On longest circuits in certain non-regular planar graphs
On the chiral Archimedean solids.
On the monotonicity of the volume of hyperbolic convex polyhedra.
On the notion of the combinatorial -parametric property for polyhedra.
On the number of facets of three-dimensional Dirichlet stereohedra. II: Non-cubic groups.
On the volume of unbounded polyhedra in the hyperbolic space.
Paths of low weight in planar graphs
The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are: 1. Every 3-connected simple planar graph G that contains a k-path, a path on k vertices, also contains a k-path P such that for its weight (the sum of degrees of its vertices) in G it holds 2. Every plane triangulation T that contains a k-path also contains a k-path P such that for its weight in T it holds 3. Let G be a 3-connected simple planar graph of circumference...
Platonic hypermaps.
Poznámka o čtyřúhelníku
Poznámka o sférické trigonometrii
Pseudo-Petrie operators on Grünbaum polyhedra
Quelques théorèmes de géométrie à dimensions
Quelques théorèmes sur les tétraèdres dont les arêtes opposées sont égales deux à deux, et solution de la question 1272
Relations among rhombic, Platonic and Archimedean solids
Rigidity and flexibility of virtual polytopes
All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.
Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach
An analysis of all possible icosahedral viral capsids is proposed. It takes into account the diversity of coat proteins and their positioning in elementary pentagonal and hexagonal configurations, leading to definite capsid size. We show that the self-organization of observed capsids during their production implies a definite composition and configuration of elementary building blocks. The exact number of different protein dimers is related to the...
Self-dual non-Hamiltonian polyhedra with only two types of faces
Simple 3-polytopal graphs with edges of only two types and shortness coefficients
Solution des exercices sur le tétraèdre proposés par M. Genty
Subdivision Algorithms and the Kernel of a Polyhedron.