# The Smallest Projective Space*

## by Steven H. Cullinane

The figures below show a way to visualize the 15 points of the smallest
projective space*, which has 15 points and 35 lines.

If we regard the lines within the squares as nonzero elements in the
two-element field GF(2), then three points are collinear if and only if the
three corresponding squares have inner lines that sum to zero.

The note below, from December 1978, shows how this works.

For related material, see Geometry of the 4x4 Square and
Diamond Theory.
***** "Space" in the sense "point,
line, plane, space...."

Copyright © 2002 by Steven H. Cullinane. All rights reserved. Page
created May 21, 2002.