Isohedra with dart-shaped faces. (English summary) Selected papers in honor of Helge Tverberg. Discrete Math. 241 (2001), no. 1-3, 313–332. In Euclidean 3-space a (possibly non-convex) polyhedron is said to be an isohedron if all its faces are equivalent under the action of its group of symmetries. The authors consider isohedra whose faces are darts, that is, non-convex quadrangles. They show that there exist many such isohedra if self-intersections are admitted. In particular, they construct those whose symmetry groups are the tetrahedral, octahedral or icosahedral reflection groups, and which have the additional property that the edges lie in planes of reflective symmetry. The idea of the construction is surprisingly simple
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