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World desk4 min

Why Do Some 3D-Printed Optical Illusions Look Different From Each Side?

A printed illusion can look like one shape from a chosen angle and another from the side. Here’s how perspective, ambiguous projections, and lenticular surfaces create the effect.
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They look different because the object is designed to produce different visual readings from particular viewpoints. In a common printed example, its outline matches a familiar shape only when viewed from a chosen direction; the solid itself bends in depth, so another angle exposes a different shape. Other illusions rely on ambiguous projections or lens-like surfaces, so the mechanism depends on the object.

Why viewpoint changes the apparent shape

Your eyes receive a two-dimensional projection of a three-dimensional object. A designer can shape a printed solid so that its outline from one carefully selected direction resembles a simple, familiar figure—even though the object’s full geometry does not match that figure. Move to the side or above it, and the projection changes, revealing bends and depth that the preferred view conceals.

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The impossible arrow and its mirror image

In the arrow example described by Science Buddies, the design begins with a two-dimensional outline and maps its boundary into three-dimensional curves. From the intended direction, those curves project into an arrow. From other directions, the top and side surfaces reveal the underlying construction. As the guide puts it, “from the correct viewing angle, your brain interprets the top of the object as flat.”

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A related effect, anomalous mirror symmetry, is associated with mathematician Kokichi Sugihara. The direct view can appear to show an arrow pointing one way while the mirror image appears to point the other. In the guide’s described design, turning the object 180 degrees can still leave the direct view reading as a right-pointing arrow. The object has not physically transformed: the viewing direction or reflection changes the projection your visual system interprets.

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Different illusions use different mechanisms

“Looks different from each side” can describe several distinct effects. The table compares the projection-based examples with lenticular objects; it does not imply that every printed illusion uses all of these methods.

Type What produces the effect Viewpoint and physical construction
Angle-specific silhouette A shaped solid projects a familiar outline from a selected direction. The intended view is constrained; other angles reveal the object’s depth and bends.
Triply ambiguous projection A picture’s parallel edges can be interpreted in three ways when viewed obliquely, with a gravity cue helping the interpretation. The design is based on projection geometry rather than a lens-and-image surface.
Lenticular surface Lens-like surface elements direct light from different portions of a color pattern toward viewers at different angles. Appearance varies with viewpoint; the cited research pipeline uses a lens surface and calculated color pattern.

Three readings from an ambiguous projection

In a 2020 paper, Sugihara describes a design principle for rectangular objects whose orthographic projection has three groups of parallel edges. When the picture is on a horizontal plane and viewed obliquely, one group can appear vertical on the retina. The visual system can then interpret the projection as a vertically compressed three-dimensional object, yielding three readings. A real object that indicates gravity can strengthen the effect. Sugihara summarizes the process: “This process gives three different interpretations of the picture, and thus creates triple ambiguity.”

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This is not simply an arrow-shaped solid viewed from several sides. The ambiguity comes from how the projection can be interpreted, as described in Sugihara’s paper in the Journal of Graphic Science of Japan.

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Images revealed through lenticular surfaces

Lenticular objects work differently again. Rather than relying only on a silhouette, their lens-like surfaces direct light from different areas of an underlying color pattern toward viewers at different angles. The MIT CSAIL project describes an editor that takes a 3D model, desired viewpoints, and target images, then calculates lens placement and the color pattern. Its paper page describes a single-pass multimaterial printing pipeline for curved objects.

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The project page reports up to 19 appearances per object in digital ray-tracing simulation. It also says fabrication inaccuracies prevented those simulated results from being achieved physically in the reported work, while describing four application examples with simulated and physical results. That figure is a research-specific simulation result, not a demonstrated capability of ordinary consumer 3D printers.

Why the effect has a history beyond 3D printing

Perspective-based impossible forms predate consumer 3D printing. The Science Museum Group catalogue records models of the impossible triangle and staircase designed and made by Roger and Lionel Penrose in England between 1955 and 1959. The listed models use birch plywood, paper, and adhesive. The catalogue notes that real objects viewed from particular positions can create the impression of inconsistent drawings.

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3D printing makes such geometry easier to design, preview, and reproduce, but it does not remove the perspective constraint: the intended visual reading still depends on the right projection.

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How to make and inspect an angle-specific print

The Science Buddies project guide outlines a practical workflow for its arrow-style illusion. You need a way to design the geometry and access to a 3D printer or print service. If you do not own a printer, the guide suggests checking a school, library, or makerspace. A mirror is optional for demonstrating the reflected-arrow effect, not a requirement for every optical illusion.

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  1. Define the outline. Start with the intended two-dimensional shape and its upper and lower curves.
  2. Build the 3D curves for the chosen view. Shape the boundaries so their projection from that direction produces the intended outline.
  3. Preview and iterate. Check the target view as well as top and side views; revise the geometry if the intended outline is unclear.
  4. Export an STL and check units. STL files do not encode units, so choose the appropriate units when exporting or importing.
  5. Print and compare. Compare the physical object with its screen preview, then inspect it from above, from the side, from the target direction, after a 180-degree rotation, and in a mirror if demonstrating the reflection.

The guide encourages iteration and comparing the print with the preview; a downloaded design is not guaranteed to work from arbitrary angles or print perfectly without adjustment.

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