Procedure for constructing acyclic chemical networks is delineated through the example of polyenoids, CNHN+2. Chirality in two-dimensional space is introduced to enumerate polyenoids. Cis-trans dichotomies, each arising from a 2D chiral center, are stacked to form stereoisomers. Redundancy caused by rotating the molecular plane in 3D space is eliminated to obtain the net count of isomers.