Affine double spaces of order 3 (Q1120122)

Let (P,\({\mathcal L},\|_{\ell},\|_ r)\) be a double space of order 3. It is shown that every prism configuration in P closes. Thus, by the author, \textit{H. J. Kroll} and \textit{K. Sörensen} [J. Reine Angew. Math. 262/263, 153-157 (1973; Zbl 0265.50003)] it has an algebraic representation in terms of a group with kinematic fibration which is given explicitly.