pentagonal symmetry is present in a molecule but not in crystal why?

Molecular symmetry in chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry as it can predict or explain many of a molecule's chemical properties such as its dipole moment and its allowed spectroscopic transitions (based on selection rules such as the Laporte rule).E 2C5 2C52 5C2 ?h 2S5 2S53 5?v: pentagonal: Example-Ruthenocene. Perfect crystal structures can contain pyramids, cubes, or hexagons, but not pentagons. The five-fold symmetry of a pentagon is impossible to replicate over and over in space to make a conventional crystal. But copper does display five-fold symmetry–as a liquid. Liquid copper, like other metals, is not entirely disordered but forms temporary small-scale structures. X-ray experiments on thin liquid films have suggested the pentagons and the new work confirms those findings with direct measurements on “bulk” samples. The research validates a decades-old prediction and suggests that five-fold symmetry may be widespread in liquid metals. read less

1.The question indicates a misunderstanding of the terminology 'crystal'. Crystals are of course structures made by atoms with certain geometrical regularity. As a matter of fact their symmetrical (in terms of geometry) features can be generally classified into point groups and space groups. 2. Point group speaks of the type of a geometrical symmetry with at least one point fixed. This includes the five fold (same as pentagonal) symmetry mentioned in the question. Basically any molecule (or any object, for that sake) looking same for every one fifth of a complete rotation (ie every 36 degrees rotation) is said to have a five fold symmetry about the mentioned axis.For a simple pentagon this axis is the perpendicular to the plane of the same, passing through its geometrical center. To have an object with more than one axis for five fold symmetry, take a soccer ball and see the three dimensional polyhedra marked on it (follow the line markings on it). This polyhedra is called truncated icosahedron and is comprised of 12 pentagons (not touching each other) surrounded by 20 hexagons. It is left as an exercise to you to find the different five fold axes of symmetry (report to me if you cannot). Warning: With rotational symmetry, don't think the types of point groups are exhausted. 3. Space groups are types of symmetries those are found in structures extending to configuration space (we like them when they are found in one dimensional, 2 dimensional and 3 dimensional space). Bravais lattices are examples for space group. Bravais latices are those structures having any elementary geometric cell when translated periodically will fill the space with no voids. An example (in two dimension) is a square. If [( a real number a) multiplied by (unit vector along X axis] represents one of its sides and [(a) multiplied by (unit vector along Y axis)] represents another side of the same (origin being the vertex where the two sides meet), then it can be seen [(an integer number l) multiplied by the vector representing one of the mentioned sides] plus[(an integer number m ) multiplied by the vector representing the other side], having l and m taking all values ranging from 1 to infinity, generates those vectors (infinitely many), translated through which, the initially considered square will generate a Bravais lattice (2 dimensional) filling the space all the way. It is left to you as an exercise to think of different types of 2 dimensional Bravais lattices (apart from the one we right now imagined). Besides, you can think of 3 dimensional ones too! Exciting enough? There are such crystals which simultaneously form point groups and space groups. Yet again, it is also possible for you to prove pentagon (in 2 dimensional space) cannot form a Bravais lattice, however you try, by translational vectors (defined similarly as above). Hexagon forms one, though counter intuitively, if you are a beginner with these lessons. read less