Rolling up a frieze
A frieze, that is a drawing which keeps repeating through a translation, is here rolled up on a cylinder, paying attention that the length of the base circumference of the cylinder is exactly n times the length of the translation vector (here n=5): we thus get on the decorated cylinder an example of a prismatic 3d symmetry group (that is: all the elements of the group fix a given line).
If, like in this picture, we start from a frieze with symmetry type *∞∞, we get a decorated cylinder with symmetry type *nn.
You can see an other example, among the seven possible cases.
Or you can have a look at the Conway notation in the further information pages.
© matematita
immagine di Riccardo Moschetti
The image belongs to the sections...:
*∞∞ (pm11) (Symmetry)
Friezes ans prismatic groups (Symmetry)
(3D geometry)
(2D geometry)
