  Given a sextuple of distinct points $A, B, C, D, E, F$ on a conic, arranged
into an array $\left[\begin{array}{ccc} A & B & C F & E & D
\end{array}\right]$, Pascal's theorem says that the points $AE \cap BF, BD \cap
CE, AD \cap CF$ are collinear. The line containing them is called the Pascal of
the array, and one gets altogether sixty such lines by permuting the points. In
this paper we prove that the initial sextuple can be explicitly reconstructed
from four specifically chosen Pascals. The reconstruction formulae are encoded
by some transvectant identities which are proved using the graphical calculus
for binary forms.
