A geometrical (meta)model of theories of physics, based on Planck's four fundamental constants and represented as a four-dimensional polytope: the hexadecachoron.
Planck's hexadecachoron — 4D projection
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.
No gravity. No light-speed limit. No quantum effects. No temperature. The motion of objects under forces — ∑ Fi = ma — where modern science began.
Every other piece in this puzzle gets its position from this starting point. It still works perfectly for everyday speeds and scales.
Visual: The complex equilibrium of forces of a surfer.
A gas is trillions of colliding particles. Boltzmann's constant kB connects a particle's average energy to the temperature of the whole gas.
With it, heat, entropy, and pressure emerge from statistics. Boltzmann's tombstone in Vienna reads simply: S = kB log W.
Visual: Terms such as "hot" and "cold" depend on the activation energy.
Every mass in the universe pulls on every other. Newton's constant G governs falling apples and orbiting planets with the same equation.
G is the only one of Planck's four constants still not measured to full precision — experiments to nail it down are ongoing today.
Visual: Mercury, Venus, Earth (with moon) and Mars elipses around the Sun.
When gravity and thermodynamics meet, stars are born. A gas cloud collapses when gravitational energy outweighs thermal pressure — the Jeans mass.
No relativity, no quantum mechanics needed. The universe builds stars with just G and kB.
Visual: Star formation — simplest astrophysics.
Nothing travels faster than light. Einstein's 1905 theory derived E = mc², time dilation, and unified electricity and magnetism.
The constant that matters is c⁻¹ — as c → ∞, special relativity collapses back to Newton. Maxwell's equations live here too.
Visual: The twin paradox — a classic thought experiment in special relativity.
What temperature does a moving body have? This question has been debated since 1907 and remains unresolved.
Planck, Einstein, and others proposed different answers — and all may be correct, depending on how you define temperature for a moving system. A rare case of a theory that is more puzzle than solution.
Visual: What is the temperature of a moving body?
Particles don't have definite positions until measured. Energy comes in discrete packets. Planck's constant h sets the scale at which this strangeness kicks in.
The 1920s formulations of Schrödinger and Heisenberg transformed physics. Einstein protested: "God does not play dice." The dice disagree.
Visual: Entanglement of particles — their state cannot be described independently anymore.
Truly identical particles can all pile into the same state (bosons) or refuse to share one (fermions). This gives us superconductors and Bose–Einstein condensates.
Planck's 1900 black-body law — the first quantum formula — lives here too.
Visual: A noisy qubit — the environment "leaks" information out of the qubit system.
Mass curves spacetime. Objects follow that curvature — gravity is not a force, but geometry. Einstein's 1915 equations predicted black holes, gravitational waves, and the expanding universe.
All later confirmed. The image shows space curved by a massive body — not a force pulling things down, but a shape guiding them.
Visual: Space-time geometry is curved due to the mass.
The Big Bang started hot. The universe has been cooling for 13.8 billion years. Today the cosmic microwave background reaches us at just 2.7 K.
Cosmology lives at this intersection of curved spacetime and thermodynamics, though quantum effects are never truly absent.
Visual: Cosmic microwave background radiation. The expanding universe is cooling down.
The Standard Model of particle physics. Every particle is an excitation of a field. QFT predicts the electron's magnetic moment to twelve decimal places.
The most precisely tested theory in science. Gravity is stubbornly absent: including G turns this into the elusive Theory of Everything.
Visual: Feynman diagrams — particles as excitations of quantum fields.
Planck's 1900 black-body formula was the first equation to combine c⁻¹, h, and kB — it launched quantum physics.
The Unruh effect predicts that an accelerating detector in empty space will measure a nonzero temperature. Hot vacuum: still unconfirmed experimentally, but theoretically compelling.
Visual: Three constants, the first quantum formula, and a glowing black-body.
In 1975, the COW experiment showed that a neutron beam splits and recombines with a measurable phase shift caused purely by Earth's gravity.
Quantum and gravitational effects, no relativity needed. A quiet but profound confirmation that h and G do overlap.
Visual: Neutron interferometer in Earth's gravitational field.
Ultracold neutrons bounce off surfaces like billiard balls and occupy discrete quantum states in Earth's gravity. Their measured lifetime gives two different answers depending on method.
The ~9-second discrepancy between "bottle" and "beam" experiments remains an open puzzle in physics today.
Visual: Quantum states in a gravitational bottle.
The holy grail: a single theory uniting quantum field theory and general relativity. Superstring theory and loop quantum gravity are the leading candidates.
Neither has been experimentally confirmed. The Planck length (~10⁻³⁵ m), where quantum gravity must matter, is 10²⁰ times smaller than a proton. Progress is slow, but the question is real.
Visual: String theory — one vision of the Theory of Everything.
Black holes radiate. Hawking's 1974 discovery that black holes emit thermal radiation is the clearest hint that all four constants must eventually unite.
The Bekenstein–Hawking entropy links the thermodynamics of a black hole to the area of its horizon. TORE is not yet found, but black holes are already pointing the way.
Visual: This outermost piece contains all others. The assembled puzzle is TORE.
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 four-dimensional hypercube, unfolded into rotating 3D projections. Its 16 vertices mark the 16 theories of physics. Click any vertex to step inside that theory.
The dual polytope of the tesseract, bounded by 16 tetrahedra. Different projection angles reveal the nested tetrahedral structure underlying Planck's model of physics.
Press & Media
From science communication contests to public outreach events, PlanckPlay has been present where physics meets people.
Berlin Science Week 2026 · YouTube
A short film about my work featuring PlanckPlay, submitted to the Berlin Science Week × LNdW call for early-career researchers.
Lange Nacht der Wissenschaften 2026 · Instagram
A short reel documenting PlanckPlay in action — physics as something you can touch, build, and play with.
Coming soon
Two complementary experiences are in development: an extended reality application for navigating the hexadecachoron in space, and a series of interactive environments where the sixteen theories become playable.
Navigate the hexadecachoron in three-dimensional space. Enter each theory, understand its physical significance, and visualise its relationship to neighbouring theories through immersive environments.
Being developed as part of a Teaching Portfolio for secondary school physics education.
Register for early access →Each environment explores one or more of the sixteen theories through play. Navigate phenomena normally invisible — from quantum superposition to relativistic time dilation — as spatial, embodied experiences.
Finding your star — a stellar map of the night sky. Interact with constellations, galaxies, and planets, tracing the physics that governs each from Newtonian orbits to relativistic light-bending.
More environments to follow →Research surveys
We are collecting data to evaluate the educational impact of PlanckPlay and the Hypercube of Physics. Your feedback directly informs the development of new models, XR experiences, and teaching materials. Please select the survey that best corresponds to your profile.
● For adults
This survey is for visitors, museum-goers, and anyone with a general interest in physics who has interacted with the hexadecachoron model or PlanckPlay. It takes approximately 5–8 minutes to complete.
● For students
This survey is for secondary and university students who have engaged with the Hypercube of Physics in a classroom or workshop context. It takes approximately 5–7 minutes to complete.
● For educators
This survey is for physics and science teachers who have used or evaluated PlanckPlay or the Hypercube of Physics as a teaching tool. Your professional perspective is especially valuable for our grant reporting. It takes approximately 5–7 minutes.
● For children
A short, fun survey for children aged 6–12 who have tried the PlanckPlay puzzle or the paper hexadecachoron. Designed with picture buttons and face scales — parents are welcome to help. Available in German and English.
Opens as a standalone page. Works on tablets and phones. Responses are saved locally and can be exported by the event supervisor.