## N. J. A. Sloane: Various Pictures

• Putatively optimal packing of 30 antipodal points on sphere. Taken from paper on packings in Grassmannian spaces.

• 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).
• Photographs from the Oberwolfach collection.
• 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.

• Ancient graduation photo, University of Melbourne, March 9, 1960 (jpeg, tiff).
• A link to Brendan McKay's shocking gallery of "Combinatorialists I have Known". Only someone on the other side of the earth could get away with this. (If you are in Australia, click here.)