Charakteristiken und Schnittzahlformeln für p-l-s-Kegelschnitte
Chiral Polytopes from Hyperbolic Honeycombs.
Chord-decreasing homeomorphisms in Euclidean spaces
Chords and arclength of a closed space curve
Circle packing in the hyperbolic plane.
Circumcenter, Circumcircle and Centroid of a Triangle
We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula of the radius...
Classes of Graphs Which Approximate the Complete Euclidean Graph.
Classical -symbols and the tetrahedron.
Classification of dodecahedral space forms.
Classification of hyperbolic dodecahedron tilings of maximally face-transitive motion groups. (Klassifikation der hyperbolischen Dodekaederpflasterungen von maximalen flächentransitiven Bewegungsgruppen.)
Čo s nejednoznačným zadaním slovnej úlohy?
In the paper we deal with a task about two circles touching in a rectangle. The assignment of the task was formulated in a fuzzy way, so solvers understood it differently. We present extracts from the authentic solutions which reflect this phenomenon. We suggest an approach to such tasks, how to solve them and how to assess their solutions.
Cobordism of automorphisms of surfaces
Coincidences of simplex centers and related facial structures.
Colouring polytopic partitions in
Colouring polytopic partitions in
We consider face-to-face partitions of bounded polytopes into convex polytopes in for arbitrary and examine their colourability. In particular, we prove that the chromatic number of any simplicial partition does not exceed . Partitions of polyhedra in into pentahedra and hexahedra are - and -colourable, respectively. We show that the above numbers are attainable, i.e., in general, they cannot be reduced.
Combinatorics, group theory and geometric models
Compact hyperbolic Coxeter -polytopes with facets.
Compact hyperbolic tetrahedra with non-obtuse dihedral angles.
Given a combinatorial description C of a polyhedron having E edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize C is generally not a convex subset of RE. If C has five or more faces, Andreev's Theorem states that the corresponding space of dihedral angles AC obtained by restricting to non-obtuse angles is a convex polytope. In this paper we explain why Andreev did not consider tetrahedra, the only polyhedra having fewer than five faces, by demonstrating that the...
Comparing the relative volume with the relative inradius and the relative width.
Comparision of the length of infinite geodesics in manifolds with nonpositive curvature.