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The Dihedral system is a graphical representation method that lets us represent three-dimensional objects (3D) on a two-dimensional plane (2D), such as a sheet of paper or a screen.
It was developed by the French mathematician Gaspard Monge in the 18th century and it is the basis of Descriptive Geometry, essential in engineering, architecture and industrial design.
Applications: Architectural drawings, mechanical part design, layout of installations, cartography, and any precise technical representation.
The dihedral system uses two mutually perpendicular planes that divide space into four regions called quadrants:
It is the frontalplane, like a wall in front of us. On it we project the vertical projection of the objects, which shows us the cota (height Z) and the horizontal position (X).
The vertical projection of a point P is written as P'' (P with two primes).
It is the groundplane, horizontal like a table. On it we project the proyección horizontal, which shows us the distance (depth Y) and the horizontal position (X).
The horizontal projection of a point P is written as P' (P with one prime).
It is the intersection of the two planes. It is drawn as a horizontal line with two small perpendicular strokes at the ends. It is the X axis.
The height (Z) tells whether the point is above or below the PH; the distance (Y), whether it is in front of or behind the PV. Those two signs name the four quadrants:
| Quadrant | Height | Distance | How the projections look |
|---|---|---|---|
| I | + | + | on opposite sides of the ground line: P′ below and P″ above |
| II | + | − | both above the ground line |
| III | − | − | on opposite sides: P′ above and P″ below |
| IV | − | + | both below the ground line |
Special cases:
Every point in space is defined by three coordinates: notation P(X, Y, Z).
A has three coordinates: x (along the ground line), y (distance) and z (height). Here A(0, 4, 6).