Norman Johnson (mathematician)

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Norman Johnson
Norman Johnson (mathematician).jpg
Born (1930-11-12)November 12, 1930
Died July 13, 2017(2017-07-13) (aged 86)
Citizenship United States
Alma mater University of Toronto
Known for Johnson solid (1966)
Scientific career
Fields Mathematics
Institutions Wheaton College, Norton, Massachusetts
Doctoral advisor H. S. M. Coxeter

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician at Wheaton College, Norton, Massachusetts.[1]


Johnson earned his undergraduate mathematics degree in 1953 at Carleton College in Northfield, Minnesota[2] followed by Master’s degree from the University of Pittsburgh.[1] 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. From there he accepted a position in the Mathematics Department of Wheaton College in Massachusetts and taught until his retirement in 1998.[1]

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.[3][4]

Johnson is also credited with naming all the uniform star polyhedra and their duals, as published in Magnus Wenninger's model building books: Polyhedron models (1971) and Dual models (1983).[5]

Death and final works[edit]

He completed final edits for his book Geometries and Transformations just before his death on July 13, 2017.[1] His unpublished manuscript, a nearly-completed work on uniform polytopes, is expected to yet be published in some form.[1]


Norman Johnson was born on November 12, 1930 in Chicago. His father had a bookstore and published a local newspaper.[1]

After graduating in 1953, Johnson did alternative civilian service as a conscientious objector.[1]


  • The theory of uniform polytopes and honeycombs, Ph.D. Dissertation, 1966[6]
  • Hyperbolic Coxeter Groups, paper[7][citation needed]
  • Convex polyhedra with regular faces, paper containing the original enumeration of the 92 Johnson solids and the conjecture that there are no others[8]
  • N. W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5 [1]


  1. ^ a b c d e f g Norman W. Johnson (12 November 1930 to 13 July 2017), Asia Ivic Weiss and Eva Marie Stehle, The Art of Discrete and Applied Mathematics
  2. ^ Alumni Farewells: Deaths reported from May 3, 2017 to August 3, 2017
  3. ^ George Hart, Johnson solids (retrieved 10 June 2016)
  4. ^ Johnson solid, Mathworld, (retrieved 10 June 2016)
  5. ^ Wenninger, Magnus (1983), Dual Models, Cambridge University Press, doi:10.1017/CBO9780511569371, ISBN 978-0-521-54325-5, MR 0730208 p. xii
  6. ^ Johnson, Norman W; The theory of uniform polytopes and honeycombs Archived 2013-10-14 at the Wayback Machine., Ph.D. Dissertation, University of Toronto, 1966
  7. ^ The Coxeter Legacy: Reflections and Projections May 12-16, 2004 The Fields Institute Toronto, ON, Canada
  8. ^ 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.

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