Quadrilaterals

Square

Sides: Four equal sides, all four angles are equal (900). A square is therefore a regular quadrilateral. Symmetry: Four lines, rotational order 4.

The section will be split into two sections and the axis of symmetry is in x-axis means that the section will be symmetric about x-axis. This will imply that the divided parts will be mirror image of each other about the x-axis.

Point Symmetry is when every part has a matching part: the same distance from the central point. but in the opposite direction.

Basically, a figure has point symmetry when it looks the same when up-side-down, (rotated 180º), as it does right-side-up. on the figure there is another point directly opposite and at the same distance from the center. (Point symmetry can also be described as rotational symmetry of 180º or Order 2.)

Point symmetry exists when the figure is drawn around a single point. We say that the figure is symmetry about the centre. Note: When we rotate a figure about 180° and it regains its originals shape, then we say that point symmetry exists in the figure.

Crystals do appear to have 5-fold symmetry but these symmetries are not possible. In fact, when we try to combine objects with 5-fold and 8-fold apparent symmetry, we can’t combine to fill the space completely. Therefore, crystals cannot have 5, 7, 8, and other higher-fold rotational axes.

 5-fold symmetry is not allowed in crystals. This does not imply that this is the reason (for the fact) that crystals cannot have 5-fold symmetry. E.g. A regular tetrahedron cannot tile space monohedrally; however, tetrahedral symmetry (23) is observed in crystals!

In hexagonal system. …a single line, called an axis of 6-fold symmetry, about which the cell can be rotated by either 60° or 120° without changing its appearance.

3-fold Rotation Axis – Objects that repeat themselves upon rotation of 120o are said to have a 3-fold axis of rotational symmetry (360/120 =3), and they will repeat 3 times in a 360o rotation. A filled triangle is used to symbolize the location of 3-fold rotation axis.

A shape with rotational symmetry is a shape that looks the same even if you turn the shape around a little bit. The Clematis shown has 8-fold rotational symmetry (45 degrees). It has 8 flower petals arranged around the center of the flower.

5 Cubic System

They are cubic, tetragonal, hexagonal (trigonal), orthorhombic, monoclinic, and triclinic. Seven-crystal system under their respective names, Bravias lattice.

The triclinic lattice is the least symmetric of the 14 three-dimensional Bravais lattices. It has (itself) the minimum symmetry all lattices have: points of inversion at each lattice point and at 7 more points for each lattice point: at the midpoints of the edges and the faces, and at the center points.

The fourteen Bravais lattices

• Cubic (3 lattices) The cubic system contains those Bravias lattices whose point group is just the symmetry group of a cube.
• Tetragonal (2 lattices)
• Orthorhombic (4 lattices)
• Monoclinic (2 lattices)
• Triclinic (1 lattice)
• Trigonal (1 lattice)
• Hexagonal (1 lattice)

The 7 crystal systems are listed in Table 1 below. In the lowest symmetry system, triclinic, there are no restrictions on the values of the cell parameters. In the other crystal systems, symmetry reduces the number of unique lattice parameters as shown in the Table.

Copper sulfate makes triclinic crystals. It is the least symmetric (meaning that both sides are not very similar).

Copper sulfate is an inorganic compound that combines sulfur with copper. It can kill bacteria, algae, roots, plants, snails, and fungi. Copper is an essential mineral. It can be found in the environment, foods, and water.

blue

CuSO4