Concept
Polyhedron
2 essays name this object, across 2 fields. 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.
Every corner pays for itself
Count the corners of any solid, subtract the edges, add the faces. The answer is two. It is two for a cube, for a pyramid, for a football, for anything squashed or stretched — and the number is measuring the shape it is wrapped around rather than the shape itself.
Named alongside it
The objects these essays reach for when they reach for this one.
Euler characteristicAngle defectConvexityDualityGenusGraphPlanar graphPlatonic solidsTilingTopological invariant