Hexagonal tesselation including parallelograms

I’m trying to make hexagonal tessellation like this.

I made some isolated hexagons. The parallelograms come twisted though. I need to rotate flat parallelograms so that they form hexagon at the bottom.

I tried to map hexagons on a lofted surface. In order to evaluate the perpendicular vector outside, some vectors point towards the inside.

Please help.

I suggest to take a closer look at CITA 2011 project. I think hex corners must not be at the same plane:

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Interesting project! They haven’t explained the Grasshopper work flow in the final pdf document though. Moreover, the geometry is way more irregular in their project than the one I shared.

Even on the lofted surface that I shared, the hex corners are not coming in the same plane. The hexagon obviously won’t be planar since the vase surface is curved.

I am unable to figure the way in my script. Two main things I need to achieve.

The quad panels should be flat.

The vector must always point outwards.