A hedgehog is an envelope parameterized by its Gauss map (Martinez-Maure 1996). Viewed another way, a hedgehog is a Minkowski difference
of a convex body (Martinez-Maure 2003, 2004).
(correcting a sign error in Martinez-Maure 1996). A plane convex hedgehog has at least four polygon vertices where the curvature
has a stationary value. A plane convex hedgehog of constant width has at least six
vertices (Martinez-Maure 1996).
For definitions of a hedgehog in dimensions, see Martinez-Maure (2001).
Langevin, R.; Levitt, G.; and Rosenberg, H. "Hérissons et Multihérissons (Enveloppes paramétrées par leur application
de Gauss." Warsaw: Singularities, 245-253, 1985. Banach Center Pub. 20, PWN
Warsaw, 1988.Martinez-Maure, Y. "A Note on the Tennis Ball Theorem."
Amer. Math. Monthly103, 338-340, 1996.Martinez-Maure,
Y. "Hedgehogs and Zonoids." Adv. Math.158, 1-17, 2001.Martinez-Maure,
Y. "Theorie des hérissons et polytopes." Comptes Rendus de l'Académie
des Sciences de Paris, Sér. I336, 241-244, 2003.Martinez-Maure,
Y. "A Brunn-Minkowski Theory for Minimal Surfaces." Ill. J. Math.48,
589-607, 2004.
dimensions, see Martinez-Maure (2001).
