Chamfered cube geometry generator

I'm trying to create a geometry generator for a "Chamfered Cube". I've got the vertices working, but I'm stuck with creating the faces. I don't really know how I could re-arrange my algorithm to create the vertices in the right order for a triangle list / strip / fan / whatever.

This is what I've done so far: starting from the 8 vertices of a normal cube, I "push" out vertices in the shape of an eight of a sphere:

//start 0,0,0
var width = 8;
var radius = 3; 
var segments = 16;

var half = width / 2;
var segmentStepSize = Math.PI / 2 / segments;

//displacement
var w = Math.sqrt(Math.pow((half-radius),2)*2);

// the 8 original vertex vectors
var startPoints = [
    [ 1,  1,  1],
    [ 1,  1, -1],
    [ 1, -1,  1],
    [ 1, -1, -1],
    [-1,  1,  1],
    [-1,  1, -1],
    [-1, -1,  1],
    [-1, -1, -1]
]

var x, y, z, v, x1, y1, z1, j, k;

var points = [];

for(var i = 0; i < 8; i++) {
    v = startPoints[i];
    x = w * v[0];
    y = w * v[1];
    z = w * v[2];

    for(j = 0; j < segments +1; j++) { 

        for(k = 0; k < segments+1; k++) {

            x1 = x + radius * Math.cos(k*segmentStepSize) * Math.sin(j*segmentStepSize) * v[0];
            y1 = y + radius * Math.sin(k*segmentStepSize) * Math.sin(j*segmentStepSize) * v[1];
            z1 = z + radius * Math.cos(j*segmentStepSize) * v[2];
            points.push(x1);
            points.push(y1);
            points.push(z1);

        }
    }
}

module.exports = points;

This code results in this: http://requirebin.com/?gist=fdea95e3bfe069d7f363

Edit

for anyone who's interested: I've shared the code here: https://github.com/ToastCommunicationLab/mesh-primitive-chamfercube