Pensieve header: Drawing prisms for the prism construction.

θ=2π/3;
f0={1,0,0}; f1={Cos[θ],Sin[θ],0}; f2={Cos[2θ],Sin[2θ],0}; 
g0={1,0,3}; g1={Cos[θ],Sin[θ],3}; g2={Cos[2θ],Sin[2θ],3}; 
σ0=Simplex[{f0,g0,g1,g2}];  σ1=Simplex[{f0,f1,g1,g2}];  σ2=Simplex[{f0,f1,f2,g2}];
Shrink[r_][Simplex[{v0_,v1_,v2_,v3_}]] := Module[
{c=(v0+v1+v2+v3)/4},
Simplex[{c+r(v0-c), c+r(v1-c), c+r(v2-c), c+r(v3-c)}]
];
specs={ImageSize->{279.995,458.154},ImageSizeRaw->Automatic,ViewPoint->{-1.99788,-2.3842,1.33194},ViewVertical->{-0.369604,-0.292044,0.97364}};
GraphicsRow[{
Graphics3D[{σ0, σ1, σ2}, specs],
Graphics3D[{Opacity[0.7], Shrink[0.7] /@ {σ0, σ1, σ2}}, specs]
}]