In five-dimensional geometry, a **5-cube** is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.

It is represented by Schläfli symbol {4,3,3,3} or {4,3^{3}}, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge. It can be called a **penteract**, a portmanteau of tesseract (the *4-cube*) and *pente* for five (dimensions) in Greek. It can also be called a regular **deca-5-tope** or **decateron**, being a 5-dimensional polytope constructed from 10 regular facets.

It is a part of an infinite hypercube family. The dual of a 5-cube is the 5-orthoplex, of the infinite family of orthoplexes.

Applying an *alternation* operation, deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the demihypercubes.

The 5-cube can be seen as an *order-3 tesseractic honeycomb* on a 4-sphere. It is related to the Euclidean 4-space (order-4) tesseractic honeycomb and paracompact hyperbolic honeycomb order-5 tesseractic honeycomb.

The Cartesian coordinates of the vertices of a 5-cube centered at the origin and having edge length 2 are

(±1,±1,±1,±1,±1),

while this 5-cube's interior consists of all points (*x*_{0}, *x*_{1}, *x*_{2}, *x*_{3}, *x*_{4}) with -1 < *x*_{i} < 1 for all *i*.

*n*-cube Coxeter plane projections in the B_{k} Coxeter groups project into k-cube graphs, with power of two vertices overlapping in the projective graphs.

This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.