Why are there holes at the North and South Poles, and why are there different sizes in the ascending and descending grids?

See the accompanying figure. The Aqua satellite travels along the dashed line marking the center of a scan. When that center point reaches its maximum latitude, the ascending half orbit (green dots) ends, and a new descending half orbit (orange) starts. All orbits will be split at this same latitude, all the ascending orbits will reach the same maximum latitude, and all the descending orbits will reach a different (and higher) maximum latitude. This creates pole holes with different radii. The South Pole is similar, except that ascending and descending are swapped.