Word for half-hemisphere / quarter-sphere?

Solution 1:

There is no such term. You could use semihemisphere, but this is not a geographical term as far as I'm aware. Evidence of absence is always difficult and doesn't make a rewarding answer.

I would suggest a different term altogether like area or region. If you insist on the "quarter of the earth" sense, then quadrant would fit your needs.

Carlo_R has an interesting point, but quadrant is in use, geographically, and is a word that most speakers will glean meaning from. Some examples include "Mapping World Heritage Sites":

Use a dry erase marker to draw, or have a volunteer draw, the Equator and prime meridian. Then label each quadrant of the map with its hemispheric identifier: NE, NW, SE, and SW.

"Geographic Coordinate System":

The origin of the graticule (0,0) is defined by where the equator and prime meridian intersect. The globe is then divided into four geographical quadrants that are based on compass bearings from the origin. North and south are above and below the equator, and west and east are to the left and right of the prime meridian.

Earth quadrant from Webster's (1913):

n. a fourth of the earth's circumference.

Solution 2:

Why do you assume South West hemisphere is not correct? A sphere can be divided in half along any diameter, not just the Equator or zero meridian. I don't (obviously) know the original report, but it may easily be that the ESA meant the half of the world including Mexico and South Africa, but excluding Canada and Sri Lanka.

Solution 3:

There may be no official word for this in Geometry, but borrowing from semihemidemisemiquaver, a 1\128th note in music, you might use:

semihemisphere

Solution 4:

If you want what would amount to one of eight pieces (rather than four) in three dimensions, and one of 2^n th in n dimensions, in mathematics, the term for the higher dimensional analogues of quadrant is orthant. This means—for three dimensions—one of the eight subsets, each consisting of triples with the same sign pattern. So you could say an orthant of the sphere, and anyone who knows the more general meaning of orthant would understand immediately.

Perhaps, bi-orthant (a set consisting of two, presumably contiguous, orthants) of a sphere would be what you want.