A mosaic is a geometric composition of figures that cover the plane in such a way that the entire plane is filled without leaving a gap and there are no overlaps.
Depending on their composition, there are different types of mosaics:
Regular mosaic
A regular mosaic is a mosaic that consists of only one type of regular polygon:
Regular mosaic
A regular mosaic is a mosaic that consists of only one type of regular polygon:
- All polygons have the same side.
- At each vertex of the mosaic there will be a vertex of the polygon.
- All polygons have the same side.
- At each vertex of the mosaic there will be a vertex of the polygon.
Semi-regular mosaics
Semi-regular mosaics are those formed by more than one type of regular polygons.
With mosaics, both regular and semi-regular, we can form various abstract o real figures and compositions:
A clear example of mosaics in famous monuments is the Alhambra. Here, two orders of ceramic wall coverings can be observed:
Semi-regular mosaics
Semi-regular mosaics are those formed by more than one type of regular polygons.
With mosaics, both regular and semi-regular, we can form various abstract o real figures and compositions:
A clear example of mosaics in famous monuments is the Alhambra. Here, two orders of ceramic wall coverings can be observed:
- Mosaics where one or more elements are repeated, generally made by moulding, to cover a surface in a periodic manner, there being a basic figure whose translation on two axes produces the whole.
- Mosaics where one or more elements are repeated, generally made by moulding, to cover a surface in a periodic manner, there being a basic figure whose translation on two axes produces the whole.
- Tilings where a generating element cannot be isolated, as successive procedures of scale, rotation, level jumps are involved, which make an indivisible whole.
- Tilings where a generating element cannot be isolated, as successive procedures of scale, rotation, level jumps are involved, which make an indivisible whole.
The Alhambra in Granada is the only monument in the world that contains all 17 possible planar crystallographic groups.
The Alhambra was built between the 14th and 15th centuries and it was not until four centuries later when Evgraf Fedorov, a Russian mathematician, listed in 1891 the list of plane crystallographic groups that represent the description of the symmetry of crystalline structures in 2 dimensions (plane symmetry) with which a plane can be "papered" and repeated following certain symmetry rules.
The 17 groups of plane symmetry can be grouped into five sections, according to the maximum order of the rotations:
- Symmetry groups with no twists: 4 symmetry groups.
- Symmetry groups with 180° turns: 5 symmetry groups.
- Symmetry groups with 120° turns: 3 symmetry groups.
- Symmetry groups with 90° turns: 3 symmetry groups.
- Symmetry groups with 60° turns: 2 symmetry groups.
- Symmetry groups with no twists: 4 symmetry groups.
- Symmetry groups with 180° turns: 5 symmetry groups.
- Symmetry groups with 120° turns: 3 symmetry groups.
- Symmetry groups with 90° turns: 3 symmetry groups.
- Symmetry groups with 60° turns: 2 symmetry groups.
REFERENCES:
- Casel, M. (19 de julio de 2016). Los mosaicos y la geometría de la Alhambra. LegadoNazaríBlog. http://legadonazari.blogspot.com/2016/07/los-mosaicos-y-la-geometria-de-la.html
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