Some time ago I made 2 sketches of Gear Corner Turning Octahedron and asked the community what version they'd prefer to be built. Most said that the one with central face elements would be better. So, here it is.
All gears (corners and edges) have the same angular diameter and 8 teeth, but due to their different nature they turn differently. The geared basement under the moving layer has 20 teeth, so after one full turn-around all involved gears flip by 180°. This repeated again, brings the puzzle to the original state.
This design has a deep and secure gears interconnection and never skips gears (at least I could not do this when I intentionally tried).