On intrinsic isometries to Euclidean space

On Intrinsic Isometries to Euclidean Space

Compact metric spaces that admit intrinsic isometries to the Euclidean d-space are considered. Roughly, the main result states that the class of such spaces coincides with the class of inverse limits of Euclidean d-polyhedra. §

A Note on Coincidence Isometries of Modules in Euclidean Space

It is shown that the coincidence isometries of certain modules in Euclidean n-space can be decomposed into a product of at most n coincidence reflections defined by their non-zero elements. This generalizes previous results obtained for lattices to situations that are relevant in quasicrystallography.

On Isometries of Euclidean Spaces

Factoring Euclidean isometries

Every isometry of a finite dimensional euclidean space is a product of reflections and the minimum length of a reflection factorization defines a metric on its full isometry group. In this article we identify the structure of intervals in this metric space by constructing, for each isometry, an explicit combinatorial model encoding all of its minimal length reflection factorizations. The model ...

Euclidean Isometries and Surfaces

In this paper, we attempt a classification of the euclidean isometries and surfaces. Using isometry groups, we prove the Killing-Hopf theorem, which states that all complete, connected euclidean spaces are either a cylinder, twisted cylinder, torus, or klein bottle.