Ambiguous figures

Creating a New Impossible Cube: From Concept to Print

Gianni Sarcone

Impossible or undecidable figures have long fascinated artists, mathematicians, and viewers alike. Their appeal lies in a delicate tension: the structure appears perfectly logical at first glance, yet closer inspection reveals spatial contradictions that cannot exist in the physical world. My latest work revisits an idea I first explored in the 1990s—an impossible Rubik’s-style cube—now developed into a new series built across several stages, from hand-drawn construction to digital refinement and photographic interpretation.

The project began with a simple geometric framework—interlocking beams arranged to suggest a stable cubic volume. The challenge was to reinterpret an apparently ordinary three-dimensional cube into an ambiguous form that still appears structurally plausible. Through careful adjustments of line weight, contrast, and directional and formal cues, the cube gradually shifts from perceived solidity to spatial uncertainty, so that as the eye moves across the image, the object quietly reorganizes itself, producing a surreal perception in place of a coherent physical structure.

impossible cube
Here is the original version of the project, refined from my initial hand-drawn construction and carefully reconstructed using FreeHand MX

Two of the final images belong to the Op Art tradition, where sharp black-and-white geometry emphasizes visual tension and rhythmic structure. These compositions highlight the cube’s architectural clarity while allowing the paradox to emerge naturally from the viewer’s perceptual processing. The remaining two images take a different path: they present the object in a photographic setting, rendered with realistic lighting and textures.

impossible cube etched
Astraea Paradox Cube: Available as fine art print.
Rubik’s Paradox Cube: Available as fine art print.

Together, the four images form a small visual narrative—construction, transformation, and illusion—showing how a purely conceptual structure can evolve into multiple aesthetic forms. The Op Art versions focus on perceptual mechanics, while the photographic interpretations suggest how an impossible form might inhabit the physical world, even if only in appearance.

Fine art prints and canvas editions from this series are available through my official gallery shop, where each piece is produced using archival materials designed for long-term display.

Collectors and galleries interested in larger formats or special editions may also contact me directly for availability and production details. This series continues my exploration of perceptual geometry, where simple shapes become instruments for questioning how we construct space, depth, and visual certainty.

Seeing Beyond Lines: The Illusion of Form

Gianni Sarcone

We usually perceive lines and shapes as forming a figure, while the paper and surrounding white space recede into the background. Yet, under certain conditions, what we assume to be background can itself acquire form and meaning. In the illustrations shown here, a clear geometric figure emerges—even though no lines actually define it. These visual phenomena are known as illusory figures.

illusory spring
What kind of 3-dimensional shape do you see?

Illusory figures depend, in part, on the presence of regular gaps within a visual arrangement. When such gaps occur, the visual system instinctively tries to resolve them into coherent forms. These gaps can be created by simple elements, such as circles. When solid black circles and partially “chipped” ones are arranged carefully, they produce striking illusory shapes.

The most familiar example is the Kanizsa triangle. Here, an illusory contour is perceived when black disks with wedge-shaped sections removed are aligned so that their edges define a triangular form in the negative space. Remarkably, this illusory region appears brighter than the surrounding page, even though its physical luminance is identical.

Kanisza triangle
Kanizsa triangle

Etherial Cross

A pattern of black dots forms a ghostly ‘X’ shape through negative space. The arrangement of dots creates a subtle sense of motion and depth. The piece combines the Ouchi effect—where contrast between figure and background generates apparent movement—with the Kanizsa illusion, where the mind completes shapes that aren’t actually drawn.

Sarcone's Illusory Cross
Fine art prints of this Op Art piece are available for purchase through my official gallery.

The effect becomes even more dramatic when the illusion is animated. Rotate the cross, for example, and the X-shaped form—with no explicit outline—appears to emerge from a rigid grid of black dots. The shape is defined solely by subtle local distortions: small asymmetric intrusions along the contours of the X disrupt the regularity of the dots, making the form pop into perception despite having no actual boundaries.

