The Dymaxion map is 100% accurate. You only have to start distorting things when you want everything laid out all neat.
I'm curious as to how it can be 100% accurate because I believe you have to start distorting things when you project the surface of a sphere onto a flat plane. From what I can find the Dymaxion projection is more accurate but it still has some distortion.
From Wiki:
"Fuller claimed his map had several advantages over other projections for world maps.
It has less distortion of relative size of areas, most notably when compared to the Mercator projection; and less distortion of shapes of areas, notably when compared to the Gall-Peters projection. Other compromise projections attempt a similar trade-off."
From
http://www.geni.org/globalenergy/shop/geni_products/products.shtml"This map is the world's most accurate global projection. It has at most a 2% distortion at any one place."
From
http://users.design.ucla.edu/~djvmc/24/bucky/map.html"Like all flat maps, it evidences the distortions that result from the translation of the three-dimensional surface of a sphere to a flat plane. Its distortions, however, are distributed proportionately within each of its 14 segments and are nowhere extreme"
And here's a nifty site that will probably tell you more about map projections than you really want to know.
http://www.progonos.com/furuti/MapProj/Normal/TOC/cartTOC.html