Hyperbolization of a Dodecahedron

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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.

Contributed by: Michael Trott with permission of Springer (March 2011)
From: The Mathematica GuideBook for Graphics by Michael Trott (© Springer, 2004).
Open content licensed under CC BY-NC-SA




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