gtetrahedron - Maple Help

geom3d

 gtetrahedron
 define a general tetrahedron

 Calling Sequence gtetrahedron(T, gv)

Parameters

 T - name; tetrahedron gv - list; four points or planes that define a tetrahedron

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,1,0,0\right),\mathrm{point}\left(C,0,0,1\right),\mathrm{point}\left(F,0,1,0\right):$
 > $\mathrm{gtetrahedron}\left(\mathrm{T1},\left[A,B,C,F\right]\right)$
 ${\mathrm{T1}}$ (1)
 > $\mathrm{detail}\left(\mathrm{T1}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{T1}}\\ {\text{form of the object}}& {\mathrm{gtetrahedron3d}}\\ {\text{the 4 vertices}}& \left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{1}{,}{0}{,}{0}\right]{,}\left[{0}{,}{0}{,}{1}\right]{,}\left[{0}{,}{1}{,}{0}\right]\right]\\ {\text{the 4 faces}}& \left[\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{1}{,}{0}{,}{0}\right]{,}\left[{0}{,}{0}{,}{1}\right]\right]{,}\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{1}{,}{0}{,}{0}\right]{,}\left[{0}{,}{1}{,}{0}\right]\right]{,}\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{0}{,}{0}{,}{1}\right]{,}\left[{0}{,}{1}{,}{0}\right]\right]{,}\left[\left[{1}{,}{0}{,}{0}\right]{,}\left[{0}{,}{0}{,}{1}\right]{,}\left[{0}{,}{1}{,}{0}\right]\right]\right]\end{array}$ (2)
 > $\mathrm{volume}\left(\mathrm{T1}\right)$
 $\frac{{1}}{{6}}$ (3)
 > $\mathrm{_EnvXName}≔'x':$$\mathrm{_EnvYName}≔'y':$$\mathrm{_EnvZName}≔'z':$
 > $\mathrm{plane}\left(\mathrm{p1},x+y+z=1\right),\mathrm{plane}\left(\mathrm{p2},x=0\right),\mathrm{plane}\left(\mathrm{p3},y=0\right),\mathrm{plane}\left(\mathrm{p4},z=0\right):$
 > $\mathrm{gtetrahedron}\left(\mathrm{T2},\left[\mathrm{p1},\mathrm{p2},\mathrm{p3},\mathrm{p4}\right]\right)$
 ${\mathrm{T2}}$ (4)
 > $\mathrm{detail}\left(\mathrm{T2}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{T2}}\\ {\text{form of the object}}& {\mathrm{gtetrahedron3d}}\\ {\text{the 4 vertices}}& \left[\left[{0}{,}{0}{,}{1}\right]{,}\left[{0}{,}{1}{,}{0}\right]{,}\left[{1}{,}{0}{,}{0}\right]{,}\left[{0}{,}{0}{,}{0}\right]\right]\\ {\text{the 4 faces}}& \left[\left[\left[{0}{,}{0}{,}{1}\right]{,}\left[{0}{,}{1}{,}{0}\right]{,}\left[{1}{,}{0}{,}{0}\right]\right]{,}\left[\left[{0}{,}{0}{,}{1}\right]{,}\left[{0}{,}{1}{,}{0}\right]{,}\left[{0}{,}{0}{,}{0}\right]\right]{,}\left[\left[{0}{,}{0}{,}{1}\right]{,}\left[{1}{,}{0}{,}{0}\right]{,}\left[{0}{,}{0}{,}{0}\right]\right]{,}\left[\left[{0}{,}{1}{,}{0}\right]{,}\left[{1}{,}{0}{,}{0}\right]{,}\left[{0}{,}{0}{,}{0}\right]\right]\right]\end{array}$ (5)