Feb., 1916] 



Hexagon Notation 



145 



The three h-points unique to (2), (3), (4) are: 

 'aef, cdbl (5) fcab, efd] (7) feed, abf] (9) 



efa, bcd,^ (1) M ; <| abc, def ^ (1) (h.s) ; <| cde, f ab ^ (1) (h4) 

 ^fae, dbcj (6) [bca, fdej (8) [dec, bfaj (10) 



These all contain (1). 



(39) The ten hexagons in {38) are a Veronese group. 



In such a group there are ten h-points, on ten Pascal lines, 

 three h-points on each Pascal line, three Pascal lines through 

 each h-point; at each h-point two triangles in perspective, their 

 vertices h-points, their sides Pascal lines; the axis of perspective 

 being for each point the Pascal of the hexagon unique to the 

 center of the perspective. It is a group of ten Pascal lines and 

 their ten unique h-points. 



(40) Geometric relation between an h-point and its unique 

 hexagon. 



None of the hexagons, 2, 3, 4, in hi in 38 enter into the 

 h-points on the Pascal of abcdef (1), unique to (2, 3, 4). Thus 

 hi is the center of perspective and the Pascal of (1) the axis 

 of perspective for the two h-point triangles whose corresponding 

 sides are 5, 6; 7, 8; 9, 10. 



In the accompanying figure, the unique h-points and Pascals 

 are numbered as II, 2; IV, 4; etc., giving ten centers of perspec- 

 tive, ten axes of perspective; for each center a pair of triangles 

 in perspective. 



Tn: 



Fig. 1. A Veronese group as in 38 and 40. Ten such groups. 



