Beikel Rivas - fused-polyhedra in additive manufacturing

Computationally-Driven Robotic Clay Deposition for Bespoke Interlocking Structures

The project investigates the fusion of geometric principles with advanced robotic fabrication techniques, drawing inspiration from Robinson Fredenthal’s sculptural work. At its core, the research explores the spatial relationships between octahedrons and tetrahedrons, leveraging their inherent space-filling properties to generate fused polyhedra. Through computational algorithms, octahedrons are iteratively fitted within tetrahedrons, varying in scale and orientation to create bespoke interlocking structures. Boolean operations introduce curvature, transforming rigid polyhedral forms into fluid, continuous geometries that enhance both structural integrity and scalability.

Beyond geometry, the project also explores material innovation by incorporating pigment into the clay mix. Various layering methods are tested to achieve controlled gradient patterns during robotic deposition. One approach involves stacking layers of differently pigmented clay to create precise, gradual color transitions, while another method places pigments vertically, resulting in unpredictable and organic blending. These strategies balance randomness with control, offering new opportunities for both aesthetic expression and material performance in additive manufacturing.

Fabrication challenges arise from the unpredictability of clay behavior during deposition. To address this, an algorithm optimizes the orientation of each component, preventing print failures due to cantilevers and ensuring structural stability. By integrating computational design with robotic clay deposition, the project pushes the boundaries of additive manufacturing, demonstrating how fused polyhedra and pigment-layering techniques can redefine material expression and geometric interlocking in architectural and sculptural applications.

Institution: University of Pennsylvania

Lab: Advanced Research and Innovation lab

Instructor: Andrew Saunders

Co-Instructors: Claudia Campuzano, Nick Houser

Lab Managers: Nicholas Sideropoulos, Shunta Moriuchi

In Collaboration with: Kristyna Wang, Freda Odonye, Lucy Rong.

Project film

Generative Model Workflow: From Subdivision to Interlocking Systems

The generative process begins with an algorithm that iteratively subdivides a tetrahedron by embedding octahedrons within it, maintaining a structured yet adaptable geometric system. The relationship between the octahedron and tetrahedron is governed by the formula, where R octa represents the radius of the inscribed octahedron, and a is the edge length of the tetrahedron. This formula ensures precise scaling, allowing for controlled geometric subdivision.

Additionally, spheres are generated to either fit within the octahedron or touch all the corners of a tetrahedron. These spheres are then boolean-subtracted from the polyhedral framework, introducing curvature and breaking the rigidity of the original geometry. The workflow transitions into an interlocking system, where an auto-selection algorithm alternates adjacent tetrahedrons relative to their corresponding octahedrons, forming intricate, self-supporting connections. This approach enables a scalable and modular assembly, bridging computational geometry with robotic additive manufacturing.