A honeycomb member has usually hexagonal pattern shear members. Because it is closest to an isotropic solid member within the constrains of manufacturing.
Lets imagine we put a honeycomb Formica door flat and use it as a beam supporting 100lbs at the center, which will have 50lbs shear at support.
If the support end cuts the hexagons exposing the diagonal blades at abutment, they are under out of plane shear and torque, which they can poorly take and will rotate into a mechanism, starting thee chain of collapse in the entire door.
However as has been said by alephzero these 60 degree lose blades are contained in a solid frame such as a 2in solid wood and they won't develop the rotation mechanism and the door will act very stiff, supporting the load.
Why do we use the honeycomb slabs like concrete ceilings, parking slabs, shopping mall floors, is because it is the most efficient use of material for large span slabs. For a slab to have a large 'I', it needs most of material on top and bottom and the shear can be taken care of hollow, lightweight honeycomb.