Cube map — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as seam — the same set of essays touches all of them, so they are one junction rather than several.
Six flat pictures of everything
There is one way to photograph the whole sphere and keep every straight line straight, and it is to stop using one surface. Six flat pictures at ninety degrees cover everything, each of them a perfect pinhole, and the price is paid entirely at the seams — where a straight line does not bend but kinks, by an angle that reaches 45 degrees and is exactly zero for the lines lying in the seam's own plane.
The lines a surface leaves alone
Only the plane draws every straight line straight, which this site has measured and which gets read as though a curved surface bent everything. It does not. Every curved picture surface here keeps a one-parameter family of world lines exactly straight, and the family is a curve on the sphere of lines rather than a region of it — so a grid of samples finds none of it, which is what the first version of this measurement reported.
Named alongside it
The objects these essays reach for when they reach for this one.
AnisotropyBeltramiDemonstrationGnomonicPicture surfaceSeamStraight familyArea scaleConformalCylindrical projectionDegeneracydegrees of freedom