Isohedra with dart-shaped faces (Q5951944)

A polyhedron \(P\) in the Euclidean space is called an isohedron if all its faces are equivalent under the symmetries of \(P\). NEWLINENEWLINENEWLINERecently the authors have constructed isohedra with nonconvex faces without selfintersections [J. Geom. 63, No. 1-2, 76-96 (1998; Zbl 0938.51016)]. In the present paper the authors use their earlier method of Möbius nets of the three reflection groups of the five Platonic solids to construct isohedra \(P\) with dart-shaped faces (and selfintersections) whose edges lie in planes of mirror symmetry of \(P\). Some of the enumerated possible types of isohedra with dart-shaped faces are described and illustrated by figures.