In geometry, a **9-cube** is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces.

It can be named by its Schläfli symbol {4,3^{7}}, being composed of three 8-cubes around each 7-face. It is also called an **enneract**, a portmanteau of tesseract (the *4-cube*) and *enne* for nine (dimensions) in Greek. It can also be called a regular **octadeca-9-tope** or **octadecayotton**, as a nine-dimensional polytope constructed with 18 regular facets.

It is a part of an infinite family of polytopes, called hypercubes. The dual of a 9-cube can be called a 9-orthoplex, and is a part of the infinite family of cross-polytopes.

Cartesian coordinates for the vertices of a 9-cube centered at the origin and edge length 2 are

(±1,±1,±1,±1,±1,±1,±1,±1,±1)

while the interior of the same consists of all points (*x*_{0}, *x*_{1}, *x*_{2}, *x*_{3}, *x*_{4}, *x*_{5}, *x*_{6}, *x*_{7}, *x*_{8}) with −1 < *x*_{i} < 1.

Applying an *alternation* operation, deleting alternating vertices of the *9-cube*, creates another uniform polytope, called a *9-demicube*, (part of an infinite family called demihypercubes), which has 18 8-demicube and 256 8-simplex facets.