Animated Sarcone's Illusory Cross

Etherial Circle

Using the same technique, we can replace the X with a large O. Now the regular arrangement of black circles is disrupted by a ghostly central shape that seems to lift off the background, almost floating. As above, this Op Art piece combines the Ouchi effect—where the contrast between figure and background creates apparent motion—with the Kanizsa effect, where the mind completes shapes that aren’t actually drawn.

Floating O
Fine art prints of this Op Art piece are available for purchase through my official gallery.

It is also interesting to add a rotational motion to this Op Art piece. I experimented with different solutions, and this one is the simplest yet striking nonetheless.

To conclude this journey into the world of contour illusions, still using black disks as our starting point, here are a few further experiments. They explore negative superpositions, translucent effects, and the emergence of more complex forms—showing how simple elements can give rise to unexpected visual structures.

hidden beauty
Fine art prints of this Op Art piece are available for purchase through my official gallery.

Ananke’s Die

Gianni Sarcone

A simple study in visual perception—an exploration of how a plain hexagon can evolve into the illusion of a cube. Through precise geometry and controlled form blending, static lines awaken into rhythm and volume, giving rise to a subtle sense of depth and movement.

Constructing the Illusion

Fig. A — The Base Shape
Start with a regular hexagon. Divide it into three equal diamond shapes (rhombuses)—these represent the three visible faces of the cube. Each diamond has four equal sides: two acute angles (60°) and two obtuse angles (120°). Together, they form the geometric foundation of the cube.

Fig. B — Building Volume with Shape Blends
In Illustrator, or any other vector software, use the Blend Tool to create a shape blend inside each diamond. Start with a small central circle and blend it toward the outer edge of the diamond. Adjust the number of blend steps to control how smooth or tight the transition appears. This process builds the cube’s apparent volume and visual tension. You’ll notice that the distance from corner to corner in the nested, diamond-like shapes is slightly greater than from side to side, creating subtle gaps that lead the eye to perceive an X across the surface.

Fig. C — Perspective and Transformation
Distort slightly the hexagon to set the three diamonds in perspective. This step transforms the flat figure into a die-like cube, giving it spatial depth and presence.

ananke cube

Enhancing the Optical Effect
Next, add horizontal background lines and some color, as shown in the two examples in the image. You can also adjust the illusion by making the visible faces of the die appear slightly concave, as in the figure on the right. This effect is created by shifting the concentric, nested diamond shapes slightly off-center—the position of the central ellipse determines whether the die appears concave or convex.

two Ananke dice

Below is the finished stage of the work. Curiously, the cube appears to hover, slide, and even emit a faint blue glow—though it remains entirely black and motionless.
Ananke’s Die is a study I began in 2010, a continuing exploration of how repetitive lines and geometric precision can trick the mind into sensing motion and color where none exist.

Ananke die

You can get Ananke’s Die as a fine art print or canvas, available in different sizes and finishes.
👉 Buy it here

Why Ananke’s Die

I titled this work Ananke’s Die after Ananke, the Greek goddess of necessity and fate.
The cube, a symbol of structure, represents order and control. Yet the three visible faces that seem to define its volume are an illusion—shifting and unstable.
Under the viewer’s gaze, the shape changes, its meaning shifts, yet the form remains.
This illusory die shows the balance between order, perception, and destiny, reminding us that what we think we control often exists within the unpredictable interplay of vision and inevitability.

This image also triggers multiple associations in a loop: hexagon, cube, die, chance, illusion, order, fate, contradiction. These connections show how perception mixes stability and randomness, revealing that what we see is shaped as much by the mind as by reality.

The Cube That Lies

Gianni Sarcone

I’ve always been drawn to the architecture of geometry. The hexagon, with its quiet strength and symmetry, sits at the root of so many spatial illusions—it’s the seed of cubes, isometric grids, and 3D paradoxes. From this shape, I began exploring structures that bend logic and perception, eventually giving life to a trio of optical works: Enigma 1, Enigma 2, and Enigma 3.

enigma 1
Enigma 1 – Prints & T-shirts.
enigma 2
Enigma 2 – Prints & T-shirts.
enigma 2
Enigma 3 – Prints & T-shirts.

