dash={0.02,0.023};
H = 1.5; (* height of graph; for to scale, set H=2Pi *)
box={
{Dashing[dash],Line[{{0,0,0},{0,0,H}}]},
{Dashing[dash],Line[{{1,0,0},{1,0,H}}]},
{Dashing[dash],Line[{{1,1,0},{1,1,H}}]},
{Dashing[dash],Line[{{0,1,0},{0,1,H}}]},
(* bottom *)
{Dashing[dash],Line[{{0,0,0},{1,0,0}}]},
{Dashing[dash],Line[{{0,0,0},{0,1,0}}]},
{Dashing[dash],Line[{{1,0,0},{1,1,0}}]},
{Dashing[dash],Line[{{0,1,0},{1,1,0}}]},
{Dashing[dash],Line[{{0,1,0},{1,1,0}}]},
(* top *)
{Dashing[dash],Line[{{0,0,H},{1,0,H}}]},
{Dashing[dash],Line[{{0,0,H},{0,1,H}}]},
{Dashing[dash],Line[{{1,0,H},{1,1,H}}]},
{Dashing[dash],Line[{{0,1,H},{1,1,H}}]},
{Dashing[dash],Line[{{0,1,H},{1,1,H}}]}
};

ptsSize = 12;
SingularSetTE = 
{
{Thick,Line[{{1/2,1/2,0},{1/2,1/2,H}}]},
{AbsolutePointSize[ptsSize], Point[{0,0,0}]},
{AbsolutePointSize[ptsSize], Point[{0,1,0}]},
{AbsolutePointSize[ptsSize], Point[{1,1,0}]},
{AbsolutePointSize[ptsSize], Point[{1,0,0}]},
{AbsolutePointSize[ptsSize], Point[{0,0,H/2}]},
{AbsolutePointSize[ptsSize], Point[{0,1,H/2}]},
{AbsolutePointSize[ptsSize], Point[{1,1,H/2}]},
{AbsolutePointSize[ptsSize], Point[{1,0,H/2}]},
{AbsolutePointSize[ptsSize], Point[{0,0,H}]},
{AbsolutePointSize[ptsSize], Point[{0,1,H}]},
{AbsolutePointSize[ptsSize], Point[{1,1,H}]},
{AbsolutePointSize[ptsSize], Point[{1,0,H}]}
};

gTE=Graphics3D[{box, SingularSetTE},Boxed->False,ImageSize->{306.2921514890229`,415.85980538787715`},ViewPoint->{28.649631508956674`,-14.636805932332045`,10.486301850521295`},ViewVertical->{0.413031244919874`,-0.22017905182482353`,0.9500704946610741`}]

Options[]

ptsSize = 10;
SingularSetTM = 
{
{Thick,Line[{{0,0,0},{0,0,H}}]},
{Thick,Line[{{0,1,0},{0,1,H}}]},
{Thick,Line[{{1,0,0},{1,0,H}}]},
{Thick,Line[{{1,1,0},{1,1,H}}]},
{Dashing[dash],Line[{{1/2,1/2,0},{1/2,1/2,H}}]},
{AbsolutePointSize[ptsSize], Point[{1/2,1/2,H/4}]},
{AbsolutePointSize[ptsSize], Point[{1/2,1/2,3/4 H}]}
};

gTM=Graphics3D[{box, SingularSetTM},Boxed->False,ImageSize->{306.2921514890229`,415.85980538787715`},ViewPoint->{28.649631508956674`,-14.636805932332045`,10.486301850521295`},ViewVertical->{0.413031244919874`,-0.22017905182482353`,0.9500704946610741`}]

both=Show[GraphicsArray[{gTE, gTM},GraphicsSpacing->0.6]]

Export["~/writing/WIP/contact/singularSets.pdf", both]