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it intuitively feels impossible because it sounds like the definition of "can pass through itself" is really "has at least one orientation where all of the side
by ratelimitsteve 1y ago
it intuitively feels impossible because it sounds like the definition of "can pass through itself" is really "has at least one orientation where all of the sides of one instance are at most as long as all of the sides of the other instance" and then however you define an orientation an instance of a shape in orientation X should be able to pass through an instance of the same shape and size in the same orientation
- hyperhello 1y agoYes, and when you think of it that way, it sounds like a partial ordering with a base case. If angle A can pass through angle B, and angle B can pass through angle C…
- strbean 1y agoThe criteria is "pass through itself without cutting in half". Presumably that extends to "without deleting the object entirely", which is what would happen to pass through in the same orientation.
- jibal 1y agoNotably, a sphere is non-Rupert (but a soccer ball is not ... it can pass through a tiny fringe).
- thaumasiotes 1y ago> Notably, a sphere is non-Rupert (but a soccer ball is not ... A soccer ball is a sphere. It has decorative polygons projected onto its spherical surface, but having a color scheme doesn't stop it from being a sphere.
- jibal 1y agoA soccer ball in this context is considered to have planar faces (IRL those faces aren't planar because of the air pressure bowing them).
- jibal 1y agoMy intuition is very different (and happens to fit reality). Note that convex polyhedra can have asymmetries.