A parallelepiped is a geometric body.
The Greek word parallēlepípedon derived from the late Latin parallelepipĕdum , which is the closest etymological antecedent of parallelepiped : a geometric body that is limited by six parallelograms and that has its opposite faces parallel and equal.
It should be noted that, in geometry , a body or solid is an object that has the three most important dimensions (height, width and length). In the specific case of the parallelepiped, it is a polyhedron : a body made up of flat surfaces.
What is a parallelepiped
Parallelepipeds, in short, are hexahedrons (polyhedra that have six faces). All of its faces are parallelograms ( quadrilaterals with their opposite sides parallel and equal); Among the parallelograms of the parallelepiped, those that oppose each other are identical and parallel.
Each parallelepiped has eight vertices and twelve edges. Since the vertices are arranged in a pair of parallel planes, the parallelepiped is a prismatoid . The edges, for their part, are parallel and equal in groups of four.
The bricks are parallelepipeds.
Classification according to type
According to their characteristics, it is possible to differentiate between different particular types of parallelepipeds. The parallelepiped whose parallelograms are square is called a cube or regular hexahedron . The parallelepiped formed by rhombuses, meanwhile, is an oblique parallelepiped or rhombohedron , while the parallelepiped made up of rectangles is a rectangular parallelepiped or orthohedron . If all six faces of the parallelepiped are rhomboids, it is a rhombohedron .
We can find parallelepipeds in many everyday situations. A brick , to mention one case, is a parallelepiped: it usually has four rectangles (opposite two by two) and two squares (also opposite each other).
Calculation of the properties of parallelepipeds
The calculations of its properties are relatively more complex than those of a two-dimensional figure, since the parallelliped has three; However, as usually happens in these cases, they rely on the formulas of the two-dimensional universe as a starting point. Take for example the volume, that is, the magnitude that is defined as the three-dimensional extension of a region: to calculate it, you must first find the area of one of its faces (it can be any of them) and then multiply it by the height of the figure starting from it.
The formula that responds to this calculation is expressed as follows: V = A h , where V is the volume, A is the area and h is the height. This is used in most cases, but there is one that considerably simplifies the calculation: the one in which all the faces of the parallelliped are perpendicular to each other. To do this, simply multiply its height, width and length, starting from any of its vertices and measuring the three edges that converge on it.
These lengths are represented by three letters, which give their names to the edges, and the resulting formula is the following: V = wuv . Of course, there is an even simpler case, although it is more related to the previous one than to the first: the cube. Let us not forget that this figure has all its edges of equal extension, just as a square has four identical sides. In this case, it is enough to cub this extension: V = l 3 .
On the other hand, we can affirm that if we understand the three edges that are at the same vertex to be three vectors , then to calculate their volume we can find the mixed product and then, their absolute value: V = |a. (bxc)| . This shows us that the way to study the same geometric figure depends on its particular characteristics, but also on the needs, knowledge and preferences of the person. When transferring this to a computer, the choice of one method or another sometimes depends on how demanding it is on the processor.