We have all heard that the earth is not exactly a sphere but more of an oblate spheroid due to the flattening of the earth at its north and south extremities. The flat part of the earth's polar regions is, in actuality, due to the absence of material where the openings exist at the poles. Many have often conjectured what the actual dimensions of the openings may be. With the known polar diameter of the earth, and its difference from the equatorial diameter, we can calculate (with a few assumptions) the size of the openings. Allow me to demonstrate:
1. Equatorial radius of the earth: 3963.34 mi
2. Polar radius of the earth: 3949.99 mi
3. Distance from top of polar opening rim to opposite rim: 650 mi
distance = 2 * ((equatorial radius)^2 - (polar radius)^2)^0.5
4. Approximate crust thickness at equator: 800 mi
5. Approximate crust thickness at pole: 400 to 600 miles (you choose)
6. Approximate polar opening: 250 miles (for crust thickness at poles of 400 mi) to 50 miles (for crust thickness at poles of 600 mi)*
polar opening = 650mi - 2 * (polar crust thickness / 2)
* If the crust thins to a mere 200 miles at the poles, then the opening would be 450 miles for a theoretical range of 50 to 450 miles for the size of the polar opening.
My approximation is that the opening at its narrowest point is most likely 50 to 80 miles wide.