What kind of map perserves shape and perserves size?

A map that preserves both shape and size is known as an equidistant map projection. This type of projection maintains distances accurately, allowing for both shape and scale to be represented correctly. However, it's important to note that while some projections can preserve shape (like conformal projections) or size (like equal-area projections), few can do both simultaneously across the entire map. As a result, equidistant projections often compromise on one of these properties to maintain the other.