This looks like a perfect project for a glowforge.
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Being a physicist, I love the geometry and form that went into that to make it a visual art form. One of the things I hope to make on my GF. - Rich
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A dodecahedron is the first thing I attempted to draw up in Fusion360, for eventual construction with GlowForge-cut pieces.
My most fundamental challenge arose from the desire for solid edges, without the regular rectangular pattern of an intersecting cut hinge.
My eventual goal on that front is to separately create a jig for beveling the edges of each face, for a solid joint at each edge. --a work in progress for thicker materials like acrylic or wood. The beveling shouldn’t be necessary for card-stock, however, so that can be the initial test material.
I’m anxiously awaiting the exciting times ahead!
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Just out of curiosity, would it be faster to cut the sections on the GF. Then make a template to set the angle on a table saw, and bevel on that?
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I saw this the other day and thought the same thing. Really beautiful stuff!
The trick, though, would be to figure out how to use the forge to make the joints as well.
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Oooohhh, add this to my wants
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I was imagining a template/jig for a dremel tool rotary attachment, as I’ve no table saw. But I like your idea! Exactly the kind of thing I’m thinking about. Use new tools to build newer tools! 
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Is there anyway to make a router table for a dremel? Then a jig at an angle, or the dremel at an angle.
I’m figuring that’s where the GF comes in, for fashioning such a jig out of, say, wood or maybe delrin.
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I have a dremel router table (Was mentioned in other earlier thread). Would be perfect for edges like these.
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ooooooh, I finally treated myself to one of these. How do you use it for making the beveled edges? Do you use a wedge-shaped jig to hold the wood and a strait bit to run the angle? Sadly, the dremel router bits are tiny and the range of angles/shapes are limited.
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It would not be hard to make an angle wedge to place in the GF to do a second operation on the wood pieces to cut the angles at the edges. 
- Rich
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I considered the wedge inside GF idea, but some pieces will be too tall when placed on an angled wedge. I think the cutting limit is .25 inches.
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With the tray removed, you have 50mm to play with. It sounds perfect with the edge to be cut angling up. - Rich
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I know it’s definitely on my testing list.
Sorry I misunderstood your response about cutting limit. I plan to make this from 1/8" ply or maybe a little thicker, but certainly within the cutting limits of the GF. - Rich
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np… I’d love to see how/if the GF could put a nice 45 degree bevel (or, better yet, N-degree bevel as needed) on the edge of a piece of wood. The angled-wedge-as-jig is a great idea, but only for small sheets of wood, unfortunately. (by small sheets, I mean - if I’ve got a 5 inch piece of wood, and I angle it on a big enough wedge, it will stick up farther than 2 inches)
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Getting a smooth bevel on wood will be oh-so-difficult! The wood grain will cause all sorts of irregularities in the surface. I’m just hoping it will work with acrylic.
In dreamland, I could see it capturing the grain pattern with the camera and adjusting the power to different levels over the surface. Ah, sweet dreams.
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Yeah, I was thinking after the panel is cut out and small enough for the wedge idea to work. It may just be easier to set up my radial arm saw to cut the angles. It has an incredibly good wood working blade that leaves no chips in wood. - Rich
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