,0,0,0,0,0,0), (0,±1,0,0,0,0,0,0), (0,0,±1,0,0,0,0,0), (0,0,0,±1,0,0,0,0),
(0,0,0,0,±1,0,0,0), (0,0,0,0,0,±1,0,0), (0,0,0,0,0,0,0,±1), (0,0,0,0,0,0,0,±1)

Every vertex pair is connected by an edge, except opposites.

It is used in its alternated form **5**_{11} with the 8-simplex to form the **5**_{21} honeycomb.