#### 10.9.14 HollowFacet

• HollowFacet( <polyhedron> [, thickness+i*(mode 0/1), inside])
• Description: that macro hollows each facet of the <polyhedron> leaving a <thickness> at the edge (0.25 by default), if <mode> is zero (default value) the cut is done parallel to the edge, if the <mode> is $1$, the cut is done by a polyhedron whose vertices are taken on each edge of a given facet (see example below) . The removed pieces are put in the variable called <inside> if this one is present.

 \begin{texgraph}[name=HollowFacetbis,export=pgf]   view(-5,5,-2.5,2.5), Marges(0,0,0,0), size(7.5),   F:=for z in carre(3-3*i,3+3*i,1) do z,0 od,   theta:=-pi/2,phi:=0, ep:=2,SaveWin(),   view(-5,0,-2.5,2.5),ChangeWinTo([-5-5*i,5+5*i]),   DrawFacet(HollowFacet(F,ep), [color:=lightblue]),   Arrows:=2,Ligne3D([-3+3.25*i,0,(-3+ep/2)+3.25*i,0],0),   Arrows:=0,Label(-3+ep/4+4*i,"ep/2"),   RestoreWin(),SaveWin(),   view(0,5,-2.5,2.5), ChangeWinTo([-5-5*i,5+5*i]),   DrawFacet(HollowFacet(F,ep+i), [color:=lightblue]),   Arrows:=2, Ligne3D([3+3.25*i,0,(3-ep)+3.25*i,0],0),   Arrows:=0,Label(3-ep/2+4*i,"ep"),   RestoreWin(),   Label(-2.5-2*i,"mode=0"), Label(2.5-2*i,"mode=1")   \end{texgraph}

(HollowFacet) mode values

 \begin{texgraph}[name=HollowFacet, export=pgf]   ModelView(central), Marges(0,0,0,0), size(7.5),   background(full,darkblue),   P:=Parallelep(M(-2.5,-2.5,-2.5), 5*vecI,                 5*vecJ, 5*vecK), nb:=15,   Y:=[1,1,0], R:=[1,0,0],   Build3D(       for k from 1 to nb do         P:=HollowFacet(P, 0.25+i, aux),         C:=((nb-k+1)*R+(k-1)*Y)/nb,         bdFacet(P, [color:=RgbL(C)]),         P:=aux, sep3D       od),   Display3D()   \end{texgraph}

HollowFacet: example