Concept
Duality
2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
Why the list of perfect solids stops at five
There are infinitely many regular polygons and exactly five regular solids. The reason is not deep, but it is very sharp, and it can be checked on a single row of corners.
The plane, divided by whoever is nearest
Scatter some points and colour every other point of the plane by which one is closest. The result is a tiling nobody designed, and its dual triangulation has a property that no part of the construction mentions.
Named alongside it
The objects these essays reach for when they reach for this one.
ConvexityEuler characteristicTilingAngle defectCircleDelaunay triangulationNearest neighbourPerpendicular bisectorPlanar graphPlatonic solidsPolyhedronVoronoi diagram