Skip to main content
U.S. flag

An official website of the United States government

Dot Gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.


The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Geometric Properties of The Icosahedral-hexagonal Grid On The Two-sphere


An icosahedral-hexagonal grid on the two-sphere is created by dividing the faces of an icosahedron and projecting the vertices onto the sphere. This grid and its Voronoi tessellation have several desirable features for numerical simulations of physical processes on the sphere. While several methods to construct the icosahedral grid mesh have been proposed over the past decades, and empirical data have been collected to understand and help improve the grid, rarely have analytical analyses been done to investigate the basic geometric properties of the grid. In this paper, we present an analytical analysis of several geometric properties of the icosahedral grids based on two basic constructions: recursive and nonrecursive construction. We point out that these geometric properties can be improved with modified construction procedures. We demonstrate how these improvements impact the numerical integration of PDEs over the sphere.

Article / Publication Data
Available Metadata
Accepted On
June 13, 2011
Fiscal Year
Publication Name
Siam Journal On Scientific Computing
Published On
June 01, 2011
Final Online Publication On
October 01, 2011
Print Volume
Print Number
Page Range
Submitted On
June 05, 2009


Not available


Authors who have authored or contributed to this publication.

Not available