  \noindent The algebraic characterization of classes of locally isomorphic
aperiodic tilings, being examples of quantum spaces, is conducted for a certain
type of tilings in a manner proposed by A. Connes.
  These $2$-dimensional tilings are obtained by application of the strip method
to the root lattice of an $ADE$-Coxeter group.
  The plane along which the strip is constructed is determined by the canonical
Coxeter element leading to the result that a $2$-dimensional tiling decomposes
into a cartesian product of two $1$-dimensional tilings.
  The properties of the tilings are investigated, including selfsimilarity, and
the determination of the relevant algebraic invariant is considered, namely the
ordered $K_0$-group of an algebra naturally assigned to the quantum space.
  The result also yields an application of the $2$-dimensional abstract gap
labelling theorem.
