<p>I can download a file from Tinkercad as any of these:</p>

<pre><code>.STL
.OBJ
.X3D
.VRML
</code></pre>

<p>Is there a way to convert any of those file types to .DWG?</p>

In short, I don't think printing the full tetrahedral honeycomb design is a good approach considering the application of the part. Here are few things to note when attempting to 3D print the tetrahedral honeycomb:
I wouldn't recommend trying to 3D print this with a an FDM/FFF printer as you will most likely need supports and there would not be enough strength laterally. You may be able to
print
the design using SLA, but handling would be very difficult before post-processing as the part is very brittle post-print until a heat treat or curing process is done to chemically solidify. The post-process of the SLA could determine how strong the part is (ie. stainless steel powder, infused with bronze in a heat treat process would be good for such a part).
While SLS may be the best method for 3D printing this type of design, for that size part (30x30x10cm) you're looking at an expensive print regardless of whether or not you print it yourself.
Instead, I would highly recommend finding (or designing your own) a joint connector that would allow you to join wood/plastic dowels in the tetrahedral honeycomb shape. Not only will this be cheaper for you in the long run (easier to replace a few broken segments than an entire 3D printed model), but it could provide more structural strength for something that could potentially get banged around, like a tricopter.
For example,
this model
on Thingiverse (not my model) shows an example of how you can utilize 3D printing complex or custom joints that allow you to connect dowels in the shape you're looking for. It'd kind of be like building with
K'Nex
.
As far as designing said joint, you could model a single "inner" joint that has 18 connectors (8 on XY plane, 6 on YZ plane, and 4 on XZ plane). Below is a crude example of what I mean drawn in Google SketchUp: