The latitude where a tetrahedron intersects a sphere if the tetrahedron fits perfectly inside the sphere is 19.47 degrees north or south depending on the orientation of the tetrahedron.
At this latitude one finds lines of increased activity on the surface of the sphere. For example, the Big Island of Hawaii is both the largest active volcano and the largest mountain on Earth (taller than Mt. Everest when measured from the sea floor to summit) and sits exactly at 19.47 degrees north.
Dolphins and whales go to the bays on either side of the Big I. to give birth exactly at 19.47 degrees. There is increased sun spot activity on the Sun at 19.47 degrees, the Big Red Spot vorticular storm has stayed at 19.47 degrees on Jupiter ever since humans first observed it over 350 years ago and as well, anomalies occur in triangular areas on Earth at 19.47 degrees north and south.
Most people are familiar with the The Bermuda Triangle, however there are many other areas where unexplained phenomenon have been occurring for decades including the somewhat known Devil's Triangle south of Japan. Notice where the triangle is off the western coast of Australia...