Hyperbolization of a Dodecahedron

Platonic solid

tetrahedron

octahedron

cube

dodecahedron

icosahedron

hyperbolicity

This Demonstration shows how to "hyperbolize" a dodecahedron (and other Platonic solids). Effectively, hyperbolization with parameter

α

means to apply the map

rr

α

(r.r)

to all points

r

of the surface of a dodecahedron. Positive values of

α

generate sharp 2D cusps along the edges. Negative values of

α

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.

External Links

Dodecahedron (Wolfram MathWorld)

Hyperbolic Cube (Wolfram MathWorld)

Hyperbolic Dodecahedron (Wolfram MathWorld)

Hyperbolic Icosahedron (Wolfram MathWorld)

Hyperbolic Octahedron (Wolfram MathWorld)

Hyperbolic Polyhedron (Wolfram MathWorld)

Hyperbolic Tetrahedron (Wolfram MathWorld)

The Mathematica GuideBook for Graphics

Permanent Citation

Michael Trott, Michael Trott

"Hyperbolization of a Dodecahedron"
http://demonstrations.wolfram.com/HyperbolizationOfADodecahedron/
Wolfram Demonstrations Project
Published: August 26, 2008