2 thoughts on “A Tessellation Featuring Regular Enneagons and Triangles, as Well as Equilateral Three-Pointed Stars”

This tessellation is very special. It is missing from the two pages of images in the book Tiling and Patterns by Branko Grünbaum and G.C. Shephard (1987) entitled “Figure 2.5.4 Some uniform tilings using regular star polygons. These are probably the only types of such tilings in which not all corners are vertices.” When we look at the centers of rotational symmetry, this tessellation has (3,3,3) symmetry–see centers of triangles, stars and enneagon–which is not shared by any of the Archimedean tilings or any of the other uniform star tilings, many of which have (2,3,6) symmetry.

The notation for the tessellation is (3 . 9 . 3*π/9 . 9). This identifies the shapes around a vertex. All vertices are the same since this is a uniform tessellation. π/9 (should be a subscript) gives the angle of the star point.

This tessellation is very special. It is missing from the two pages of images in the book Tiling and Patterns by Branko Grünbaum and G.C. Shephard (1987) entitled “Figure 2.5.4 Some uniform tilings using regular star polygons. These are probably the only types of such tilings in which not all corners are vertices.” When we look at the centers of rotational symmetry, this tessellation has (3,3,3) symmetry–see centers of triangles, stars and enneagon–which is not shared by any of the Archimedean tilings or any of the other uniform star tilings, many of which have (2,3,6) symmetry.

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The notation for the tessellation is (3 . 9 . 3*π/9 . 9). This identifies the shapes around a vertex. All vertices are the same since this is a uniform tessellation. π/9 (should be a subscript) gives the angle of the star point.

LikeLiked by 1 person