Free boundary of a tetrahedral mesh has interior-crossing edges

I have the following tetrahedralized solid, a right prism with a non-convex base,

load data

%Solid display
tetramesh(TET,'FaceAlpha',1); axisProps()

I am trying obtain the triangulated mesh trExt of its external surfaces. I approach this as below, but confusingly, the plot of the final triangulation seems to have edges that run through the interior of the solid (e.g. from the lower left corner at [-1,0,-1] to the centeral point on the upper curved edge [0,+1,+1]). Shouldn't freeBoundary() ensure that I do not get these?

%Surface triangulation (attempted)
figure;
[F,P]=freeBoundary(TET);
trExt=triangulation(F,P);
trisurf(trExt,'FaceAlpha',0.2);
axisProps()

It should look like this:

%Surface triangulation (ideal)
figure;
trisurf(trIdeal,'FaceAlpha',0.2);
axisProps()

function axisProps()

 axis equal; grid off
 xlabel('x'); ylabel('y'); zlabel('z');
 view(+40,25); 

end

Answer 1

[Matt J]

OK, my bad. The solid was built from smaller, triangular sub-prisms, each subsequently split into tetrahedrons. While neighboring sub-prims share a rectangular face, the rectangles were triangulated in some cases with upward-sloping diagonals for one sub-prism but with downward sloping diagonals for its neighbor. Thus, the neighbors didn't truly have any triangular faces in common, creating a free boundary in the interior of the solid.

load data

[F,P]=freeBoundary(TET);
trExt=triangulation(F,P);
trisurf(trExt,'FaceAlpha',0.2);

zlim([-0.75,0.75])
ylim([0.1,0.75])
xlim([-1,0])
view([167,27])

●

[Jose]

muy buen ejercicio