I started from oak lumber, which I cut down to size and then planed. I made six 308 mm wide panels.

To create the pentagons with a 190 mm edge length, I used a table saw and made a jig with an offset at 18 degrees.

The blade angle was set it to 31.7 degrees because, according to Wikipedia, the dihedral angle of a dodecahedron is 2arctan(ϕ), where ϕ is the golden ratio.

For assembly, I used flat glue and secured the joints with tape to ensure everything held together while the adhesive cured. This method allowed for a clean finish.

Now, I just hope my cat will use it! 😉