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I'm making a dodecahedron and an icosahedron from struts of wood with compound mitre cuts. I have a compound mitre saw. I've made some test joints and the dodecahedron joints seem fine: re while the icosahedron ones are pretty awful:icosa

I used a stop and 90 degree offset and changed sides to do each side of the cut: enter image description here

How can I make this more fast, safe and accurate?

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While you're probably breaking every manufacturer safety recommendation in the book, there are a couple of improvements you can make.

Something like a rectangular chunk of ply (should be 3/4" or so thick) can be clamped on the saw table to help you hold the piece being cut at 90 degrees.

A small (sacrificial) stick parallel to the fence can keep the workpiece from being dragged through the fence. If it's something like 3 or 4 inches wide, you can put it flat on the saw table and (since it looks like you have a slider) you won't have to cut through it every time. Plus, if you clamp it in place, the kerf will indicate the cut line and you'll be able to set up faster.

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If all of the pieces you are cutting are the same width, then make a fixture that constrains the work piece to exactly where you need it, then attach that fixture to the saw and clamp the work to the fixture.

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