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\title{Geometry Seminar\\
        Tuesday Oct 10 in room 613 WWH at 6:00 P.M\\
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        {\bf
Some Aperiodic Species of tilings of $ E^3$
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\author{
Ludwig Danzer\\ Dortmund University
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\begin{center}{\bf Summary}\end{center}
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The interest in aperiodic tilings arose from the detection of quasicrystals
in 1984. The talk will deal with four different species of  such tilings,
the prototiles being
\begin{itemize}
\item the two Kowslewski-(Aumann-) parallelotopes,
\item the four Socolar-Steinhardt rhombohedra,
\item the four tetrahedra $A, B,C, K$ and
\item the $SCD$ (a biprism).
\end{itemize}

The first three are based on icosahedral symmetry (the third being 
equivalent to the second), while the last one has a single prototile 
only and does  not even tile $E^3$ in a quasiperiodic manner.

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