Configuration space — where it appears
Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.
A state no motion reaches
Flat-foldability asks whether a folded state exists. Rigid-foldability asks whether there is a path to it. The two sets are different, and the difference can be counted on a single vertex.
Two things called folding
A protein folds and a sheet folds, and the word is the same word by accident. Both have exponentially many states and that is not the difference. The difference is that one of them can be filtered by four conditions checked at a single point, and the other cannot be filtered by anything local at all.
Every move leaves the verdict
The only change a folder can make to a lettering without breaking it is to push one vertex through, flipping two creases at once. Try every such move on five tessellation patches, from two different letterings each: nineteen of two thousand nine hundred and sixty-four survive the conditions, and not one of the nineteen turns a lettering that agrees with itself into one that does not, or the other way about.
Named alongside it
The objects these essays reach for when they reach for this one.
AssignmentReachabilityThe big-little-big lemmaBuried creaseConnectivityCountingCrimpLayer orderLocal moveLocalityNecessary conditionProtein folding