The list of points in Euclidean 4-House having a similar distance R from a set level P0 sorts a hypersurface called a three-sphere. The hyper-volume from the enclosed Room is:
Lagrange wrote in his Mécanique https://hamzasfaf240746.ltfblog.com/29137727/the-smart-trick-of-tahta-4d-that-nobody-is-discussing