Lines of the projective geometry PG(3,24) with sub-geometry

This analysis is given for just q=2: a partial analysis is given for q=3 elsewhere. The terminology is the same as that used for simpler geometries. The notation is derived from that used then: just the letter and first subscript are meaningful, the other subscripts are arbitrary.

There are secants, there are 3 sorts of tangents, and 8 sorts of exterior line. On the other side, there are 5 sorts of point. There are 5 sorts of plane to match.

The number of points (lines) of each type is given in the first column (row) of the table following.

PG(3,24)
  No 35 1260 210 2520 1344 20160 1680 20160 13440 6720 112 2520
No Name s t11 t12 t2 x0 x11 x12 x21 x22 x3 x4 x5
15 C0 3,7 1,84 1,14 1,168 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0
420 C11 12,1 4,12 0,0 0,0 0,0 1,48 0,0 2,96 1,32 3,48 0,0 6,36
70 C12 2,1 0,0 4,12 0,0 0,0 0,0 1,24 0,0 1,192 0,0 5,8 1,36
2520 C21 0,0 12,1 12,1 8,8 15,8 12,96 12,8 9,72 9,48 6,16 0,0 10,10
1344 C22 0,0 0,0 0,0 8,15 2,2 4,60 4,5 6,90 6,60 8,40 12,1 0,0

The complete design above is a BIBD with λ=1.


Last Updated on 22/02/2004
By D.H.Rees