Tesseract

The tesseract, or tes, also sometimes called the 8-cell or octachoron, is one of the 6 convex regular polychora. It has 8 cubes as cells, joining 3 to an edge and 4 to a vertex. It is the 4-dimensional hypercube and also the 4-4 duoprism, 2-2 duoantitegum and the 8-3 gyrochoron.

The tesseract is the first in a series of tetrahedral swirlchora (the second is a polychoron with 16 identical chiral truncated triangular prisms and the third is the icositetrachoron).

It is one of the three regular polychora that can tile 4D space, similar to hypercubes of any other dimension.

The tesseract has the same circumradius as its edge length.

Vertex coordinates
The vertices of a tesseract of edge length 1, centered at the origin, are given by:
 * (±1/2, ±1/2, ±1/2, ±1/2).