Dense Sets of Polytopes in P3
Détermination et construction nouvelle du cercle qui coupe trois cercles sous trois angles donnés et de la sphère qui coupe quatre sphères sous des angles donnés
Die Dehnsche Zerlegungsinvariante für hyperbolische Polyederbausteine.
Discrete Groups and Internal Symmetries of Icosahedral Viral Capsids
A classification of all possible icosahedral viral capsids is proposed. It takes into account the diversity of hexamers’ compositions, leading to definite capsid size.We showhowthe self-organization of observed capsids during their production results from definite symmetries of constituting hexamers. The division of all icosahedral capsids into four symmetry classes is given. New subclasses implementing the action of symmetry groups Z2, Z3 and S3 are found and described. They concern special cases...
Dürer polyhedra: the dark side of melancholia
Dürer's engraving Melencolia I famously includes a perspective view of a solid polyhedral block of which the visible portion is an 8-circuit bounding a pentagon-triple+triangle patch. The polyhedron is usually taken to be a cube truncated on antipodal corners, but an infinity of others are compatible with the visible patch. Construction of all cubic polyhedra compatible with the visible portion (i.e., Dürer Polyhedra) is discussed, explicit graphs and symmetries are listed for small cases ( ≤ 18...