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Amplituhedra Models

Completed: February 2026

10-piece model with magnets

Description:

I developed a set of 3D-printed, magnetic, snap-together models of amplituhedra as part of a project with Prof. Lauren Williams at Harvard. Amplituhedra are geometric objects whose shapes encode relationships in particle physics, and although they arise from high-dimensional mathematics, their structure can be understood through the chambers formed by hyperplane arrangements.

To make these abstract shapes tangible, I printed each chamber as a separate piece with embedded magnets so the pieces assemble cleanly into the full object. The result is a tactile model that helps students and researchers visualize and physically explore the geometry behind modern scattering-amplitude theory.

MATLAB-generated rendering of example with four chambers.

Physical model with four chambers.

Fabrication process:

  1. Generate individual STL files using MATLAB code.
  2. Import STLs into CAD modeling software and extrude magnet holes. (Or, simply open the attached .f3d file and edit parameters to desired magnet size.)
  3. Export each chamber to slicing software, separating by colors.
  4. Send to 3D printers. Print pegs as well.
  5. Assemble adjacent faces with peg-hole pairs.

Files