Polyhedron is the 3-D solid that consist of collective faces which are joined at the edges for example- a cube. The polyhedra’s Euler’s formula is an easy but extraordinary statement: -

If the numbers of edges (E), Vertices (V) and the faces (F) are counted, it shows that F-E+V=2. This formula seems very easy but has done wonders in the various fields. It changed the perceptions of mathematicians, encouraging the enhancements of a novel type of geometry i.e., topology.

In case of topology the known concepts like angles and lengths have no roles and the distinctions are not made between the circles, squares and triangles. Lines can stretch or bend. However, they are not permitted to be ripped apart. If two geometrical figures are given, the question of whether they are same topologically is natural.

This question is surprisingly tough to answer by just looking at the given figure. Thus, this is where Euler’s formula is bought into picture. It can differentiate among the geometric objects by counting the number of vertices, faces and edges. Therefore, if there is a need to seek if a polyhedron is equivalent topologically to another solid. It can be calculated by F-E+V and comparing the results.

Additionally, topology also has various applications in biology. For instance- the pair of spiraled-staircases that winds around together, the pair of strands that creates DNA are intertwined intricately. Molecular biologists and the mathematicians make use of topology in order to analyze the turns and twists and understand how various biological process relies on the geometric structures.