hexeracts

A hexeract is the four-dimensional analogue of a cube. Just as a cube is formed by connecting the vertices of two squares, a hexeract is formed by connecting the vertices of two cubes. It is a regular polychoron, meaning it is a four-dimensional solid with congruent, regular, and identically oriented faces. The hexeract has 16 vertices, 32 edges, 24 square faces, and 8 cubic cells. It is also known as an 8-cell or a cubic prism.

Visualizing a hexeract is challenging for humans, as our perception is limited to three dimensions. We can understand it through analogies and projections. For instance, a cube can be projected into 2D as a square with its vertices connected to a smaller, similar square, with corresponding vertices linked. Similarly, a hexeract can be projected into 3D, often appearing as a larger cube containing a smaller, concentric cube, with their vertices connected. This projection, however, is a distorted representation of its true four-dimensional form.

The term "hexeract" is derived from the Greek word "hepta," meaning seven, and "hēkton," meaning "sixth." This naming convention is part of a system for higher-dimensional polytopes, where prefixes indicate the number of dimensions. While the name might suggest a connection to seven dimensions, it specifically refers to the eight bounding cells (cubes) that define its structure. The hexeract is a fundamental object in the study of geometry and is used in various theoretical fields.