The Borromean Tribar

This form belongs to the family of impossible figures, more specifically to the Penrose triangle, or tribar.

At first glance, it looks entirely manufacturable. The structure appears to be made from three identical square rings (fig. 1), each pierced by a circular opening and arranged in three mutually perpendicular planes (fig. 2). Together, they seem to interlock seamlessly, forming an impossible three-dimensional tribar, that evokes a trefoil knot and its endless over-under weaving.

If this sculpture looks physically realizable to you, congratulations: your visual system has just accepted a geometric impossibility.

the making of the borromean tribar

Could such an object be built? Not exactly. One solution would be to twist one of the junctions slightly, but that trick would be immediately noticeable here because some of the angles would no longer appear perfectly square (90°), as shown in the picture below. Another possibility would be to leave a small gap at one junction and view the sculpture from a carefully chosen angle, allowing perspective to hide the discontinuity.

This is how a real 3D Borromean Tribar would appear