Trivariate standard normal

A rare visual of a trivariate standard normal distribution is created below, simulated from a sample size of 300.  All three variables (e.g., x, y, z) are, of course, jointly independent of one another.  It can be shown that the marginal distribution through this shape has a bivariate Gaussian distribution on its plane.

Note that a quadvariate version is possible, though more complicated than simply the shape below, passing through an animated display through time.