SGDL AI
Forms in Becoming:
A Dialogue Between Age-Old Geometry and Creative Algorithms
Explore SGDL.AI
Familiar Yet Radically New
Before you stand forms that seem at once familiar and radically new.
Consider "Boustrophedon 5", an 110 cm tall polyhedron in polished resin, its facets catching the light in a complex dance.
Or "Boustrophedon 6" and "Boustrophedon 7", two slightly larger structures in resin with iridescent cover that embodies an almost living mathematical rigor.
The Creative Process
Born in 2025
These works are the result of a unique creative process.
AI of Form Intelligence
Here, the artist acts not as a sole creator, but as the pilot of a sophisticated tool: an AI of Form Intelligence named SGDL.AI.
Guided Exploration
By providing the initial inputs, the artist guides the algorithm to explore a universe of geometric possibilities, thus giving material form to abstract mathematical concepts.
The Historic Fascination with Polyhedra
To understand the significance of these creations, we must trace history back to where art and science first met around these very same forms.
The Renaissance Connection
The allure of polyhedra has spanned centuries.
The Renaissance, in particular, made them a subject of intense study. Artist-scientists like Leonardo da Vinci, with his illustrations for the treatise De Divina Proportione, and Albrecht Dürer, in his enigmatic engraving Melencolia I (1514), saw the polyhedron as much more than a simple shape. It was at once a technical challenge for mastering perspective, a symbol of the quest for knowledge, and a means of rationalizing space.
From Simple Rules to Complex Forms
By analyzing the transformations of Platonic solids, their duality, and their ability to tile space, Kappraff provided a language to understand how complex forms can arise from simple rules—an idea that finds a powerful echo in today's digital creation.
Geometric Foundation
The creative process behind the exhibited works is anchored precisely in this grammar.
Skew Truncation
Their forms often derive from the work of geometer Jean-François Rotgé and his "skew truncation" method. This is a highly elegant geometric algorithm that can generate complex polyhedra, like the snub cube, from simpler solids.
Mathematical Constants
The method relies on dividing the edges according to precise mathematical constants, such as the famous golden ratio or the Tribonacci constant.
From Theory to Creative Partnership
These mathematical principles, theorized by Rotgé, have been translated into the algorithm used by SGDL.AI, which leverages this method not to reproduce, but to explore and generate infinite variations, thus becoming a creative partner that extends the vision of both the geometer and the artist.
The Intelligence of Forms.
The Intelligence of Forms
The Intelligence of Forms is the reasoning of model of SGDL.AI
But how does SGDL.AI transition from a theoretical principle to a physical object?
1
Knowledge Search
It engages in a series of "reflection" phases to solve a typical spatial reasoning challenge: to prove the existence of, and then realize, a complex form, such as a convex polyhedron where all faces are identical but non-regular pentagons.
First, the AI undertakes a near-exhaustive search of accessible knowledge on the web—spanning mathematics, crystallography, and art history—to validate the potential existence of such objects.
2
Topological Mapping
Once relevant leads are identified, it establishes the topological characteristics of the candidate polyhedron: its fundamental structure (number of vertices, edges, faces) and how these elements are connected.
3
Projective Geometry
Once this conceptual skeleton is known, the AI shifts to projective geometry, a more general framework than our Euclidean geometry. This step is crucial: it guarantees the perfect planarity of the faces and the integrity of their adjacencies, all while lending itself to symbolic calculations of absolute rigor.
4
Validation & Realization
At this stage, the polyhedron can be drawn in perspective, its structure validated.
Upon this projective skeleton, the AI then grafts the mathematical forms that define the volume, calculates the precise coordinates of each vertex in a rational form, and establishes a complete map of all relationships between vertices, edges, and faces.
At the end of this reasoning process, it produces a metric, Euclidean digital twin—a perfect replica ready to be sent, in STL or CADCAM format, to a 3D printer or a milling machine for its physical realization.
From Theory to Structure
This alliance of form and algorithm is reminiscent of the research conducted by the Structural Topology Group (GTS) in Montreal. In the 1980s, this collective of architects, engineers, and mathematicians was already exploring how abstract geometric properties could solve concrete construction problems.
By studying the rigidity of polyhedral structures and their ability to fill space, they demonstrated that form, connectivity (topology), and physical performance are inseparable.
A Dialogue with the Present
Architectural Potential
The works you see here are heirs to this vision: they are not just sculptures, but potential architectures, a materialization of a perfect balance between aesthetics and structural stability.
Contemporary Context
By linking a historical quest to a cutting-edge creative tool, these polyhedra place themselves squarely within the field of contemporary art. They enter into a dialogue with the work of artists like Olafur Eliasson, for whom geometric forms and natural phenomena are foundational elements in an investigation of perception.
Creation in the Digital Age
Ultimately, these works question the status of creation in the digital age. They show us that geometry, far from being a static discipline, remains a living language, capable of reinventing itself to generate forms that continue to fascinate us and stimulate our imagination.