In a world constrained by three dimensions, the concept of 4D Art opens doorways to realms beyond ordinary perception. As a 4D artist known as Pardesco (Randall Morgan), my passion lies in visualizing these higher dimensional spaces through innovative techniques that bridge complex mathematics, AI technology, and fine art sculpture.

What is the Fourth Dimension in Art?

My artistic exploration began with a deep fascination for geometric complexity. While most sculptors work within the familiar confines of height, width, and depth, I found myself drawn to the mysterious fourth dimension—a realm that exists mathematically but remains beyond direct human perception.

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This curiosity led me to spend years developing proprietary techniques for creating detailed geometric visualizations. What started as an examination of models in specialized software like Stella4D evolved into a profound artistic quest to make the invisible visible.

The Tech Stack: AI-Collaborative 4D Visualization

For years, I worked with static projections—frozen moments of four-dimensional forms. But I envisioned something more: watching these shapes rotate in real-time through four-dimensional space, their edges curving and morphing as they turn through planes (like the XW or YW planes) that we cannot directly perceive.

Stereographic Projection: Seeing the Curves

The key to authentic 4D art lies in the projection method. Most visualizations use perspective projection, which straightens lines. I utilize Stereographic Projection. This technique preserves the angles at which curves meet, resulting in "blooming" geometries that reveal the true topology of the hypersphere.

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The 120-Cell: 600 Vertices of Symmetry

Watch the most complex regular 4D polytope rotate through higher-dimensional space. In this visualization, straight edges in 4D appear curved in 3D, similar to how lines of longitude curve on a map.

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The 120-cell contains 120 dodecahedral cells, 1,200 edges, and 600 vertices—the 4D equivalent of a dodecahedron's symmetry elevated to an entirely new dimension.

Gallery: A Taxonomy of Higher-Dimensional Forms

Each 4D polytope has a unique "personality" when projected. As a 4D artist, I categorize them by their symmetry and complexity.

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Tesseract (Hypercube)

8 cubic cells • 16 vertices

The 4D equivalent of a cube. Watch the inner cube expand to become the outer cube as it rotates.

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10-Pen (Decachoron)

10 tetrahedral cells • 10 vertices

Five tetrahedra joined in perfect 4D symmetry. Simple, yet elegantly complex in rotation.

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10-Pen Variation

Alternate rotation axis

The same polytope rotated through a different 4D plane, revealing entirely different visual characteristics.

From Code to Metal: The Physical Art

While digital visualization is powerful, my ultimate goal as a 4D artist is to bring these objects into our physical reality. The challenge is immense: How do you cast a projection of a form that exists in four dimensions?

Using the data from my custom software, I export 3D printable meshes of these stereographic projections. These serve as the "lost wax" masters for casting in bronze and silver.

Sitphi

3,600 Edges of a 4-Dimensional Object

Medium Digital 4D Projection

Geometry 120-Cell Derivative

Status Available

Sitphi represents the culmination of this process. It captures the 120-cell at a precise moment of rotation, freezing the hyper-dimensional curvature into a static object that our minds can explore. It is not just a sculpture; it is a shadow cast by a higher dimension.