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Hyperbolic Dodecahedron

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HyperbolicDodecahedron

A hyperbolic dodecahedron is a hyperbolic version of the Euclidean dodecahedron.

Hyperbolic space in three dimensions can be tessellated with hyperbolic dodecahedra whose intermediate dihedral angles are 60, 72, or 90 degrees.

A decorated hyperbolic dodecahedron has been used as the logo for Mathematica since Version 2. Trott (2004, §8.3.10) gives a heuristic reconstruction of the cover image and explicitly notes that his construction is not a genuine hyperbolic dodecahedron.

See also

Hyperbolic Cube, Hyperbolic Icosahedron, Hyperbolic Octahedron, Hyperbolic Polyhedron, Hyperbolic Tetrahedron, Spikey

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References

Rivin, I. "Hyperbolic Polyhedra Graphics." https://library.wolfram.com/infocenter/Demos/4558/.Trott, M. "The Cover Image: Hyperbolic Platonic Bodies." §8.3.10 in The Mathematica GuideBook for Graphics. New York: Springer-Verlag, 2004. https://www.mathematicaguidebooks.org/.Trott, M. "Making the Mathematica 6 Spikey." Wolfram Blog. May 22, 2007. https://blog.wolfram.com/2007/05/22/making-the-mathematica-6-spikey/.Weber, M. "Cover Art." Not. Amer. Math. Soc. 47, 340, 2000.Weeks, J. "Curved Spaces." https://www.geometrygames.org/CurvedSpaces/.

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Hyperbolic Dodecahedron

Cite this as:

Weisstein, Eric W. "Hyperbolic Dodecahedron." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HyperbolicDodecahedron.html

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