Nested Penrose Triangles

This is an illusory geometric structure that cannot exist in our 3D world. Let’s Explore its captivating depths and intrigue.

Here’s how to create this impossible structure. Start by drawing two parallel lines spaced apart from each other and divide them into 7 equally spaced lines.

Then follow the visual steps A, B, C, and D illustrated below. At the beginning (fig. A), you will need to replicate the alignment of the 9 parallel lines three times while applying a 60-degree rotation to each one, finally arranging them to form a triangle. Subsequently, follow the visual directions in B and C to obtain the figure shown in fig. D.

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At last, you can add color and gradients to the structure as illustrated below.

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Discover prints and merchandise featuring this op art masterpiece at my online gallery

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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.
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