Let us deign three perpendicular tubes as shown below left.
An immediate reaction is that let us subtract a smaller cylinder from a larger one giving a tube, which is shown in below right. Then, take two more instances of this tube, each of them is rotated an appropriate angle, compute the union of these three tubes, and the result is shown in the following figure.
But, the result is not quite right, because the inner junction of the tubes are blocked as see in the right figure above. A correct solution is design two instances of three perpendicular cylinders, one larger and the other smaller. Then, subtracting the smaller from the larger yields the designed result as shown below.
