Norman Johnson (mathematician)

This article is about the pure mathematician Norman Johnson. For the statistician, see Norman Lloyd Johnson.

Norman Johnson
Born	November 12, 1930(1930-11-12)
Citizenship	United States
Fields	Mathematics
Institutions	Wheaton College, Norton, Massachusetts
Alma mater	University of Toronto
Doctoral advisor	H. S. M. Coxeter
Known for	Johnson solid (1966)

Norman W. Johnson (born November 12, 1930) is a mathematician, previously at Wheaton College, Norton, Massachusetts. He earned his Ph.D. from the University of Toronto in 1966 with a dissertation title of The Theory of Uniform Polytopes and Honeycombs under the supervision of H. S. M. Coxeter.

In his 1966 doctoral thesis Johnson discovered three uniform antiprism-like star polytopes named the Johnson antiprisms. Their bases are the three ditrigonal polyhedra - the small ditrigonal icosidodecahedron, ditrigonal dodecadodecahedron and the great ditrigonal icosidodecahedron.

In 1966 he enumerated 92 convex non-uniform polyhedra with regular faces. Victor Zalgaller later proved (1969) that Johnson's list was complete, and the set is now known as the Johnson solids.

More recently, Johnson has participated in the Uniform Polychora Project, an effort to find and name higher-dimensional polytopes.

Works

• Hyperbolic Coxeter Groups
• Convex Solids with Regular Faces (or Convex polyhedra with regular faces), Canadian Journal of Mathematics, 18, 1966, pages 169–200. (Contains the original enumeration of the 92 Johnson solids and the conjecture that there are no others.)
• The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966

External links

• Norman W. Johnson at the Mathematics Genealogy Project.
• Norman W. Johnson Endowed Fund in Mathematics and Computer Science at Wheaton College