Click flag. Set "ratio" to golden ratio (1.618 or 0.618) for a dodecahedron. Slide ratio to about 1.4 for a pyritohedron. Slide ratio to 1 for a (skewby) cube. Use mouse, touch screen, or arrow keys to turn.
In a dodecahedron, the length of pentagons' diagonals are larger than the sides by the golden ratio (1.618 or 0.618). The ratio of several other dodecahedron's distances also are the golden ratio or it's inverse. The 20 points (vertices) of this polyhedron morph into different shapes when you change the ratio. WIth a ratio of 1, you see a cube with cuts through the center, orthogonal to the main diagonals, creating half-cubes (just like a skewb). A pyritohedron, a form iron pyrite often takes, with one long side in each pentagon, results with a ratio around 1.4. While the dodecahedron has great symmetry, the pyritohedron beautifully breaks that symmetry with one shared long side for each pentagon. Many other scratchers have done something like this to make dodecahedra.
