Question

What map displays our 3-dimension earth on a 2 dimensional surface

Answer 1

All maps tend to do that. Google Maps and OpenStreetMaps, like most Web maps, uses Web Mercater. This projection is unique as even when the world is laid out as a rectangle, the distance between two places on the map can be used to find the distance in real life. Other projections include the spherical Mercater and WGS84.