A new pyramid-like shape always lands the same side up

Potential applications and analogies

• Many comments jump to moon/Mars landers: a self-righting lander could help with recent tipping/crashes, though concerns remain about the “point” digging into soft regolith.
• Other suggested uses: drones with retractable props, turtle exoskeletons, vehicles on slopes, interplanetary landers in general, and tamper or shock/tilt detectors that mechanically encode “disturbed vs undisturbed” states.
• Gaming/dice jokes abound: a “D1” die, always-critting D&D dice, and comparisons to novelty one-sided dice and Möbius-strip-like shapes.

Density, center of mass, and relation to Gömböc

• A recurring theme: this object relies on extreme non-uniform density—hollow frame plus a very heavy base plate—so some find it less impressive than a uniform-density Gömböc.
• Others note that even with free choice of density, discovering a tetrahedron that is stable on exactly one face with only flat faces and sharp edges is nontrivial.
• The Gömböc is repeatedly referenced as the smooth, homogeneous analog; people point out animal shells (like turtles) that approximate it and wonder about better exoskeletons.
• Some argue that for rigid bodies, only the outer geometry and center of mass matter; others reply that if you require uniform density and no voids, you lose the freedom this construction uses.

Mathematical background and controversy

• Discussion references earlier work: Conway & Guy (1969) on stability of polyhedra, questions about whether a homogeneous monostable tetrahedron is possible, and later constructions of monostable polyhedra with many faces.
• There is back-and-forth about a short argument by Goldberg that all homogeneous tetrahedra must have at least two stable faces; some commenters say it’s unconvincing or known to be flawed, and cite later work (e.g., Dawson) for more solid reasoning.
• One commenter notes having previously built a crude bamboo/lead-foil model realizing a similar idea and shares photos.

Design constraints, practicality, and perception

• Several people suggest simpler weighted shapes (balls or cones with a flat, heavy side) that trivially self-right, emphasizing that the challenge here is specifically a tetrahedron with only planar faces.
• Some feel the “new shape” headline overstates it, since this is really a particular rigid body with carefully tuned mass distribution rather than a purely geometric shape.
• Others frame it as an example of “simple” inventions enabled only recently by precision computation, optimization, and manufacturing—similar to bicycles or precise instruments in physics.