Rectangular six with leg in the corner

Dia 1: Corner shape  

If Black plays b or c, then (other than ko threats) the only thing left in the corner is the (double-)gote hane-connect.

This is a shape between a walkie talkie seven and a rectangular six in the corner. If White has sente, the vital point in the former (walkie talkie seven) is a, in case of no outside liberties, and in the latter (rectangular six in the corner) is b or c depending on whether there are still outside liberties.

So which is it here?

Dia 3: Dead  

Shortage of liberties at a

Dia 5: Dead  

Expanding the eye space does not help

Dia 6: Ko  

In summation, the best White can achieve with sente is a ko by starting at 1 in diagram 2 above.