# Generating the vertices and edges of an n-cube in javascript

An n-cube is a geometric shape analogous to a cube, but in an arbitrary number of dimensions.

The algorithm I’ve laid out does a recursive routine for finding the vertices and then looks for all edges within one unit of each to define the edges.

The function becomes non-response with values over 14. This is because the number of points in an n-cube is given by 2n and the number of edges is n2n-1. So the expected memory usage of this function is O(2n), which is going to blow up with any fairly large value.

``````var nCube = function(n) {

if (n == 1) {
return {
"points" :[, ],
"edges" : [[0, 1]]
};
} else {
var L, i, j, prev = nCube(n - 1), out = {
"dimensions" : n,
"points" : [],
"edges" : []
};

for (i = 0; i < prev.points.length; i++) {
for (j = 0; j < 2; j++) {
(function() {
var fit = prev.points[i].slice();
fit.push(j);
out.points.push(fit);

})();
}
}
// surely there is a faster recursive method of defining edges, but...
for (i = 0; i < out.points.length; i++) {
for (j = i; j < out.points.length; j++) {
if (i == j) continue;
if (distance(out.points[i], out.points[j]) == 1) {
out.edges.push([i,j]);
}
}
}

return out;
}
};

``````