Bulletin of the Australian Mathematical Society Bull. Austral. Math. Soc. 0004-9727 ALNBAB 2005 72 2 10.wxyz/CV72P2 http://www.austms.org.au/Publ/Bulletin/V72P2/ Günter F. Steinke 14 February 2006 2006 2 14 213 223 722-5079-Steinke-2005 10.wxyz/C2005V72P2p213 http://www.austms.org.au/Publ/Bulletin/V72P2/722-5079-Steinke/ We provide examples of flat Laguerre planes of Kleinewillingh\"ofer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, \textsl {Results Maths.} (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, \textit {Canad. Math. Bull.} (1995) but no examples were given there. 51H15, 51B15 MR2183404 02246385 H. Groh Abh. Math. Sem. Univ. Hamburg MR234343 H. Groh; Topologische Laguerreebenen I., \textit{Abh. Math. Sem. Univ. Hamburg} \textbf{32} (1968), pp.~216--231. H. Groh Abh. Math. Sem. Univ. Hamburg MR257857 H. Groh; Topologische Laguerreebenen II, \textit{Abh. Math. Sem. Univ. Hamburg} \textbf{34} (1970), pp.~11--21. R. Kleinewillinghöfer (Ph.D. Thesis) TH, Darmstadt R. Kleinewillingh\"ofer; \textit{Eine Klassifikation der Laguerre-Ebenen}, (Ph.D. Thesis) (TH, Darmstadt, 1979). R. Kleinewillinghöfer Arch. Math. MR593774 R. Kleinewillingh\"ofer; Eine Klassifikation der Laguerre-Ebenen nach ${L}$-Streckungen und ${L}$-Translationen, \textit{Arch. Math.} \textbf{34} (1980), pp.~469--480. R. Löwen and U. Pfüller Geom. Dedicata MR886776 R. L\"owen and U. Pf\"uller; Two-dimensional Laguerre planes over convex functions, \textit{Geom. Dedicata} \textbf{23} (1987), pp.~73--85. B. Polster and G.F. Steinke Canad. Math. Bull. MR1360598 B. Polster and G.F. Steinke; Cut and paste in 2-dimensional projective planes and circle planes, \textit{Canad. Math. Bull.} \textbf{38} (1995), pp.~469--480. B. Polster and G.F. Steinke J. Austral. Math. Soc. Ser. A MR1427632 B. Polster and G.F. Steinke; The inner and outer space of 2-dimensional Laguerre planes, \textit{J. Austral. Math. Soc. Ser. A} \textbf{62} (1997), pp.~104--127. B. Polster and G.F. Steinke Bull. Austral. Math. Soc. MR1819316 B. Polster and G.F. Steinke; A family of 2-dimensional Laguerre planes of generalised shear type, \textit{Bull. Austral. Math. Soc.} \textbf{61} (2000), pp.~69--83. B. Polster and G.F. Steinke Encyclopedia of Mathematics and its Applications Cambridge University Press MR1889925 B. Polster and G.F. Steinke; \textit{Geometries on Surfaces}, Encyclopedia of Mathematics and its Applications (Cambridge University Press, Cambridge 84, 2001). B. Polster and G.F. Steinke Results Math. MR2093467 B. Polster and G.F. Steinke; On the Kleinewillingh\"ofer types of flat Laguerre planes, \textit{Results Math.} \textbf{46} (2004), pp.~103--122. G.F. Steinke Results Math. MR911473 G.F. Steinke; Semiclassical topological flat Laguerre planes obtained by pasting along a circle, \textit{Results Math.} \textbf{12} (1987), pp.~207--221. G.F. Steinke J. Geom. MR950570 G.F. Steinke; Semiclassical topological flat Laguerre planes obtained by pasting along two parallel classes, \textit{J. Geom.} \textbf{32} (1988), pp.~133--156.