According to the whimsical and delightful book by Jean Pierre Petit "Le Topologicon", it can be pictured as a planet with only a single pole (the "south" pole would be on the inside immediadely below the north pole on the "other side" of the single-sided surface).
Meridian strips leading from the north pole to the south pole and back form single sided Moebius bands:
THREE MOEBIUS BANDS THROUGH THE POLES - - - - - - - - MERIDIAN LINES
Similarly an equatorial band also forms a (triply twisted) Moebius band:
EQUATORIAL BAND - - - - - - - - - - - - - - - - - - - - - - - - - - "PARALLEL CONTOURS"
Sometimes it is easier to visualize this surface in a "cubist" realization
-- and it is definitely easier to make a cardboard model in this form:
T = TRIPLE POINT; - - - - - - - - - - - - - - - - - - - - - - - - - - - - P = POLE.
<-- Up to CS 294-3 HomePage