4D art is artwork built from genuine four-dimensional geometry, projected into three dimensions so it can be seen. In my work the fourth dimension is spatial, not time: each piece begins as a real, catalogued four-dimensional polytope, which is then projected stereographically into our space and rendered or cast. The form is not invented or imagined — it is translated.

Is the fourth dimension in 4D art the same as time?

No. In physics the fourth dimension is often time, but in this work it is a fourth spatial dimension — perpendicular to length, width, and depth in a direction we cannot point. Just as a cube is bounded by six flat squares, a tesseract is bounded by eight solid cubes. These objects are fully described mathematically; they simply cannot be constructed here.

Why do straight edges look curved in 4D artwork?

Because of stereographic projection. Placing a polytope's vertices on a four-dimensional sphere and projecting them into three-space is the same projection that flattens a globe into a map, lifted one dimension higher. Edges that are perfectly straight in four dimensions arrive as curved arcs — the same reason lines of longitude bow outward on a paper map. The curvature is a geometric consequence, not a stylistic effect.

How many four-dimensional shapes are there?

There are exactly six regular convex polychora — the 5-cell, tesseract, 16-cell, 24-cell, 120-cell, and 600-cell — which are the four-dimensional analogues of the five Platonic solids. Beyond those are ten regular star polychora and well over a thousand uniform polychora, most of which have never been rendered by anyone.

Is 4D art made with AI image generators?

Not in my work. There is no diffusion model in this process and no prompt produced any of these images. The geometry comes from mathematics, the projection from a chosen method, and the light from a renderer. I did use agentic AI as an engineering collaborator to build the rendering pipeline — I directed, it implemented — which let one artist build tooling that would otherwise have taken a team.

Can I see 4D polytopes rotating in real time?

Yes. The free 4D polytope viewer at 4d.pardesco.com renders over 1,700 higher-dimensional forms rotating in real time in the browser, and lets you choose which four-dimensional plane they rotate through. Rotating through an XW, YW, or ZW plane produces the characteristic effect of the inner structure swelling outward to become the outer shell.

Has Pardesco's 4D art been exhibited?

Yes. Two works were selected for the 2026 Joint Mathematics Meetings art exhibition, juried by The Bridges Organization: Sitphi (2025), a giclée print of the small tripesic hecatonicosachoron projected into three dimensions, and Seven Stars (After Dürer, 1521), a laser-etched maple panel applying a {6,4} hyperbolic tessellation to Dürer's knotwork.

What Is 4D Art? A Sculptor's Guide to the Fourth Dimension

Q: What is a 4D sculpture actually a sculpture of?

It is a three-dimensional record of a four-dimensional object's shadow. I export printable meshes of the stereographic projection and use them as masters for lost-wax casting in bronze and silver. The result is not a sculpture representing a higher dimension, and not an artist's impression of one — it is a shadow the object actually cast, caught in metal.

Q: Where can I collect Pardesco 4D art?

Eleven projections are released as single editions in the Prism Neon series at pardesco.art, each a seamless rotation of one polytope through a four-dimensional plane, minted one of one. Physical work — including 120-cell projections cast in silver — is made in the studio.

By Randall Morgan · Updated 2026-07-27

4D art: the 120-cell polytope rendered as glowing crystal, stereographically projected from four dimensions into three — 120-cell · stereographic projection · rendered as glass

Projections from a higher space

There is a shape that cannot exist in our world. It has six hundred cells, or one hundred and twenty; sometimes it is twenty-four cubes folded into a single four-dimensional body. We cannot hold it. We cannot even see it directly — our eyes were built for three dimensions. But we can see its shadow. 4D art is the practice of casting those shadows deliberately, and I have spent years learning to cast them well.

I'm Randall Morgan, and I work as Pardesco. Everything on this page began as an actual mathematical object — a real four-dimensional polytope — projected down into our space and set slowly turning. Nothing is modeled by hand, and nothing is imagined. The geometry is the source of truth; my work is the translation.

What is 4D art?

4D art is artwork built from genuine four-dimensional geometry, projected into three dimensions so that we can see it. The term gets used loosely — sometimes for kinetic work where the fourth dimension is time, sometimes for anything with a lenticular shimmer. That isn't what I mean by it.

The medium, precisely

The "fourth dimension" in this work is not time. It is a fourth spatial dimension, perpendicular to length, width, and depth in a direction we have no way to point. Just as a cube is bounded by six flat squares, a tesseract is bounded by eight solid cubes. Those objects are fully described by mathematics and entirely real to it. They are simply not constructible here.

So a 4D artist is a translator. The work is not inventing the form — the form has been catalogued for over a century. The work is choosing how to bring it into view, and what is preserved or lost in the crossing.

That choice is where the art lives. A four-dimensional object can be flattened into our space in many ways, and each one tells a different truth about it. Most visualizations pick the method that keeps things tidy. I pick the one that keeps things honest.

Why straight edges arrive curved

To bring a polytope into view, I place its vertices on the surface of a four-dimensional sphere and project them stereographically into three-space — the same projection that flattens the globe into a map, lifted one dimension higher.