Each piece is built around the visual tension of the impossible cube, created by merging two tribars in perfect isometric perspective. The lines suggest solidity, yet the form escapes reality—what looks structurally sound unravels the moment the eye tries to make sense of it. That’s the game I love to play: where geometry behaves, but perception rebels.

These “Enigmas” are spatial riddles dressed in stripes and angles, each one twisting the viewer’s reading of depth, volume, and continuity in its own way.

Enigma 1 – Prints & T-shirts.
Enigma 2 – Prints & T-shirts.
Enigma 3 – Prints & T-shirts.

Relative Size Illusions

Gianni Sarcone

Here are two relative size illusions I described back in 1997 and 2013.

The first, called Sarcone’s Crosses, challenges classic illusions like the Ebbinghaus illusion (Titchener Circles, 1898) and the Obonai square illusion (1954). It features a cross (the test shape) surrounded by squares of different sizes.

As shown in Fig. 1.a, 1.b, and 1.c, the three blue crosses are all the same size — yet the one on the left (Fig. 1.a) appears larger. Surprisingly, the illusion still works even when smaller squares completely cover the cross (Fig. 1.c).

So, the size of surrounding shapes doesn’t always dictate how we perceive the central one.

In the second illusion (Fig. 2.a and 2.b), due to assimilation, the red diagonal inside the larger ellipse seems longer — but the blue line is actually the longest.

Perception loves to play tricks on us.

sarcone's relative sizze illusions

You can explore more of my illusions and visual inventions on my official site: giannisarcone.com

Hypnotic Disc

Gianni Sarcone

Take a moment to focus on the circular pattern. How many spirals do you see? The surprising answer is none. There are no spirals here—just alternating black and yellow discs, slightly off-center and layered to create a striking illusion of swirling depth and motion.

© G. Sarcone, 1990

I began crafting pieces like this in the early ’90s, drawing inspiration from Duchamp’s Rotoreliefs. I was captivated by how simple rotation could deceive the eye, inviting the viewer into a world of optical illusions. It’s a unique experience—seeing motion and depth in something entirely flat, both puzzling and mesmerizing.

This op art pattern comes to life across various mediums and transforms into artistic expressions on different objects. In my online gallery, you’ll find art prints and everyday items featuring this work, all available for purchase.

Perspective Optical Illusions: The art of circling the square

Gianni Sarcone

When bending the sides of a square structure forward, each edge forming a sine wave shape, the structure reveals a circle when viewed from the reverse angle. This illusion plays with perspective, specifically utilizing an effect known as “anamorphosis“.

Anamorphosis refers to a artistic technique that uses perspective to create distorted images that can only be viewed correctly from a specific angle.

Triangles of Beauty

Gianni Sarcone

Introducing my latest creation, Triangles of Beauty—a minimalist mosaic that blends geometric precision with visual intrigue. This op art piece showcases a striking arrangement of triangular shapes in sepia tones, merging rich shades of brown and beige. The triangle, a timeless symbol, embodies the balance of masculine and feminine energies, forming a harmonious third element that transcends duality. It represents strength, unity, and the divine—a visual echo of the trinity, where individual components unite into something greater.

Step back and let the patterns unfold to reveal the depth within this thought-provoking piece.

This thought-provoking op art piece is available in my online galleries:

· Redbubble

· Fine Art America

Moona Lisa

Gianni Sarcone

In 1997, I reimagined Leonardo da Vinci’s Mona Lisa through a system of 142 color beads, each precisely positioned at the nodes of an invisible two-dimensional triangular grid. Up close, the pattern appears abstract, yet from a distance, the arrangement resolves into the familiar features of the portrait, inviting viewers to recognize the image through perception and suggestion.

hidden mona lisa
Hidden Mona Lisa (1997), © Gianni A. Sarcone
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