Regular incidence-polytopes with Euclidean or toroidal faces and vertex-figures

Regular incidence-polytopes are combinatorial generalizations of regular polyhedra. Certain group-theoretical constructions lead to many new regular incidence-polytopes whose faces and vertex-figures are combinatorially isomorphic to classical Euclideanly regular polytopes or regular maps on the torus.     

The existence of non-tiles and non-facets in three dimensions

Non-tiles are convex polytopes, of which isomorphic copies will not tile the space locally finite and face-to-face (that is, neighbouring tiles meet in a face of each). Non-facets are convex polytopes, of which isomorphic copies will not fit together as the facets of a higher dimensional convex polytope. It is proved that there are infinitely many 3-dimensional convex polytopes which are non-tiles as well as non-facets, thereby answering a question of Danzer.     

Eine Formel für schiefsymmetrische bilineare Räume mit vier maximal totalisotropen Unterräumen

Ohne Zusammenfassung     

Locally toroidal regular polytopes of rank 4

The paper studies various relationships between locally toroidal regular 4-polytopes of types {6, 3,p} and {3, 6, 3}. These relationships are based on corresponding relationships between the regular honeycombs with the same Schläfli-symbol in hyperbolic 3-space. Also the paper discusses regular tessellations (secretions of rank 3) which are locally inscribed into regular 4-polytopes. In particular, this leads to local criteria for the finiteness of the polytopes.     

Flat regular polytopes

At the centre of the theory of abstract regular polytopes lies the amalgamation problem: given two regularn-polytopesP ₁ andP ₂, when does there exist a regular (n+1)-polytopeP whose facets are isomorphic toP ₁ and whose vertex-figures are isomorphic toP ₂? The most general circumstances known hitherto which lead to a positive answer involve flat polytopes, which are such that each vertex lies in each facet. The object of this paper is to describe an analogous but wider class of constructions, which generalize the previous results.     

Pressure induced spectral diffusion as investigated by linewidth studies of polymers doped with dye molecules

Photochemical hole burning at 1.5 K was used to study the influence of uniaxial pressure on the homogeneous line profile of the S₁←S₀ transition of free base phthalocyanine in polyethylene (PE) and polymethylmethacrylate (PMMA) matrices. The line profiles which were observed show already at pressure changes which were as small as 100 hPa substantial broadening effects. At higher pressures of up to 3 x 10⁴ hPa we observed irreversible line broadening phenomena, which we attribute to irreversible site changes of the host-guest system.     

Studies on highly oxidized cyclohexanes. Structure and absolute configuration assignments.

The absolute configurations of pipoxide, ferrudiol and zeylenol, pictured below, are found to parallel those of crotepoxide and senepoxide, suggesting a unified biogenesis.