Distortion-free map of all continents I've been searching for a map that shows all continents in their actual size that is free of projection distortion, to no avail. Every map I found was of a particular projection type and as such showed continents out of proportion. Even this one, that claims to "not lie" seems rather distorted.

I am no expert in the area, but I do have some 3D graphics background, so I decided to give it a go. I took a spherical projection map of the continental plates, projected it onto a sphere, then created a polygonal mesh encompassing all continents onto the sphere, then brought that into 2d space and relaxed edge length to correspond to their relative length in 3d space as much as possible and transferred the pixel information to the resulting UV map. Note that I did not account of the planet being an imperfect sphere, so that may be a source of minor inaccuracy. And the result:



It does look a lot like a Dymaxion projection, although my result seems less distorted, probably because the former is project onto a rather low resolution mesh before unfolding:


Is my result accurate enough, or is my workflow missing something? And in case of the latter, I'd appreciate a reference to an accurate representation, or at least some info on what I did wrong and how to improve my result.
I've been searching for a map that shows all continents in their actual size that is free of projection distortion, to no avail


That's because such a thing does not exist. A projection by definition has distortion, otherwise it would not be a projection.

The only way to have a distortion free view of the planet is by having a physical globe, and looking at it with both eyes so your brain gets the three dimensional perception (assuming going to space is not an option). Anything else will result in distortion.

Now that we have this covered, there are all kinds of projections with all kinds of distortions. Distortions can affect areas, distances, shapes, etc. to various degrees. It's your choice to determine which types of distortions and their magnitudes are acceptable to you, personally. There is no need to reinvent the wheel, there are enough projections out there already.