Pentakis Dodecahedron

A press-fit pentakis dodecahedron, with pieces laser cut from wood.

Software: Python, Fusion 360, Adobe Illustrator. Hardware: CNC Later Cutter. Materials: Wood.

I was looking for a shape to create which was a spherical approximation which had a single shape for each face and a consistent dihedral angle from each face to it's neighbors through out. This way the design could be limited to one piece for the face, and one for the joiner. The pentakis dodecahedron has 60 identical isosceles triangles as it's faces, with an equal angle between the center-point of each to those of it's neighbors.

Based on the research material, I created a quick Python script which calculated relevant measurements based on a radius of my choosing.

I then used the information from the research and the calculations in order to design the face and the joiner. The joiner would use the dihedral angle at it's bottom to angle the faces according to the dihedral. The face is an isosceles triangle, and uses the long edge calculation as the measurement for it's base, and the short edge calculation for the other two edges. Slots were made for the press fit on each edge.

To avoid wasting material and time, I checked my calculations by modeling the pentakis dodecahedron in Fusion 360.

I performed a test for the press fit, and reduced the width of the joiner gap by .25mm from the thickness of the wood 2 x 1.

The sketches for each piece were exported from Fusion 360 as a DXF, then imported into Adobe Illustrator. I copied each piece based on the numbers for faces and edges found in the research. I laid the pieces out in a way to reduce material waste.

Research of the pentakis dodecahedron showed that the shape should be assembled with equal angles on each face joined together. I labeled the corners of each face, and joined them accordingly. Unfortunately, during the final cut, the material subtracted from the cutting process was more than during the test. This may have been due to how the illustrator file was set up with redundant lines. To aid in the assembly of the shape, a bucket was used to keep the pieces pressed together.

The calculations were correct, but the joints were too loose to keep the shape stable. In future iterations, I'll be sure to compensate even further for the kerf of the laser, and avoid redundant cuts.