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The idea of the 4 Corners Cube to a dodecahedron.
This puzzle is a cousin of a 8 Corners Rhombic Dodecahedron from the same inventor, itself a shape variant of the Trifurcation Cube.
The 8 Corners Dodecahedron is a jumbling-only puzzle with 24 turning axes. It is not a shape-mod of the Trifurcation Cube geometrically, i.e., the axes of the two puzzles do not point to same directions. However, if one compares them carefully, he will find out that every piece on one puzzle has its counterpart on the other. In other words, scrambling and solving of the two puzzles would be the same if overhang bandaging is not taken into consideration.
To explain this phenomenon, one may think the geometry of this puzzle as a non-sweet spot of a family of 24-sided polyhedrons or a degenerate geometry. When the cuts are shallow enough, the non-sweet spot only reveals the first jumble layer so that the behavior is more or less the same as the sweet spot, which is face-turning triakis octahedron.
The puzzle would not work without filleting. That is to say, if you look at the sketch of the current design, there are some very small intersectional parts. Just a little bit of filleting would eliminate them.
Image 11 shows the underlying face-turning polyhedron.
Image 12 shows the results of changing the 8 Corners Dodecahedron into a cube. You can see that the symmetry has been reduced to some extent in both cases.
Printed on an Ender-3 S1.
Edge length: 36 mm
Height: 80 mm
Weight: 169 grams
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8 Corners Dodecahedron
