Abstract: The invention relates to an air-compressing internal combustion engine, comprising at least one piston (1) having a combustion chamber trough (3) substantially rotationally symmetrical to a piston axis (2), which has a trough bottom (4) with a substantially cone-like elevation (5) and a circumferential trough wall (6), wherein the trough wall (6) forms a substantially torus-like first section (6a) having a maximum inner first trough diameter (d1), a second section (6b) having a minimum inner second trough diameter (d2) smaller than the inner first trough diameter (d1), and a third section (6c), wherein—as seen in a meridian section of the piston (1)—the first section (6a) has a concave first radius of curvature (R1) and the second section (6b) has a convex second radius of curvature (R2), and wherein the third section (6c) forms a first annular surface (8) adjoining the second section (6b) and a second annular surface (9) terminating in the piston end surface (7), which second annular surface (9) defines an a