A packing exponent formula for the upper box dimension of certain self-projective fractals

In this note, we prove a packing exponent formula for the upper box-counting dimension of attractors of certain projective iterated function systems. In particular, this shows the upper box-counting dimension of the Rauzy gasket lies between 1.6910 and 1.7415, and partially affirms a conjecture of De Leo

The Inradius of a Hyperbolic Truncated nn-Simplex

Hyperbolic truncated simplices are polyhedra bounded by at most $$2n+2$$hyperplanes in hyperbolic $$n$$-space. They provide important models in the context of hyperbolic space forms of small volume. In this work, we derive an explicit formula for their inradius by algebraic means and by using the concept of reduced Gram matrix. As an illustration, we discuss implications for some polyhedra related to small volume arithmetic orientable hyperbolic orbifolds