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The Ohio Journal of Science [Vol. XVI, No. 4, 



(41) To write the six Veronese groups. 



Select the six hexagons of two conjugate g-points and treat 

 each as was (1) in (38). 



(42) A Veronese group may also be sorted out thus: 

 Start with any hexagon abcdef(l). Hold a, c fixed, 



permute all the other letters cyclically (forward) ; then hold 

 c, e fixed; then e, a, giving: 



fa b c d e f (1) 

 I a f c b d e (2) 

 ' a e c f b d (3) 



a d c e f b (4) 

 I c b e d f a (5) 

 i c a e b d f (6) 

 [c f e a b d (7) 



e d a f b c (8) 



e c a d f b (9) 



e b a c d f (10) 



(43) The six Veronese groups may be formed as in (42), 

 by starting with the six lines of two conjugate g-points. 



(44) No two h-points of a Veronese group and no g-point 

 and h-point of such a group are connected by a G-line. These 

 lines tie the difi'erent groups, one h-point from each of three 

 groups, and a g-point from a fourth. 



(45) The ten g-points in any Veronese group lie on five I -lines, 

 four points on each line, two lines through each h-point. {The 

 arrangement of the ordinary five point star, four point star, or 

 three point star). 



Write a b c d e f forwards and backwards as in 



ab, cd, ef (F) 



af, ed, cb (B) 



Form from (F) and (B) two groups as follows: 



'ab, cd, ef (F) 1 faf, ed, cb (B)' 



ab, ef, dc (2) , /* \ J af , cb, de (5) 



ab, dc, fe (3) [ ^ '■ ' | af, de, be (6) 



[ab, fe, cd (4) J [af, be, ed (7) 



Here are seven hexagons in the Veronese group of (42). 

 On writing out the g-points on the Pascals of (Ai), they will 

 be gi, gs, g6, gv of 34; those on the Pascals of (Aa) are gi, gio gg, gs- 



(A2) 



