In five-dimensional geometry, a **5-orthoplex**, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.

It has two constructed forms, the first being regular with Schläfli symbol {3^{3},4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol {3,3,3^{1,1}} or Coxeter symbol **2**_{11}.

It is a part of an infinite family of polytopes, called cross-polytopes or *orthoplexes*. The dual polytope is the 5-hypercube or 5-cube.

**pentacross**, derived from combining the family name *cross polytope* with *pente* for five (dimensions) in Greek.
**Triacontaditeron** (or *triacontakaiditeron*) - as a 32-facetted 5-polytope (polyteron).
Cartesian coordinates for the vertices of a 5-orthoplex, centered at the origin are

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

There are three Coxeter groups associated with the 5-orthoplex, one regular, dual of the penteract with the C_{5} or [4,3,3,3] Coxeter group, and a lower symmetry with two copies of *5-cell* facets, alternating, with the D_{5} or [3^{2,1,1}] Coxeter group, and the final one as a dual 5-orthotope, called a **5-fusil** which can have a variety of subsymmetries.

This polytope is one of 31 uniform 5-polytopes generated from the B_{5} Coxeter plane, including the regular 5-cube and 5-orthoplex.