Any ideas on how to build this?

a few layers of thin pieces of wood, laminated and clamped to a caul.
or – one big piece of wood hollowed out by hand and machine.
it would be easier (much easier) to make just the top part. sort of like
a bench with rounded corners.

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-- there is no educational alternative to having a front row seat in the School of Hard Knocks. --

You could either do bent lamination or dovetails then round them. For dovetails you’ll need to start with especially thick stock to get that much of a curve.
Look here for some inspiration

Depending on the size of the rounded corners, you could make it like a band saw box. Either build up the corners with stock to allow for the corner to allow for the sawing of it or use thick stock and increase the amount of work in sanding. That is if you have a big enough of a saw.

-- If guns cause crime all of mine are defective Randy

To make things easier and it would still look nice… how about just making it square? A fraction of the work and a nice looking unit.

-- The smell of wood, coffee in the cup, the wife let's me do my thing, the lake is peaceful.

Plus one on making it like a band saw box, IF you are dead set on making it like the photo. If it were me, I’d leave the interior side square and just round over the outside ends.

-- OleGrump

Laminated thin sheets of plywood (1/8th”), glued, clamped to a form, then veneered.

-- WWBBJ: It is better to be interesting and wrong, than boring and right.

You could either do bent lamination or dovetails then round them. For dovetails you ll need to start with especially thick stock to get that much of a curve.
Look here for some inspiration

- GrantA

That would be cool. You could also just use box joints. If you want the inside corners rounded, you might want to do that before you glue it together

For the bent lamination, depending upon how big you are planning to making you could use long sheets of thin veneer and just start gluing and wrapping them around a form until you get the desired thickness. You may need a form that allows you to compress it after the glue sets to make removal easier.

-- Nathan, TX -- Hire the lazy man. He may not do as much work but that's because he will find a better way.

I’d do dovetails or box joints and then round the corners. Fellow LJ Derek Cohen did a coffee table recently that has a similar form, just a difference of scale.

In the project writeup, he’s also got a link to a blog post about doing the dovetails.

-- https://www.jtplaneworks.com - In theory, there is no difference between theory and practice. In practice, there is.

I’m working, but this is the just of it. If you want to try it this way and have questions I can get back with you later tonight.

Wow. Thanks for all the quick responses and great suggestions.

I need to look over all of them and think about it some more.

I’ll try to remember to follow up with progress.

Thanks again everyone!

-- You can't always control WHAT happens, but you can always control HOW you respond.

I would first ascertain if the rounded corners were the most important part of this. Looking at the picture I note that there are a series of plants stuck into the top of what could be any shape. If she is looking just for the planter part of this, does she care if the sides are rounded, or squared as already suggested.

I’m a firm believer that anyone, can do anything they set their mind to do. That said there is no doubt making a wooden rectangle with squared corners is far easier work, then making those shoulders rounded. If you are set to make them rounded, then also as suggested making it a few sizes thicker, and either routing, bandsawing, or even filing, and rasping the corners round are the smart way to go. Also as suggested either a DT, or finger jointed joinery is going to be needed to hold the corners tight, and not reveal the joinery as you would with loose tenon, dowel, spline, or especially pocket hole joinery.

-- Think safe, be safe

Cutting that cove, should you decide to do it that way, is pretty easy with a cove cutting jig. Rockler, I think, sells one. But it’s not hard to make your own.

Clamp 2 boards (1×4, or whatever) diagonally across the saw table, bracketing the blade. The boards should be spaced the width of the board you’ll be making the cove in. Raise the blade while sighting across the table to see what kind of curve you will get. Varying the angle of the diagonal will change the curvature. Sight at table level. To cut the cove, raise the blade by small increments, running the board down the slot repeatedly until you have the curve you want. You can make quite a large cove this way. Of course you will need to do some sanding.

-- I admit to being an adrenaline junky; fortunately, I'm very easily frightened

A firm believer in doing anything, yet has no projects posted here…

Listen to the one professional who replied on the thread. That’s LeeRoyMan. His suggestion is the winner in my book. If I were trying to build what you’re describing, his is the way I’d do it.

-- Half of what we read or hear about finishing is right. We just don’t know which half! — Bob Flexner

How about making it out of plexiglass?

My quick suggestion, glue a box together (say 1/2” stock). Glue cove molding into each of the corners. Then using a router, round over the outside corners. The trick is to make cove molding whose edge is sharp. Commercial cove molding will have 1/8” or bigger edge. You could buy some cove molding and rip it so the edge is sharp and glue in place.