// Construct new tetrahedra
for(int i = 0; i < 2; i++) {
    Node child = new Node();
    child.Vertices = new Vector3[4];
    for(int j = 0; j < 4; j++) {
        if(Lookups.TetrahedronVertexOrder[i, j] == -1) {
            child.Vertices[j] = midpoint;
        }
        else {
            child.Vertices[j] = node.Vertices[Lookups.TetrahedronVertexOrder[i, j]];
        }
    }
    child.Depth = node.Depth + 1;
    node.Children[i] = child;
}


public static readonly int[,] TetrahedronVertexOrder = {
    {1, 2, -1, 3}, // Tetrahedron A (bottom tetrahedron in figure 4 of http://kennyweiss.com/papers/Weiss10.eg_star.pdf)
    {0, 3, -1, 2}, // Tetrahedron B (top tetrahedron in figure 4)
};