Using a Graphics3D
object from that file (4th object down from the top of slide 8)

(which I'm calling p) we can reconstruct your graphic as follows:
z = Union@
Cases[p[[1]], {x_Real, y_Real, z_Real} :> {{x, y},
z}, {0, \[Infinity]}];
d2 = DiscretizeGraphics@
Graphics@
Replace[p[[1]], {x_Real, y_Real, z_Real} :> {x,
y}, {0, \[Infinity]}];
b = BoundaryMesh[
RegionProduct[d2, MeshRegion[{{0}, {1}}, Line[{1, 2}]]]];
iz = Quiet@Interpolation[z];
len = RegionBounds[b][[1, 2]];
mc = MeshCoordinates[
b] /. {{x_, y_, 0.} :> {x, y, iz[x, y]}, {x_, y_, 1.} :> {x, y,
iz[x, y] + 1}};
mr = MeshRegion[mc, MeshCells[b, 2]];
m2 = Show[mr,
TransformedRegion[
TransformedRegion[mr, RotationTransform[Pi, {1, 0, 0}]],
TranslationTransform[{0, 0, len*2}]]];
out = Show[m2,
Graphics3D[
GeometricTransformation[
GeometricTransformation[
m2[[1]], {RotationMatrix[90 Degree, {0, 1, 0}]}],
TranslationTransform[{-50.8, 0, 50.8}]]],
Graphics3D[
GeometricTransformation[
GeometricTransformation[
m2[[1]], {RotationMatrix[90 Degree, {1, 0, 0}]}],
TranslationTransform[{0, 50.8, 50.8}]]]]

EdgeDetect
for the pattern image 2. Extraction of the contours, possibly usingImageValuePositions
and constructing closed paths from that data. 3. Creating a hollowed region (hollow within some boundary you chose). 4. Deforming the region in 3D, using e.g. a 2D-Gaussian. 5. Extruding the deformed region by the target thickness you desire. 6. Constructing something of the shape by translation and rotation, e.g. something like the cube you mentioned. As I said: Interesting! $\endgroup$BoundaryRegion
and continue with the steps from my last comment, saving you the hassle of dealing with pixelated input. $\endgroup$