24 citations · 24 across the 4 of their papers we have counts for
6 papers
Orthocentric simplices and their centers
Allan L. Edmonds, Mowaffaq Hajja, Horst Martini
A simplex is said to be orthocentric if its altitudes intersect in a common point, called its orthocenter. In this paper it is proved that if any two of the traditional centers of…
Coincidences of simplex centers and related facial structures
Allan L. Edmonds, Mowaffaq Hajja, Horst Martini
We investigate the geometric properties of simplices in Euclidean d-dimensional space for which two or more of the analogues of the classical triangle centers (including the centro…
Embedded Surfaces in the 3-Torus
Allan L. Edmonds
Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the somewhat intricate case when t…
The Geometry of an Equifacetal Simplex
Allan L. Edmonds
Equifacetal simplices, all of whose codimension one faces are congruent to one another, are studied. It is shown that the isometry group of such a simplex acts transitively on its…
Homology Lens Spaces in Topological 4-Manifolds
Allan L. Edmonds
For a closed 4-manifold X and closed 3-manifold M we investigate the smallest integer n (perhaps infinity) such that M embeds in the connected sum of n copies of X. It is proven th…
Homologically Trivial Group Actions on 4-Manifolds
Allan L. Edmonds
It is proved that an arbitrary finite group acting locally linearly, homologically trivially, and pseudofreely on a closed, simply connected 4-manifold must in fact be cyclic and a…