Cospherical points

Remarks

This is the form of Mathlib's EuclideanGeometry.Cospherical. In the Euclidean plane, cospherical points are the same as concyclic points. In $\R^n$, any $n + 1$ affinely independent points are cospherical, and their sphere is the circumsphere of the simplex they span.

Example: the eight vertices $(\pm 1, \pm 1, \pm 1)$ of a cube in $\R^3$ are cospherical. Each lies at distance $\sqrt 3$ from $c = (0, 0, 0)$.

Non-example: the points $(0, 0)$, $(1, 0)$, $(2, 0)$ of $\R^2$ are not cospherical. A point equidistant from the first two has $x$-coordinate $1/2$, and a point equidistant from the last two has $x$-coordinate $3/2$, so no centre exists.