Understanding the Laser Cutter Machine

I measured the cardboard's thickness with a caliper to accurately design the joints — critical for press-fit assemblies, where dimensions must account for both material thickness and laser kerf.

What Is a Dodecahedron

According to Wolfram MathWorld, a dodecahedron is one of the five Platonic solids: 12 pentagonal faces, 30 edges, and 20 vertices, with three faces meeting at each vertex. Its high symmetry makes it a good starting point for exploring parametric construction from repeated geometric relationships.

Decoding the Dodecahedron (C# Grasshopper)

Using a custom scripting component, I broke down the dodecahedron's geometry and reconstructed it with a C# library in Grasshopper.

Rather than modeling the form directly, I explored how its vertices, edges, and pentagonal faces relate to one another and translated those relationships into a parametric workflow.

Mock-Up Model

I built two mock-ups, roughly 50 cm and 30 cm in diameter, to test how the geometry, joints, and material behaved at different scales.

Joint dimensions were adjusted for the 6.8 mm cardboard thickness, and each module was laid out flat before laser cutting.

The 20.91° joint angle is derived from the relative orientation between adjacent connectors, allowing the planar modules to assemble into the overall 3D geometry.

Assembly

Assembly was the most fun part — since the joints were already calibrated to the material thickness, each segment locked tightly into place without any extra fasteners or adhesive.

Understanding the Vinyl Cutter Machine

To test the vinyl cutter's capabilities, I designed a pattern with increasingly intricate, closely spaced lines — pushing how precisely it could handle fine geometry, thin lines, and small gaps before cutting and weeding became physically limited.

What Is a Moiré Pattern

According to Wikipedia, a moiré pattern is a large-scale interference pattern created when two similar repetitive patterns are overlaid, slightly displaced, rotated, or spaced differently. These small differences generate a new pattern that appears to shift as the layers' relationship changes.

Circular Moiré Pattern (p5.js)

I used p5.js to generate the pattern by overlaying two sets of curved parallel lines with slightly different spacing, frequency, distortion, and phase — a sine-based distortion warps each line by its distance from the center, and a circular mask constrains it into a disc. Adjusting these parameters let me quickly experiment with line density and interference before preparing the pattern for cutting.

Clean Up and Applying the Sticker

The vinyl cutter reproduced the pattern with surprisingly high detail, though the intricate, closely spaced lines meant manually weeding the unwanted areas with tweezers — a process that took about one hour. I then applied the finished sticker to my iPad as a test.