Norman Johnson (mathematician)


Norman Johnson
Norman Johnson (mathematician).jpg
Born(1930-11-12)November 12, 1930
DiedJuly 13, 2017(2017-07-13) (aged 86)
CitizenshipUnited States
Alma materUniversity of Toronto
Known forJohnson solid (1966)
Scientific career
InstitutionsWheaton College, Norton, Massachusetts
Doctoral advisorH. S. M. Coxeter

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

Early life and education

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

Johnson earned his undergraduate mathematics degree in 1953 at Carleton College in Northfield, Minnesota[2] followed by a master's degree from the University of Pittsburgh.[1] After graduating in 1953, Johnson did alternative civilian service as a conscientious objector.[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

He completed final edits for his book Geometries and Transformations just before his death on July 13, 2017, and nearly completed his manuscript on uniform polytopes.[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 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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