Centering formula for spindle in 12-holes sphere of Spherebot

spherebot_spindle_centering.js

function p2d(a, r) {
    return [
        r * Math.cos(a),
        r * Math.sin(a),
    ];
}

function p_distance(a0, r0, a1, r1) {
    var d0 = p2d(a0, r0);
    var d1 = p2d(a1, r1);
    return Math.sqrt(Math.pow(d0[0] - d1[0], 2) + Math.pow(d0[1] - d1[1], 2));
}

function p_length(p0, p1, p2, pN) {
    var res = 0;
    var a0 = arguments[0][0];
    var r0 = arguments[0][1];
    for (var i = 1; i < arguments.length; i++) {
        var ai = arguments[i][0];
        var ri = arguments[i][1];
        res += p_distance(a0, r0, ai, ri);
    }
    return res;
}

function p_lengths(anchors, holes) {
    var res = [];
    for (var i = 0; i < anchors.length; i++) {
        res[i] = p_length.apply(null, [anchors[i]].concat(holes));
    }
    return res;
}

const SEG = Math.PI / 6;

var anchors = [
    /* 0 */ [0, 0],
    
    /* 1 */ [0*SEG, 1],
    
    /* 2 */ [0*SEG, 2],
    /* 3 */ [1*SEG, 2],
    /* 4 */ [1.5*SEG, 2],
    /* 5 */ [2*SEG, 2],
    /* 6 */ [3*SEG, 2],
    
    /* 7 */ [3*SEG, 1],
];

console.log(p_lengths(anchors, [
    [3*SEG, 4],
    [7*SEG, 4],
    [11*SEG, 4],
]));

console.log(p_lengths(anchors, [
    [0*SEG, 4],
    [3*SEG, 4],
    [6*SEG, 4],
    [9*SEG, 4],
]));

console.log(p_lengths(anchors, [
    [0*SEG, 4],
    [1*SEG, 4],
    [2*SEG, 4],
    [3*SEG, 4],
    [4*SEG, 4],
    [5*SEG, 4],
    [6*SEG, 4],
    [7*SEG, 4],
    [8*SEG, 4],
    [9*SEG, 4],
    [10*SEG, 4],
    [11*SEG, 4],
]));

console.log(p_lengths(anchors, [
    [1*SEG, 4],
    [2*SEG, 4],
    [4*SEG, 4],
    [5*SEG, 4],
    [7*SEG, 4],
    [8*SEG, 4],
    [10*SEG, 4],
    [11*SEG, 4],
]));