Norman Johnson (mathematician)

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This article is about the pure mathematician Norman Johnson. For the statistician, see Norman Lloyd Johnson.
Norman Johnson
Norman Johnson (mathematician).jpg
Born (1930-11-12) November 12, 1930 (age 85)
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.[1]

The literature on polytopes contains several references to a manuscript by Johnson titled Uniform Polytopes. Although a few paper copies were circulated in the 1990s, the manuscript is still unpublished (as of 2015) and copies of it are hard to find.


  • Hyperbolic Coxeter Groups [2]
  • Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics 18: 169–200. doi:10.4153/cjm-1966-021-8. ISSN 0008-414X. MR 0185507. Zbl 0132.14603.  Contains the original enumeration of the 92 solids and the conjecture that there are no others.
  • The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966[3]


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