1-Dimensional Orbits in Flat Projective Planes.
2-frieze patterns and the cluster structure of the space of polygons
We study 2-frieze patterns generalizing that of the classical Coxeter-Conway frieze patterns. The geometric realization of this space is the space of -gons (in the projective plane and in 3-dimensional vector space) which is a close relative of the moduli space of genus curves with marked points. We show that the space of 2-frieze patterns is a cluster manifold and study its algebraic and arithmetic properties.
2-manifold surfaces and space partitions
3D illustrations to Chapter 8 of Cromwell's Polyhedra
A 2-metric Characterization of the Euclidean Plane.
A case of the 3-dimensional problem of Appollonius.
A characterization of all equilateral triangles in .
A characterization of compact convex polyhedra in hyperbolic 3-space.
A characterization of compact convex polyhedra in hyperbolic 3-space (Corrigendum).
A characterization of continuous associative operations whose graphs are ruled surfaces.
A Characterization of Motions as Bijections Preserving Inradius or Circumradius One.
A characterization of regular saddle surfaces in the hyperbolic and spherical three-space.
A characterization of spheres among compact 3-bodies satisfying Crofton's theorem
A class of inequalities related to the angle bisectors and the sides of a triangle.
A combinatorial theory of Grünbaum's new regular polyhedra, Part II: Complete enumeration.
A combinatorial theory of Grünbaum's new regular polyhedra, Part I: Grünbaum's new regular polyhedra and their automorphism group.
A conjecture of Stein on plane dissections.
A consistency equation for three geometries.
A decomposition of a set definable in an o-minimal structure into perfectly situated sets
A definable subset of a Euclidean space X is called perfectly situated if it can be represented in some linear system of coordinates as a finite union of (graphs of) definable 𝓒¹-maps with bounded derivatives. Two subsets of X are called simply separated if they satisfy the Łojasiewicz inequality with exponent 1. We show that every closed definable subset of X of dimension k can be decomposed into a finite family of closed definable subsets each of which is perfectly situated and such that any...
A Desarguesian dual for Nagel's middlespoint.