A parallelepiped is a polyhedron bounded by six parallelograms. It can be defined from three given directed segments having a common initial point.

To access the information related to a parallelepiped pp, use the following function calls:

This function is part of the geom3d package, and so it can be used in the form parallelepiped(..) only after executing the command with(geom3d). However, it can always be accessed through the long form of the command by using geom3d[parallelepiped](..).

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

$\mathrm{point}\left(A\,0\,0\,0\right),\mathrm{point}\left(B\,4\,0\,0\right),\mathrm{point}\left(C\,5\,5\,1\right),\mathrm{point}\left(E\,0\,2\,5\right)\:$

$\mathrm{dsegment}\left(\mathrm{d1}\,\left[A\,B\right]\right),\mathrm{dsegment}\left(\mathrm{d2}\,\left[A\,C\right]\right),\mathrm{dsegment}\left(\mathrm{d3}\,\left[A\,E\right]\right)\:$

$\mathrm{parallelepiped}\left(\mathrm{pp}\,\left[\mathrm{d1}\,\mathrm{d2}\,\mathrm{d3}\right]\right)$

$\mathrm{pp}$

$\mathrm{form}\left(\mathrm{pp}\right)$

$\mathrm{parallelepiped3d}$

$\mathrm{DefinedAs}\left(\mathrm{pp}\right)$

$\left[\mathrm{d1}\,\mathrm{d2}\,\mathrm{d3}\right]$

$\mathrm{detail}\left(\mathrm{pp}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{pp}\\ \text{form of the object}& \mathrm{parallelepiped3d}\\ \text{the 6 parallelogram faces of the object}& \left[\left[\left[0\,0\,0\right]\,\left[4\,0\,0\right]\,\left[9\,5\,1\right]\,\left[5\,5\,1\right]\right]\,\left[\left[0\,2\,5\right]\,\left[4\,2\,5\right]\,\left[9\,7\,6\right]\,\left[5\,7\,6\right]\right]\,\left[\left[0\,0\,0\right]\,\left[4\,0\,0\right]\,\left[4\,2\,5\right]\,\left[0\,2\,5\right]\right]\,\left[\left[4\,0\,0\right]\,\left[9\,5\,1\right]\,\left[9\,7\,6\right]\,\left[4\,2\,5\right]\right]\,\left[\left[5\,5\,1\right]\,\left[9\,5\,1\right]\,\left[9\,7\,6\right]\,\left[5\,7\,6\right]\right]\,\left[\left[0\,0\,0\right]\,\left[5\,5\,1\right]\,\left[5\,7\,6\right]\,\left[0\,2\,5\right]\right]\right]\\ \text{coordinates of the 8 vertices}& \left[\left[0\,0\,0\right]\,\left[4\,0\,0\right]\,\left[5\,5\,1\right]\,\left[9\,5\,1\right]\,\left[0\,2\,5\right]\,\left[4\,2\,5\right]\,\left[5\,7\,6\right]\,\left[9\,7\,6\right]\right]\end{array}$