An attempt at an optimal covering with
1082 points
on the sphere.
The picture shows the convex hull of the points.
The picture has the symmetry of the det +1 icosahedral
group of order 60, because we constructed it that way.
There are 12 pints with 5 neighbors, the rest
have 6 neighbors.
Constructed by R. H. Hardin and N. J. A. Sloane. For further
information see our web page
Spherical codes (packings, coverings and max volume arrangements with icosahedral symmetry).
(The different colors indicate very small variations in the circumradius of the triangles. For most purposes the colors can be ignored.)
An attempt at an optimal covering with
3002 points
on the sphere.
The picture shows the convex hull of the points.
The picture has the symmetry of the det +1 icosahedral
group of order 60, because we constructed it that way.
There are 12 pints with 5 neighbors, the rest
have 6 neighbors.
Constructed by R. H. Hardin and N. J. A. Sloane. For further
information see our web page
Spherical codes (packings, coverings and max volume arrangements with icosahedral symmetry).
(The different colors indicate very small variations in the circumradius of the triangles. For most purposes the colors can be ignored.)
An attempt at an optimal covering with
55472 points
on the sphere.
The picture shows the convex hull of the points.
The picture has the symmetry of the det +1 icosahedral
group of order 60, because we constructed it that way.
There are 12 pints with 5 neighbors, the rest
have 6 neighbors.
Constructed by R. H. Hardin and N. J. A. Sloane. For further
information see our web page
Spherical codes (packings, coverings and max volume arrangements with icosahedral symmetry).
(The different colors indicate very small variations in the circumradius of the triangles. For most purposes the colors can be ignored.)
An attempt at an optimal covering with
48002 points
on the sphere.
This picture is especially interesting because the
angular separation between the points is very close to 1 degree
- this answers a question we are often asked by geographers
and others: how should one place the smallest possible number of points
on the sphere so that they are 1 degree apart?
The picture shows the convex hull of the points.
The picture has the symmetry of the det +1 icosahedral
group of order 60, because we constructed it that way.
There are 12 pints with 5 neighbors, the rest
have 6 neighbors.
Constructed by R. H. Hardin and N. J. A. Sloane. For further
information see our web page
Spherical codes (packings, coverings and max volume arrangements with icosahedral symmetry).
To obtain explicit coordinates for these points,
go that page,
enter 48002 as the number of points and click the
button for "Covering".
An attempt at an optimal packing of
8192 points
on the sphere.
The picture shows the network
of points at the minimal separation.
More precisely: we join two of the 8192 points by a line
if they are at the min. distance of the packing to within epsilon.
The picture has the symmetry of the det +1 icosahedral
group of order 60, because we constructed it that way.
Constructed by R. H. Hardin and N. J. A. Sloane. For further
information see our web page
Spherical codes (packings, coverings and max volume arrangements with icosahedral symmetry).
The picture at the top right of this page is taken from
For All Practical Purposes: Introduction to Contemporary
Mathematics, "Spotlight 10.2: Neil Sloane",
W. H. Freeman, NY, 3rd edition, 1994, pp. 308-309.
Picture of me taken by the photographer Laine Whitcomb, 105 East 2nd St. NY NY 10009; (212) 677 6754
(small, large).
Link to
photo of Susanna Cuyler and me
on our porch, taken by Nadia Heninger, Aug 27, 2005.
Small pic of me:
here.
Graduation photo, University of Melbourne, March 9, 1960
(jpeg, tiff).
Taken by my father, Charles Ronald Sloane (1915-2004).
