The gtetrahedron(T,gv) function defines a tetrahedron from the four vertices or planes gv.

For more details on the tetrahedron T, use geom3d[detail].

The command with(geom3d,gtetrahedron) allows the use of the abbreviated form of this command.

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

$\mathrm{point}\left(A\,0\,0\,0\right),\mathrm{point}\left(B\,1\,0\,0\right),\mathrm{point}\left(C\,0\,0\,1\right),\mathrm{point}\left(F\,0\,1\,0\right)\:$

$\mathrm{gtetrahedron}\left(\mathrm{T1}\,\left[A\,B\,C\,F\right]\right)$

$\mathrm{T1}$

$\mathrm{detail}\left(\mathrm{T1}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{T1}\\ \text{form of the object}& \mathrm{gtetrahedron3d}\\ \text{the 4 vertices}& \left[\left[0\,0\,0\right]\,\left[1\,0\,0\right]\,\left[0\,0\,1\right]\,\left[0\,1\,0\right]\right]\\ \text{the 4 faces}& \left[\left[\left[0\,0\,0\right]\,\left[1\,0\,0\right]\,\left[0\,0\,1\right]\right]\,\left[\left[0\,0\,0\right]\,\left[1\,0\,0\right]\,\left[0\,1\,0\right]\right]\,\left[\left[0\,0\,0\right]\,\left[0\,0\,1\right]\,\left[0\,1\,0\right]\right]\,\left[\left[1\,0\,0\right]\,\left[0\,0\,1\right]\,\left[0\,1\,0\right]\right]\right]\end{array}$

$\mathrm{volume}\left(\mathrm{T1}\right)$

$\frac{1}{6}$

$\mathrm{\_EnvXName}≔'x'\:$$\mathrm{\_EnvYName}≔'y'\:$$\mathrm{\_EnvZName}≔'z'\:$

$\mathrm{plane}\left(\mathrm{p1}\,x+y+z=1\right),\mathrm{plane}\left(\mathrm{p2}\,x=0\right),\mathrm{plane}\left(\mathrm{p3}\,y=0\right),\mathrm{plane}\left(\mathrm{p4}\,z=0\right)\:$

$\mathrm{gtetrahedron}\left(\mathrm{T2}\,\left[\mathrm{p1}\,\mathrm{p2}\,\mathrm{p3}\,\mathrm{p4}\right]\right)$

$\mathrm{T2}$

$\mathrm{detail}\left(\mathrm{T2}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{T2}\\ \text{form of the object}& \mathrm{gtetrahedron3d}\\ \text{the 4 vertices}& \left[\left[0\,0\,1\right]\,\left[0\,1\,0\right]\,\left[1\,0\,0\right]\,\left[0\,0\,0\right]\right]\\ \text{the 4 faces}& \left[\left[\left[0\,0\,1\right]\,\left[0\,1\,0\right]\,\left[1\,0\,0\right]\right]\,\left[\left[0\,0\,1\right]\,\left[0\,1\,0\right]\,\left[0\,0\,0\right]\right]\,\left[\left[0\,0\,1\right]\,\left[1\,0\,0\right]\,\left[0\,0\,0\right]\right]\,\left[\left[0\,1\,0\right]\,\left[1\,0\,0\right]\,\left[0\,0\,0\right]\right]\right]\end{array}$