Norman Johnson (mathematician)

Norman Johnson (mathematician)
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.


  • Hyperbolic Coxeter Groups [1]
  • 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


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