In geometry, a **7-cube** is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces.

It can be named by its Schläfli symbol {4,3^{5}}, being composed of 3 6-cubes around each 5-face. It can be called a **hepteract**, a portmanteau of tesseract (the *4-cube*) and *hepta* for seven (dimensions) in Greek. It can also be called a regular **tetradeca-7-tope** or **tetradecaexon**, being a 7 dimensional polytope constructed from 14 regular facets.

It is a part of an infinite family of polytopes, called hypercubes. The dual of a 7-cube is called a 7-orthoplex, and is a part of the infinite family of cross-polytopes.

Applying an *alternation* operation, deleting alternating vertices of the hepteract, creates another uniform polytope, called a demihepteract, (part of an infinite family called demihypercubes), which has 14 demihexeractic and 64 6-simplex 6-faces.

Cartesian coordinates for the vertices of a hepteract centered at the origin and edge length 2 are

(±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}) with -1 < x_{i} < 1.

Hepteract 7D simple rotation through 2Pi with 7D perspective projection to 3D.