‘On a ledge with no safety net’

A starshaped polyhedron with no net

A simple construction is given for a polyhedron which establishes the following theorem of A. S. Tarasov: There exist polyhedra of spherical type, with convex faces, which admit no planar nets. The net of a polyhedron P consists of a connected collection of polygons, congruent to the faces of the polyhedron, arranged in one plane (conveniently thought of as a sheet of cardboard) without overlap...

A safety net for diabetics.

www.sciencemag.org SCIENCE VOL 343 7 MARCH 2014 COVER Precession image reconstructed from x-ray diffraction data collected from a benzene single crystal. For the past 100 years, x-ray crystallography has been a key tool for determining the structures of ever more complex chemical and biochemical systems. See the special section beginning on page 1091 and at www.sciencemag.org/special/crystallog...

Building a better safety net

Nurse staffing effects on patient outcomes: safety-net and non-safety-net hospitals.

BACKGROUND Nurse staffing has been linked to hospital patient outcomes; however, previous results were inconsistent because of variations in measures of staffing and were only rarely specific to types of patient care units. OBJECTIVE To determine the relationship between nurse staffing in general and intensive care units and patient outcomes and determine whether safety net status affects thi...

No-net Polyhedra

1. Introduction. It is often said that when the conditions are right, discoveries are made by different people at the same time. The discovery of the non-Euclidean geometry, and the invention of calculus are the most frequently mentioned examples. Here is another example (with an incomparably less significant subject) which I noticed recently. My note [4] described a starshaped polyhedron which...