First convex polyhedron found that can't pass through itself

Clarifying the Rupert Property and Problem Scope

• Discussion centers on the “Rupert property”: one copy of a convex polyhedron can pass straight through a hole in another congruent copy, leaving nonzero material (“not cutting it in half”).
• In practice, this is phrased as: does there exist an orientation where one 2D projection (“shadow”) of the shape fits strictly inside another projection of the same shape?
• Commenters stress that equality of shadows is trivial and uninteresting; a strict margin is required.
• The result concerns convex polyhedra only; several people note the article’s “shape” title is misleading without that qualifier.

Spheres, Limits, and Nonconvex Shapes

• Many initially point to a sphere (and donuts, cylinders) as obvious shapes that can’t pass through themselves.
• Others counter: spheres and torii are not convex polyhedra, so they were never part of the conjecture.
• Attempts to treat a sphere as a “limit” of increasingly fine polyhedra are rejected: limiting behavior is subtle, the limit object is no longer a polyhedron, and properties like Rupertness need not carry over.
• Nonconvex examples (donut, T-tetromino) are easy noperts, reinforcing why convexity is central.

Computation and Search Strategy

• The core difficulty is ruling out all orientations for a candidate polyhedron; brute force is impossible.
• The proof strategy uses projections and parameter-space pruning: if a protruding “shadow” requires large rotations to fix, whole regions of orientations can be discarded.
• More faces and symmetry make checking Rupertness harder; earlier work (e.g., triakis tetrahedron) already revealed extremely tight fits.
• The computational part is implemented in SageMath and shared openly; some plan to 3D-print the resulting Noperthedron from provided STL files.

Rotation and Motion

• Several ask whether twisting or helical motion (sofa-around-a-corner style) could allow passage where straight motion cannot.
• Replies note the standard Rupert problem assumes straight-line passage and, for convex shapes, rotation during transit likely doesn’t fundamentally change the feasibility condition defined via shadows.

Communication, Naming, and Audience

• Multiple comments criticize the title’s looseness (“shape” vs “convex polyhedron”) but praise the article’s level of detail as accessible yet substantial.
• Debate arises over whether Quanta targets laypeople or a technically inclined audience, and whether its headlines verge on clickbait.
• The coined name “Noperthedron” triggers a deep side thread on how portmanteaus work in English (and even comparisons to Mandarin), illustrating the community’s fondness for linguistic as well as mathematical play.

Value and Funding of Pure Math

• Some question why such problems are studied at all; others defend curiosity-driven math as legitimate and historically fruitful, with applications often emerging decades later.
• There’s discussion about who pays for such work (sometimes hobbyists, sometimes institutions), and analogies to past “useless” mathematics that later underpinned computer graphics and logic.

Broader Context and Cultural Reactions

• Commenters connect this result to a recent popular video exploring Rupert/nopert problems and attempts to show familiar solids (e.g., snub cube) are non-Rupert.
• There’s enthusiasm for the aesthetics of the shape, suggestions to include it (and other recent mathematical curiosities) on future space probes, and general appreciation for the whimsy, history, and bet-driven origins of the problem.