Pardesco · Randall Morgan · Cincinnati
Projections from a Higher Space
Real four-dimensional polytopes — cast down into our world as crystal, and set slowly turning.
The Work
Three shadows, turning
Each is an actual four-dimensional solid, projected into three dimensions and rendered as refractive crystal. 4D rotation · GPU path-traced · seamless loop · 2026.
The Instrument · The Story
Coded, not modeled
Nothing here is modeled. Each form is a real four-dimensional solid — a uniform polychoron whose vertices are exact coordinates in four-space. You cannot sculpt such a thing, and no camera can photograph it. The only honest way to see one is to build the machine that projects it — so I did.
I designed a four-dimensional viewer from the mathematics up and built it with AI coding agents writing to my specification: it turns the polytope through a plane of four-space, projects it into three dimensions, and carries each point's depth in the fourth dimension forward as the thickness of the light that draws it. The rotation is plain linear algebra, accurate to one part in a quadrillion, and every loop closes on itself perfectly, repeating without a seam.
The hard part is what no tutorial covers: projection singularities where points race to infinity, a stable point-count as edges sweep the pole, a turn that must return exactly to its origin. That geometry flows through Universal Scene Description into Blender, where geometry nodes grow crystal along the curves and a GPU path-tracer renders it as refractive glass, lit from a single point at the form's own center.
Not the wireframes the fourth dimension is usually drawn with, but physically path-traced crystal: hundreds of self-intersecting edges bending light like a cut gem.
I trained as an architect, and this is still architecture — drawing spaces no one can stand inside yet. Here the three things I have always chased stop being separate: the mathematics is the truth, the technology the instrument, the agentic AI the leverage that lets one person hold an entire studio. The AI is not the artist — it is what turns a lifetime's fascination with higher dimensions into something you can behold.
Turn it yourself
The 600-cell, live
The same geometry, drawn live in your browser: 120 vertices and 720 edges in four-space, turning through two planes at once and projected into three. Drag to turn it in three dimensions. Each edge's thickness and color carry its depth in the fourth dimension — the same encoding that sets the crystal's tube radius in the renders.
A lightweight sketch of the instrument. The full viewer is free at 4d.pardesco.com.
Studies
Before the crystal, a line
Every crystal starts as this: the bare edges of the form, projected and drawn in light. These plates were made for Ana & Kata, a book on the fourth dimension I am finishing now. This is where I decide what a shape is, before deciding how it should look.
The version that failed
Thirty-one plates, drawn twice
I framed the first set by eye, turning each shape until it looked right. Most came out busy and a little lopsided, and none of them settled. The fault was the viewpoint: a polytope has axes where its symmetry lines up, and I was looking from between them.
The second pass used a tool I specified for the job. It turns a cell, face or edge centre of the shape onto the pole of the projection, finds the axis of highest rotational symmetry and points the camera straight down it, with a mirror line vertical. The geometry and the projection stayed the same. The viewpoint changed, and I redid the palettes alongside it.
It broke things on the way. Seen edge-first, one edge runs through the projection pole, out to infinity and back; it rendered as a flat disc aimed at the camera and had to be dropped. One plate turned out to show the truncated 16-cell under a caption that said truncated tesseract. Four shapes were too dense to read at book size and were replaced.
Exhibited
ETHDenver, 2026
A live program shown at ETHDenver 2026, built to be met in a room rather than scrolled past.
Technē is Greek for craft; genesis is becoming. I made the piece for ETHDenver under the Bitcoin motto VIRES IN NUMERIS, strength in numbers, and the numbers on screen are literal. Every value is the real data of the form at that instant, recomputed as it turns. Nothing is there for decoration.
The Artist
Randall Morgan
- PracticeDimensional art · computational geometry
- TrainingArchitecture, UC · DAAP
- Manifest GalleryNumbers, Cincinnati '26
- ETHDenverTechnē//Genesis, '26
- JMM Art ExhibitionBoston '23 · D.C. '26
- Bridges GalleryHalifax, 2023
- NFT.NYC2024
- Claire Silver AIFinalist, 2023
- Collections27 countries
- Active since2018
Randall Morgan works as Pardesco — a dimensional artist and computational geometer in Cincinnati, Ohio.
Trained in architecture at the University of Cincinnati (DAAP), he translates higher mathematics into contemplative form across laser etching, CNC carving, 3D printing, cast silver, and rendering. His research centers on four-dimensional polytopes, hyperbolic tilings, and sacred geometry — exact structures, rendered until they feel inhabited.
His work has shown at Manifest Gallery's Numbers exhibition in Cincinnati (2026), ETHDenver (2026), with the real-time piece Technē//Genesis, the Joint Mathematics Meetings Art Exhibition (Boston, 2023; Washington, D.C., 2026), the Bridges Mathematical Art Gallery (Halifax, 2023), and NFT.NYC (2024). A CNC-carved parametric work was a finalist in the Claire Silver AI art competition, and his pieces are held in private collections across twenty-seven countries.
Every piece begins as exact coordinates. Active since 2018, he chooses the forms, decides how each one turns and is lit, and directs AI coding agents to build the tools that carry the geometry to a render or to a machine — a one-person studio, human art direction with machine leverage.
In Matter
The same geometry, made physical
Before the renders, the practice was wood and metal: forms carved, etched and cast from exact geometry. Selected earlier works.
Elsewhere
Enter the geometry
We only ever see the shadow of the higher thing. The straight is made curved in its descent; the eternal form is known only as it turns. I only built the window.Pardesco