I downloaded from somewhere-or-other a doctoral thesis (2006) by a Paul Leopardi at UNSW which gives a method for dividing any N-sphere into sectors of equal area (and reasonable compactness) by lines of latitude and longitude. I haven’t finished looking through it but I suspect that its approach can be adapted to suggest a generalization of the spiral method to N dimensions.

for 0 ≤ j < N :
x[j] = (width/N) * (0.5 + (j*P)%N)
y[j] = (height/N) * (0.5 + (j*Q)%N)

function p = spherepointsgolden(n)
%SPHEREPOINTSGOLDEN Place points evently on a unit sphere
% Generate a set of evenly distributed points on a unit sphere
% using the method of the Golden Section Spiral method.
%
% Output is a 3xN matrix of points for X,Y,Z.
%
% Based on python code from Patric Boucher on http://www.xsi-blog.com

inc = pi * (3-sqrt(5));
off = 2/n;

k = 0:n-1;
y = k * off – 1 + (off/2);
r = sqrt(1 – (y.^2));
phi = k * inc;

p = [cos(phi).*r; y ;sin(phi).*r]‘;
end