The geometry of the tetrahedron and of points on and within it are examined in terms of their application to facies maps. It is shown that any interior point may be projected in five different ways on each of four faces. In addition to point projections, the tetrahedron may be sliced along percentage planes, ratio planes, or combinations of the two to provide facies classes within the tetrahedron. Maps based on such tetrahedral segments present four end members directly. Projections on selected faces provide the basis for some current facies maps, but additional possibilities for "projection facies maps" can be explored by using other projected points. Several experimental maps of the same data are presented to indicate different ways in which maps may be designed to emphasize various characteristics of stratigraphic units.