Mathematical exploration
of the Vichten Roman Mosaic

Vichten mosaic

The mosaic is on display at the Musée National d'Histoire et d’Art Luxembourg (MNHA).

Look here for a picture.

What do you see, mathematically?

Regular octagons, half square triangles, squares, pentagons (squares with a broken corner), eight-pointed stars,...
Comment: The question "Which polygons do you see?" allows for different answers. Some may choose to list only the smallest figures (disjoint pieces).

Rotational symmetry (90 degrees), two perpendicular symmetry axes, central symmetry.


Comment: Drawing an exact picture requires some mathematical considerations. For example, to draw the central star, with the computer you may easily rotate the central square. On paper you would rather mark the intersection points between the two central squares, and this requires a computation.

Shapes and size

Look here for the mathematical representation of the central part of the mosaic.
regular octagon octagon

In the former octagon you don't have a regular grid. In the latter octagon you break larger square corners.

Further explorations/Oncoming