Illusory Geometry with Dice

Forced perspective is employed to craft a well-known object: the ‘tribar.’ Emerging from an “impossible catalog,” this object takes the form of a triangular structure, with square-section bars seamlessly joining at right angles. Constructing a tribar within three-dimensional space is an illusion; in Euclidean geometry, the sum of triangle angles always equals a flat angle.

Efforts to fashion a solid object resembling the tribar have met varying degrees of success. In this instance, our construction incorporates a deliberate ‘interruption’ that, when observed from a specific angle, creates the illusion of a complete triangle.

Consider fourteen dice. Sacrifice one by cutting to detach two faces (fig. a). Adjoin the remaining dice by gluing them together (fig. b), and affix the two faces of the truncated die onto the vertical stack of dice, as shown in fig. c.

© G. Sarcone – from the book Optical Illusions.

Finally, by situating yourself with a camera directed towards the model and from a favorable vantage point, visually meld the two faces of the foreground die with the alignment of the background dice. With some patience, exceptional outcomes can be achieved!

© G. Sarcone – from the book Optical Illusions.