The QAP (quartz-alkali feldspar-plagioclase) diagram is often combined with the FAP (feldspathoid-alkali-feldspar-plagioclase) diagram in this double ternary. It works in this mirror-image way because of the way that the chemical ingredients in a magma must combine into minerals as the magma solidifies. Silica tetrahedra will build minerals that include the alkali elements (Na, K, Ca, Mg) until those elements run out, and only after that will they form quartz (SiO2), which is pure silica. In magmas that are especially rich in alkalis, the silica runs short first, and the mix generates feldspathoid minerals (usually nepheline, leucite or sodalite) to accommodate the excess alkalis. Quartz and feldspathoids, therefore, never coexist except by accident.
This is the typical QAPF double-ternary diagram. It shows how rocks with various combinations of quartz (Q), alkali feldspar (A), plagioclase (P) and feldspathoid (F) are named. The numbers are percentages of quartz (above the middle) or plagioclase (across the middle) or feldspathoid (below the middle). For details on how this diagram works, see the separate QAP diagram and FAP diagram.
The diagram is clear enough, and generations of students and professionals consult it. But I toyed with it, and on the next page I present an alternative version that fits better on a screen.