Norman Johnson | |
---|---|

Born | |

Died | July 13, 2017 | (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]}

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 PhD 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]}

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]}

- ———— (1960-05-01). "A Geometric Model for the Generalized Symmetric Group".
*Canadian Mathematical Bulletin*.**3**(2): 133–142. doi:10.4153/CMB-1960-016-7. S2CID 124822323. - Grünbaum, Branko; ———— (January 1965). "The Faces of a Regular-Faced Polyhedron".
*Journal of the London Mathematical Society*. s1-40 (1): 577–586. doi:10.1112/jlms/s1-40.1.577. - ———— (January 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. S2CID 122006114. Zbl 0132.14603. - ———— (1966).
*The theory of uniform polytopes and honeycombs*(PhD thesis). University of Toronto. OL 14849556M. Archived from the original on 2022-05-20. Retrieved 2022-05-20. - ———— (December 1969). "
*Euclidean Geometry and Convexity*by Russell V. Benson (review)".*The American Mathematical Monthly*.**76**(10): 1165–1160. doi:10.2307/2317227. JSTOR 2317227. - ———— (January 1981). "Absolute Polarities and Central Inversions". In Davis, C.; Grünbaum, B.; Sherk, F. A. (eds.).
*The Geometric Vein*. New York City: Springer Nature. pp. 443–464. doi:10.1007/978-1-4612-5648-9_28. ISBN 978-1-4612-5648-9. - ————; Weiss, Asia Ivić (July 1999). "Quaternionic modular groups".
*Linear Algebra and Its Applications*.**295**(1): 159–189. doi:10.1016/S0024-3795(99)00107-X. - ————; Weiss, Asia Ivić (December 1999). "Quadratic Integers and Coxeter Groups".
*Canadian Journal of Mathematics*.**51**(6): 1307–1336. doi:10.4153/CJM-1999-060-6. S2CID 111383205. - ————; Kellerhals, Ruth; Ratcliffe, John G.; Tschantz, Steven T. (December 1999). "The size of a hyperbolic Coxeter simplex".
*Transformation Group*.**4**(4): 329–353. doi:10.1007/BF01238563. S2CID 123105209. - ————; Kellerhals, Ruth; Ratcliffe, John G.; Tschantz, Steven T. (2002-04-15). "Commensurability classes of hyperbolic Coxeter groups".
*Linear Algebra and Its Applications*.**345**(1–3): 119–147. doi:10.1016/S0024-3795(01)00477-3. - ———— (2012). "Regular Inversive Polytopes". In Deza, Michel; Petitjean, Michel; Markov, Krassimir (eds.).
*Mathematics of Distances and Applications*. Sofia: ITHEA. Archived from the original on 2022-05-20. Retrieved 2022-05-19. - ———— (2018-06-07).
*Geometries and Transformations*. ISBN 978-1-107-10340-5. OCLC 1043026091. OL 27839953M. Retrieved 2022-05-20.