but my knowledge cannot be made intelligible
to a single one of my countrymen; and I am mocked at
--I, the sole possessor of the truths of Space
and of the theory of the introduction of Light
from the world of three Dimensions--as if I were
the maddest of the mad! But a truce to these painful
digressions: let me return to our homes.

The most common form for the construction of a house
is five-sided or pentagonal, as in the annexed figure.
The two Northern sides RO, OF, constitute the roof,
and for the most part have no doors; on the East is
a small door for the Women; on the West a much larger
one for the Men; the South side or floor is usually doorless.

Square and triangular houses are not allowed,
and for this reason. The angles of a Square
(and still more those of an equilateral Triangle,)
being much more pointed than those of a Pentagon,
and the lines of inanimate objects (such as houses)
being dimmer than the lines of Men and Women,
it follows that there is no little danger
lest the points of a square of triangular house
residence might do serious injury to an inconsiderate
or perhaps absentminded traveller suddenly running against them:
and therefore, as early as the eleventh century of our era,
triangular houses were universally forbidden by Law,
the only exceptions being fortifications, powder-magazines,
barracks, and other state buildings, which is not desirable
that the general public should approach without circumspection.