How could I make a twisted cuboid sculpture like this?

Question

I saw a decorative vase or sculpture shaped like what I can best describe as a silver twisted cuboid, please see this 3D model for what I'm talking about: https://skfb.ly/ouSsD

The horizontal cross section is a perfect square of the same size from top to bottom but rotated about the vertical axis by 90° at the bottom compared to the top with the angle interpolated smoothly in between. The height of the sculpture would be around 30-50 cm.

Specifically, I'm looking for a way to

1. recreate the shape with smooth sides (the edges don't need to be as sharp as in the model)
2. make the surface silver and reflective

ideally without breaking the bank. Any suggestions on what materials I could use and how to achieve the shape? I don't have a good idea for point 1, for 2 I was thinking about something like this silver adhesive vinyl wrap, but I doubt I could get nice wrinkle-free results with that.

Answer 1

This particular shape "screams" 3D printed. There are a number of programs which would allow one to create the model to be printed. I'm particularly fond of OpenSCAD, a descriptive language type of 3D modeling software, but many others have this capability. One would be able to configure for high resolution to reduce layer lines, as well as to print with ABS for acetone vapor smoothing. The model's height means that it might have to be printed in vertical segments, but ABS also solvent-welds with great strength and sands nicely. With finer abrasives (Micromesh™), a mirror finish can be achieved. (direct experience)

Once the model is printed, it can be coated with an electrically conductive paint. The resulting model can then be processed with electroforming:

Electroforming is a metal forming process in which parts are fabricated through electrodeposition on a model, known in the industry as a mandrel. Conductive (metallic) mandrels are treated to create a mechanical parting layer, or are chemically passivated to limit electroform adhesion to the mandrel and thereby allow its subsequent separation. Non-conductive (glass, silicon, plastic) mandrels require the deposition of a conductive layer prior to electrodeposition. Such layers can be deposited chemically, or using vacuum deposition techniques (e.g., gold sputtering). The outer surface of the mandrel forms the inner surface of the form.

This process can be accomplished at the hobby level, although for something of the size described, it may be necessary to use a commercial resource. Nickel is not particularly expensive compared to silver metal and can be quite shiny.

For the option of wrapping, silver Monokote™ exists in the radio control airplane world. This allows heat shrinking to remove wrinkles and to cause the adhesive layer to activate, but there would be a joining line on the surface.

As a final option, once the model is created and the surface is smooth to a satisfactory level, a carefully applied paint job may provide the desired results.

Answer 2

If you don't have access to a 3D printer, you could make this from stacked and glued square wafers of wood or even cardboard/chipboard. At the ends, the squares would be aligned (or better, you can use solid blocks of wood). In the twisted section, you rotate each square a tiny amount (the offset at the corners less than the thickness of the wafer). Note that it will take a lot of wafers. Once the sculpture is assembled, sand the faces smooth (each face will be a flat surface). If you use cardboard, you can harden the faces by letting them absorb some thin resin or glue.

The silver surface can be done with paint, or wrap each face with aluminum flashing tape. Use oversized tape. The aluminum will stretch a bit to conform when you press it into place and burnish it. Do one side, trim the excess, then do the next side.