Something quiet and beautiful happens in that translation. Edges that are perfectly straight in four dimensions arrive in our world as curved arcs. The curvature is not stylization and it is not an effect applied afterward. It is the honest geometric consequence of looking at a higher thing from below — the same reason lines of longitude, dead straight on the globe, bow outward on a paper map.

120-cell · one seamless rotation through the XW plane

Most renderings of 4D geometry use perspective projection instead, which straightens those lines back out and throws away the information. What you get is accurate as a diagram and dead as an image. Stereographic projection preserves the angles at which curves meet, so the lattice blooms and breathes as the form turns — and the rotation reads as a rotation rather than a jumble.

The turning matters as much as the shape. Each piece completes exactly one full rotation through a four-dimensional plane and returns precisely to where it began, so it loops forever without a seam. Watch the centre of the form above: as it rotates through the fourth dimension, the inner structure swells outward and becomes the outer shell. Nothing is growing. You are watching a rigid object turn through a direction you cannot point in.

A taxonomy of higher forms

These are not variations on a theme. Each is a distinct four-dimensional solid with an exact census — the four-dimensional analogues of the Platonic solids, and some considerably stranger relatives.

I render them in two finishes. Crystal treats the lattice as refractive glass and lets the form speak plainly. Prism Neon splits the light chromatically against a field of rays — it is the finish I release as editions. Each plate below records which.

4D artwork of the 600-cell, a four-dimensional polytope of 600 tetrahedral cells, rendered as crystal

4D sculpture render of the grand antiprism, a semiregular four-dimensional polytope, in crystal

4D artwork of the great grand stellated 120-cell, a four-dimensional star polytope, in crystal

4D art of the tesseract or hypercube, the four-dimensional analogue of a cube, in the Prism Neon finish

Four dimensional art of the 24-cell, a regular polytope with no three-dimensional equivalent

4D artwork of the bitruncated 24-cell or tetracontoctachoron in the Prism Neon finish

The full catalogue runs to well over a thousand uniform polychora, most of which have never been rendered by anyone. That is the part I find hard to put down.

Nothing here is modeled

I built a pipeline that treats the mathematics as the source of truth. A generator I wrote bakes the four-dimensional rotation and projection frame by frame, and carries each point's depth in the fourth dimension forward as the thickness of the tube that renders it — so the parts of the form sitting further away in 4D arrive as heavier strokes of light. That data flows through USD into Blender, where geometry nodes grow tubes along the curves and render them as glowing glass.

On working with AI

I should be straightforward about this, because it matters to how the work is read. I used agentic AI as an engineering collaborator to build that pipeline — I directed, it implemented. What it did not do is generate the art. There is no diffusion model anywhere in this process, and no prompt produced any image on this page. The geometry comes from the mathematics, the projection from my choice of method, and the light from a renderer. AI let one artist build tooling that would otherwise have taken a team.

That collaboration has since moved further into the work itself. The renders on this page are lit and shaded through a Blender MCP connection, with materials driven directly rather than dialled in by hand — the same division of labour as before, applied to the look instead of the tooling.

Exhibited: Sitphi

Two of these projections were selected for the 2026 Joint Mathematics Meetings art exhibition, juried by The Bridges Organization. One is a hyperbolic piece after Dürer. The other is Sitphi.

Sitphi — the small tripesic hecatonicosachoron, a complex four-dimensional polytope, projected into three dimensions and rendered as a violet luminous lattice

Sitphi projects the shadow of one of the more tangled objects in the catalogue. Where the 120-cell reads as an ordered lattice, this one arrives as interference — thousands of edges crossing at every depth, the density itself becoming the image.

A note on how this one was made

It is worth being precise, because the previous section describes a pipeline that Sitphi predates. The geometry was mathematical, as always — but the look was not. This render comes from 2025, before the current algorithmic process existed: the shaders and compositing were adjusted by hand in Blender, tuned by eye until the interference pattern read the way I wanted.

The newer work on this page is made differently, and I think it is better for it. But the older method is not something to quietly paper over — the practice changed, and a piece made under the previous one is still the piece that hung on the wall.

From projection to metal

Digital rendering is where the work is developed, but it isn't where it ends. Using the same data, I export printable meshes of these stereographic projections and use them as masters for lost-wax casting in bronze and silver.

Physical 4D sculpture: the 120-cell cast in silver by artist Pardesco — 120-cell · cast silver · held in the hand

The result is a strange thing to hold: a solid object that is a faithful record of something that cannot be solid here. Not a sculpture of a higher dimension, and not an impression of one. A shadow it actually cast, caught in metal.

Collect the work

Eleven of these projections are released as single editions on pardesco.art — the Prism Neon series, each a seamless rotation of one polytope through a four-dimensional plane, minted one of one.

Prism Neon I, the 120-cell rendered with chromatic split — a 1/1 edition on pardesco.art — Prism Neon I · Hecatonicosachoron

Cite this article

Morgan, R. (Pardesco). "What Is 4D Art? A Sculptor's Guide to the Fourth Dimension." Pardesco, 30 March 2025. https://pardesco.com/blogs/technology-art-design/exploring-fourth-dimension-4d-art