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Tilings by regular polygons. II: A catalog of tilings. (English) Zbl 0704.05010
It is assumed that an (edge-to-edge) tiling by regular polygons has, under its symmetry group, v orbits of vertices, t orbits of tiles and e orbits of edges. In the terminology by B. Grünbaum and G. C. Shephard [Tilings and patterns (1987; Zbl 0601.05001)] such a tiling would be called “v-isogonal”, “t-isohedral” and “e-isotoxal” respectively. In connection with a classification of tilings in his part I [Mitt. Math. Semin. Gießen 164, 37-50 (1984; Zbl 0584.05022)] the author gives (on 15 pages) drawings of these tilings: the three “Platonic” tilings $\left(t=1\right)$; the eight “Archimedean” tilings $\left(v=1$, $t>1\right)$; the 20 2-isogonal tilings $\left(v=2\right)$; the 39 3-isogonal tilings $\left(v=3\right)$ which are vertex-homogeneous; the 22 3-isogonal tilings $\left(v=3\right)$ which are not vertex-homogeneous; 65 vertex-homogeneous tilings with $v\ge 4$; the unique tile-homogeneous tiling which is not vertex- homogeneous; the seven tilings with $t=3$ which are not included in the earlier cases.
Reviewer: E.Quaisser

##### MSC:
 05B45 Tessellation and tiling problems 52C20 Tilings in 2 dimensions (discrete geometry) 52C22 Tilings in $n$ dimensions (discrete geometry) 52A10 Convex sets in 2 dimensions (including convex curves)