An E³ embedding of Coxeter’s regular map 8, 4 | 3 results in a regular Leonardo polyhedron

This paper is an update of a result published by Schulte and Wills in 1986. It explains in detail the construction of the polyhedral embedding of Coxeter's regular map of type 8, 4 ∣ 3 in Euclidean 3-space. The explanation is supported by numerous computer generated pictures. This polyhedron has the full octahedral symmetry group of order 48, and its combinatorial automorphism group is of order 482. It should be considered in context to additional five Leonardo polyhedra described recently by the authors in this journal.