P3 | bgcolor="#9cf"|1 || || || || || || || bgcolor="#9cf"|1 || bgcolor="#9cf"|1 || bgcolor="#9cf"|1 || || || |- style="border-bottom:2px solid #999;" ! P4 | bgcolor="#9cf"|1 || || || || || || || || || || bgcolor="#9cf"|1 || bgcolor="#9cf"|1 || bgcolor="#9cf"|1 |- ! P5 | || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 || || |- ! P6 | || bgcolor="#9cf"|1 || || || || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 || |- style="border-bottom:2px solid #999;" ! P7 | || bgcolor="#9cf"|1 || || || || || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 |- ! P8 | || || bgcolor="#9cf"|1 || || bgcolor="#9cf"|1 || || || || bgcolor="#9cf"|1 || || || || bgcolor="#9cf"|1 |- ! P9 | || || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 || || || || bgcolor="#9cf"|1 || bgcolor="#9cf"|1 || || |- style="border-bottom:2px solid #999;" ! P10 | || || bgcolor="#9cf"|1 || || || || bgcolor="#9cf"|1 || bgcolor="#9cf"|1 || || || || bgcolor="#9cf"|1 || |- ! P11 | || || || bgcolor="#9cf"|1 || bgcolor="#9cf"|1 || || || || || bgcolor="#9cf"|1 || || bgcolor="#9cf"|1 || |- ! P12 | || || || bgcolor="#9cf"|1 || || bgcolor="#9cf"|1 || || bgcolor="#9cf"|1 || || || || || bgcolor="#9cf"|1 |- ! P13 | || || || bgcolor="#9cf"|1 || || || bgcolor="#9cf"|1 || || bgcolor="#9cf"|1 || || bgcolor="#9cf"|1 || || |} To verify the conditions that make this a projective plane, observe that every two rows have exactly one common column in which 1s appear (every pair of distinct points are on exactly one common line) and that every two columns have exactly one common row in which 1s appear (every pair of distinct lines meet at exactly one point). Among many possibilities, the points P1, P4, P5, and P8, for example, will satisfy the third condition. This example is known as the projective plane of order three. Vector space construction Though the line at infinity of the extended real plane may appear to have a different nature than the other lines of that projective plane, this is not the case. Another construction of the same projective plane shows that no line can be distinguished (on geometrical grounds) from any other. In this construction, each "point" of the real projective plane is the one-dimensional subspace (a geometric line) through the origin in a 3-dimensional vector space, and a "line" in the projective plane