Star Polyhedron

A star polyhedron is a nonconvex polyhedron which contains an arrangement of symmetrically (nor nearly symmetrically) arranged spikes giving it the visual appearance of a three-dimensional star. Star polyhedra can be constructed from concave polyhedra via stellation or augmentation.


Examples include the stella octangula and Kepler-Poinsot polyhedra.

Star polyhedra appear prominently in the architecture of European churches (Tarnai et al. 2007, 2008).

See also

Augmentation, Kepler-Poinsot Polyhedron, Polyhedron, Regular Polychoron, Star Polygon, Stella Octangula, Stellation

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Conway, J. H.; Burgiel, H.; and Goodman-Strass, C. "Regular Star-Polytopes Dimension 3." Ch. 26 in The Symmetries of Things. Natick, MA: A K Peters, p. 404, 2008.Tarnai, T.; Krähling, J.; and Kabai, S. "Star Polyhedra: from St Mark's Basilica in Venice to Hungarian Protestant Churches." Paper ID209 in Proc. of the IASS 2007, Shell and Spatial Structures: Structural Architecture-Towards the Future Looking to the Past. Venice, Italy: University of IUAV, 2007., T.; Krähling, J.; and Kabai, S. "Star Polyhedra on Hungarian Protestant Churches." In Proc. of the 13th International Conference on Geometry and Graphics (Ed. G. Weiss). Dresden, Germany: Technical University of Dresden, Germany, 2008.

Referenced on Wolfram|Alpha

Star Polyhedron

Cite this as:

Weisstein, Eric W. "Star Polyhedron." From MathWorld--A Wolfram Web Resource.

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