I’m wondering if this would be legal. Anyone see any rules that would make this illegal that I may have missed?
Are you cutting away that corner? It is entirely legal however your bumpers will have to follow that cut out because its now part of your frame perimeter.
Exactly what I was going to say, with one minor addition: Make doubly sure you have 8" bumpers on each side in addition to the 1" bumper segment on the cutout.
I’d ask what the purpose is, but I’m guessing it’s either pyramid climbing in some way, or you’re having a little bit of trouble with the frame perimeter and want to give yourself 1.14 inches instead of 2 just to have a little bit of cushion.
So bumpers have to fellow the frame perimeter?
R22
ROBOTS are required to use BUMPERS to protect all outside corners of the
FRAME PERIMETER. For adequate protection, at least 8 in. of BUMPER must
be placed on each side of each outside corner (see Figure 4-2).
I don’t see how you’re going to put an 8" bumper on the 1.4" wide side of the frame corners.
I think you might be able to get away with a 1/4" chamfer on each of the four corners…
well those are 1" chamfers. The rule says “Protect all outside corners” and they will have traded one corner for two. The rule then says "at least 8inches of BUMPER must be placed on each side of the corner…so maybe any sort of corner cut under 8 inches is not allowed. At least thats what the rule would suggest. So I would have to retract my previous answer and call this illegal in that case.
There shouldn’t be a reason you would get away with getting to call your frame perimeter smaller while not following the rest of the rules that subsequently follow 
The issue of a side shorter than 8" was cleared up in the Q&A and with a rule update. It was ruled that there must be at least 8" of bumper on either side of a corner. If a side was shorter than 8", the remaining 8" of bumper must wrap around the next corner.
Im just going to keep not reading the Q&A and ask you at competition if I have questions. 
Link to the question and response please?
Wrapping is described in the bottom figure of update 2013-01-15, and mentioned in Q137.
Note that this business about the corner protection wrapping around other corners is new for this year.
That does not make sense.
Oh well…
I think the rules committee made a creative interpretation to allow a frame side to be less than 8". The rules committee does not have to make sense. To quote Lily Tomlin “They are omnipotent” :ahh: Now tell me where that quote came from.
In terms is the pic legal? Only your inspector will know for sure. But you bumper will have to comply with R29 & wrap around the 1" fillet so that is is fully supported.
R29
BUMPERS must be supported by the structure/frame of the ROBOT (see Figure 4-6). To be considered supported:
A. a minimum of 1 in. at each end of the BUMPER must be backed by the FRAME PERIMETER,
B. the gap between the backing material and the frame must not be greater than ¼ in., and
B. no section of BUMPER greater than 8 in. may be unsupported.
If you have a Q for Q&A, make sure you reach the party to whom you are speaking <snort>.
I’ve been thinking about this. That 1.414" section of Frame Perimeter would have to have its own section of bumper - complete with plywood, noodles, fasteners. Pay attention to R29A.