For most small bodies of the Solar System shapes the International Astronomical Union recommends to use a triaxial ellipsoid. Today almost all major classes of cartographic projections for the triaxial ellipsoid have been developed. They require systematization, classification and additional research. The archives of libraries accumulated a significant list of paper maps of the Soviet times which are compiled in projections developed in our country. It is necessary to implement those projections in the PROJ.4 library used by GIS. Distortions in map projections can be defined as deformation of a cell. If we imagine that the sphere is covered with a net of regular hexagons then it is possible to estimate distortions in the projection by their deformation on the plane. Now the majority of cartographers use online calculators to define the values required for mathematical cartography. Programs are usually written in JavaScript and require the user to only enter the initial data. These are only some of the problems facing modern mathematical cartography.