What did the designer have in mind? They do not show corner trim.

Its hard to say without knowledge of the materials. Who makes "pleasant planks"? Would the cedar shingles be red or white? Is it only the lantern that would be affected?

If its just at the lantern, I suppose I would add small Azek trim and paint it to match the shingles.

If your designer specified the shingles, he/she is responsible for the oversight and you are responsible for your designer. If the builder designed house, its his responsibility.

If it is just your lantern and entrance, you might consider eliminating the shingle siding in those areas and doing flat recessed panels below the window and other trim detailing so that it looks like your box bay on the first floor. I might not do that though if there is going to be a high contrast in color between your trim and shingle siding. Then you could leave the rest of the house as designed.

I'd go with the Azek trim at the transitions.

thanks Charles..we had planned on mitered edges on all
90.degree angles and felt having them suddenly appear in this one section for the 45 degree angles would stand out in a bad way