A geometric model of the sixteen areas of physics, based on Planck's four fundamental constants and their four-dimensional dual polytope: the hexadecachoron.
Cluster of Excellence Matters of Activity · Humboldt-Universität zu Berlin
About the project
In 1899, Max Planck identified four fundamental constants that define universal units for length, time, mass, and temperature. The Hypercube of Physics builds on this insight: by mapping the 2⁴ = 16 combinations of these constants onto the vertices of a four-dimensional hypercube, each vertex corresponds to a distinct physical theory.
To make this structure tangible, we work with the hexadecachoron — the four-dimensional dual polytope of the hypercube. Its sixteen tetrahedral faces represent sixteen theories, from Newtonian mechanics (0, 0, 0, 0) at the centre to the as-yet-undiscovered Theory of Really Everything (G, c⁻¹, h, kB) at its outer shell.
This project develops physical models, projections, and interactive XR experiences to make this structure accessible to students, educators, and the general public.
Physical models
01 — 3D printed
15 modular 3D-printed tetrahedra that assemble into the 16th — the TORE. Designed for home printing, museum use, and classroom exploration. Files available on Thingiverse.
View on Thingiverse →02 — Laser-cut flat pack
Precision laser-cut flat-pack model for museum shop retail. Scored fold lines, slot-together assembly — no glue required. Each face labelled with its corresponding theory.
Coming soon →03 — Paper craft
Printable net for scissors-and-glue assembly. Designed for classrooms and workshops — each face labelled with its physics theory and Planck constant coordinates.
Download PDF →The 16 theories
Each tetrahedron in the hexadecachoron corresponds to one of sixteen possible combinations of Planck's constants. Eight are well-established physical theories. Six remain open problems. Two — including the Theory of Really Everything — are speculative frontiers.
Geometry — projections
The hexadecachoron and the tesseract cannot be perceived directly. We make them visible through projections — reductions to lower-dimensional representations that preserve the key structural relationships between theories.
The dual polytope of the tesseract, bounded by 16 tetrahedra. Different projection angles reveal the nested tetrahedral structure underlying Planck's model of physics.
The four-dimensional hypercube, projected onto 3D and 2D. The Bronstein–Zelmanov cube of physics is a 3D shadow of this structure when the kB axis is removed.
An XR application that lets you navigate the hexadecachoron in three-dimensional space. Enter each theory, understand its physical significance, and visualise its relationship to neighbouring theories through interactive environments.
The app is being developed as part of a Teaching Portfolio for secondary school physics education.
Register for early access →Interactive environments
Each interactive environment explores one or more of the sixteen theories through play. Navigate phenomena that are normally invisible — from quantum superposition to relativistic time dilation — as spatial, embodied experiences.
Astrophysics · Newtonian gravity · General relativity
A stellar map of the night sky. Interact with constellations, galaxies, planets, and luminous objects — tracing the physics that governs each one, from Newtonian orbits to relativistic light-bending around massive bodies.
Environment — coming soon
A future interactive environment exploring one or more theories of the hexadecachoron. Proposals and collaborations welcome.