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

Get a point inside the cube
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$c\u2254\mathrm{ExampleSets}:\mathrm{Cube}\left(\right)\:$$p\u2254\mathrm{InteriorPoint}\left(c\right)$

${p}{\u2254}\left[{0}{\,}{0}{\,}{0}\right]$
 (1) 
For a 2D triangular set in 3D space, the command returns a point which is interior to the triangle, but lies on the boundary of the set strictly speaking.
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$\mathrm{triangle}\u2254\mathrm{PolyhedralSet}\left(\left[z=1\,1\le y\,1\le x\,x\le y+1\right]\,\left[x\,y\,z\right]\right)$

${\mathrm{triangle}}{\u2254}{\{}\begin{array}{lll}{\mathrm{Coordinates}}& {\:}& \left[{x}{\,}{y}{\,}{z}\right]\\ {\mathrm{Relations}}& {\:}& \left[{z}{=}{1}{\,}{}{y}{\le}{1}{\,}{}{x}{\le}{1}{\,}{x}{+}{y}{\le}{1}\right]\end{array}$
 (2) 
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$p\u2254\mathrm{InteriorPoint}\left(\mathrm{triangle}\right)$

${p}{\u2254}\left[{0}{\,}{0}{\,}{1}\right]$
 (3) 
The point lies on a 2 dimensional set, while the set is in a 3 dimensional space.
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$\mathrm{face\_with\_p}\u2254\mathrm{LocatePoint}\left(p\,\mathrm{triangle}\right)$

${\mathrm{face\_with\_p}}{\u2254}{\{}\begin{array}{lll}{\mathrm{Coordinates}}& {\:}& \left[{x}{\,}{y}{\,}{z}\right]\\ {\mathrm{Relations}}& {\:}& \left[{z}{=}{1}{\,}{}{y}{\le}{1}{\,}{}{x}{\le}{1}{\,}{x}{+}{y}{\le}{1}\right]\end{array}$
 (4) 
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$\mathrm{Dimension}\left(\mathrm{face\_with\_p}\right)$

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$\mathrm{nops}\left(\mathrm{Coordinates}\left(\mathrm{face\_with\_p}\right)\right)$
