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Norman Johnson (mathematician)

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Title: Norman Johnson (mathematician)  
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Subject: Cantellated 120-cell, Runcinated 120-cells, Truncated tesseract, Truncated 120-cells, Uniform 5-polytope
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Norman Johnson (mathematician)

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 Although a few paper copies were circulated in the 1990s, the manuscript is still unpublished (as of 2015) and copies of it are hard to find.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]
  • 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]


  1. ^ [1] CONVEX AND ABSTRACT POLYTOPES Workshop (2005), N.Johnson — Uniform Polychora abstract
  2. ^ The Coxeter Legacy: Reflections and Projections May 12-16, 2004 The Fields Institute Toronto, ON, Canada
  3. ^

External links

  • Norman W. Johnson at the Mathematics Genealogy Project
  • Norman W. Johnson Endowed Fund in Mathematics and Computer Science at Wheaton College
  • Information about the publication of Norman Johnson's manuscript "Uniform polytopes" (still unpublished in 2015).

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