2005/01/04 by Egon Schulte, Schulte, Egon
Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Scientific Research and Discoveries #math.CO #math.MG #msc:51M20
paper · pdf · doi:10.48550/arxiv.math/0501050
48 pages
arxiv created 2005/01/04 · arxiv updated 2009/12/01
A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean 3-space with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types 4,6, 6,4 and 6,6. Part II completes the enumeration of all discrete chiral polyhedra in 3-space. There exist several families of chiral polyhedra with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.