This Demonstration shows how to "hyperbolize" a dodecahedron (and other Platonic solids). Effectively, hyperbolization with parameter
means to apply the map
to all points
of the surface of a dodecahedron. Positive values of
generate sharp 2D cusps along the edges. Negative values of
generate round bulbs at the centers of the faces of the original Platonic solid. A decorated hyperbolic dodecahedron has been used as the
Mathematica logo since
Mathematica Version 2.
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