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Some authors exclude uniform polyhedra—which include the Platonic solids and Archimedean solids, as well as prisms and antiprisms—from their definition. The Johnson solids are named for the mathematician Norman Johnson (1930–2017), who published a list of 92 convex polyhedra conforming with the above definition in 1966. Moreover, Johnson ...
J N {\displaystyle J_ {n}}Solid NameImageVertices1582610391541220Johnson Solids. Besides the regular and semiregular solids, there are just ninety-two other convex polyhedra with regular faces. In 1966, the American mathematician Norman W. Johnson, a student of H.S.M. Coxeter at the University of Toronto in Canada, enumerated them. These polyhedra are sometimes called the Johnson solids.
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- Introduction
- Whirlwind History of Polyhedra
- Nomenclature
- Historical Development Resumed
- Norman W. Johnson
- References
The pyramids of Egypt (Figure 1) are one of the wonders of the world--ancient or modern--but the fact these pyramids date from about 4500 years ago makes them all the more remarkable. Mathematicians have idealized what one sees in the Egyptian pyramids; they are not really square-bottomed convex (no holes, tunnels, or notches) polyhedra with equila...
We have already seen that in ancient Egypt there was an interest in polyhedra. Even more work was done in ancient Greece about polyhedra, and there was attention paid to them in Euclid's Elements. Yet, it is still remarkable that no mention of the notion of convexity appears in Euclid, presumably because convex polygons and convex polyhedra are the...
In their search to understand patterns in a wide variety of domains, mathematicians (and others) create "words" designed to give meaning to the concepts and patterns that emerge from the practice of mathematics. Notation and nomenclature have long "bedeviled" mathematics, even experts. When some family of objects is interesting, there are usually d...
While much work on polyhedra was done before Euler, it was Euler who discovered (in modern terminology) that convex polyhedra obey this remarkable relation between their "parts:" Vertices (V) + Faces (F) - Edges (E) = 2 Over a period of time this powerful tool made it possible to discover many new facts about polyhedra and their properties. Where t...
Norm Johnson got his undergraduate education at Carleton College in Minnesota finishing his degree in 1953. His graduate work in mathematics was carried out at the University of Toronto. Much of his career was spent teaching at Wheaton College in Massachusetts, which does not have a doctoral program in mathematics. For many years Norm contributed i...
Alexandrov, A., Convex Polyhedra, Springer, New York, 2005. Berman, M., Regular-faced convex polyhedra. Journal of the Franklin Institute, 291 (1971) 329-336. Bisztriczky, R., et al (eds.), Polytopes: Abstract, Convex and Computational, Kluwer, Dordrecht, 1994. Brondsted, A., An Introduction to Convex Polytopes, Springer-Verlag, New York, 1983. Brü...
Johnson solid. A Johnson solid is a strictly convex regular-faced polyhedron that is not uniform. They are named after Norman W. Johnson, who in 1966 first listed all 92 such polyhedra. [1] Before him, Duncan Sommerville discovered the subset of them that are circumscribable. [2] In 1969, Victor Zalgaller proved that the list was complete. [3]
May 16, 2024 · The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" Archimedean solids, and the two infinite families of prisms and antiprisms). There are 28 simple (i.e., cannot be dissected into two other regular-faced polyhedra by a plane) regular-faced polyhedra in addition to the prisms ...
Johnson solid. J27: the gyrobifastigium. A Johnson solid is any convex polyhedron with regular faces that is not a Platonic solid, an Archimedean solid, or a prism (or an antiprism). There are 92 Johnson solids, which are named after Norman W. Johnson who was the first to catalog them in 1966. They included equilateral deltahedra and dipyramids ...
Johnson solids; Blind polytopes; CRFs; Johnson solids. In 1966 Norman Johnson defined and enumerated a new set of polyhedra, nowadays bearing his name: they are bound to be convex, built from regular polygons, but not being uniform. Here they are grouped into sets according to the types of facets they use. Facets being {3} only (cf. Deltahedra)
