Stars in the snow

Continuing the theme of maths sculptures interacting with snow fall, here are some pictures of my bamboo star. The original design was found by Akio Hizume, and I was introduced to the idea by Chaim Goodman-Strauss.  The design takes 30 lengths of bamboo, arranged in fives. Each group of 5 pass through two opposite faces of a dodecahedron, as a pentagon rotated slight with respect to the pentagons they pass through. The 30 lengths weave together in the middle, needing no other support. Though over time the star does tend to sag!

Similar designs can be achieved from the other regular polyhedra. Can you work out the polyhedron that corresponds to this pencil design?