Editing Tesseract (section)

=== Radial equilateral symmetry ===
The radius of a [[hypersphere]] circumscribed about a regular polytope is the distance from the polytope's center to one of the vertices, and for the tesseract this radius is equal to its edge length; the diameter of the sphere, the length of the diagonal between opposite vertices of the tesseract, is twice the edge length. Only a few uniform [[polytopes]] have this property, including the four-dimensional tesseract and [[24-cell#Radially equilateral honeycomb|24-cell]], the three-dimensional [[Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[hexagon]]. In particular, the tesseract is the only hypercube (other than a zero-dimensional point) that is ''radially equilateral''. The longest vertex-to-vertex diagonal of an <math>n</math>-dimensional hypercube of unit edge length is <math>\sqrt{n\vphantom{t}},</math> which for the square is <math>\sqrt2,</math> for the cube is <math>\sqrt3,</math> and only for the tesseract is <math>\sqrt4 = 2</math> edge lengths.

An axis-aligned tesseract inscribed in a unit-radius 3-sphere has vertices with coordinates <math>\bigl({\pm\tfrac12}, \pm\tfrac12, \pm\tfrac12, \pm\tfrac12\bigr).</math>