Convex bodies of constant width with exponential illumination number

Andrii Arman, Andriy Bondarenko, Andriy Prymak

We show that there exist convex bodies of constant width in ${\mathbb{E}}^n$ with illumination number at least $(\cos (\pi /14)+o(1){)}^{-n}$, answering a question by G. Kalai. Furthermore…