Model of a Lennes Polyhedron by Richard P. Baker, Baker #287

This painted metal model is of a polyhedron with seven vertices, nine faces, and fourteen edges. A paper tag on the object reads: No. 287 (/) Lennes polyhedron.

This object represents the confluence of the work of two people who obtained their doctorates in mathematics early in the years of the University of Chicago. Richard P. Baker (1866-1937), who designed the model, immigrated to the United States from Great Britain in 1888, settled in Texas, and then moved to Chicago, where he enrolled as a graduate student in mathematics in 1895. While working on his dissertation, he taught high school in Illinois. By 1903, Baker had returned to Chicago and began to sell mathematical models. He obtained a teaching position at the University of Iowa in1905, received his Chicago PhD. in 1911, and remained on the Iowa faculty for the rest of his career – making models all the while.

Nels Johann Lennes (1874-1951) immigrated to the United States from Norway in 1890 and enrolled as an undergraduate at the University of Chicago in 1896, receiving a bachelor’s degree after only two years of study. From 1898 until 1907, he pursued graduate studies at Chicago while teaching at local high schools. He received his master’s degree in 1903 and his PhD. (under E.H. Moore) in 1907. The subject of Lennes’ master’s dissertation was “Theorems on the Polygon and Polyhedron,” work eventually published in 1911 under a slightly different title. Here Lennes discussed the partition of polygons into triangles and polyhedra into tetrahedra. Not all polyhedra could be partitioned into tetrahedra that had as vertices the vertices of the polyhedron. Indeed, Lennes found a polyhedron with seven vertices in which any line joining two vertices that is not an edge of the polyhedron includes points outside the polyhedron. Such polyhedra came to be called Lennes polyhedra. This model by Baker shows one of them.

References:

Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts, Tools of American Mathematics Teaching, 1800-2000, Baltimore: Johns Hopkins University Press, 2008, esp. pp. 221-225.

N. J. Lennes, “Theorems on the Simple Finite Polygon and Polyhedron,” American Journal of Mathematics<, vol. 33, 1911, pp. 37-62.

Joseph Malkevitch, “Milestones in the History of Polyhedra,” Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination, ed. Marjorie Senechel, New York: Springer, 2013, p. 61.

Deane Montgomerery and Oswald Veblen, “Nels Johann Lennes,” Bulletion of the American Mathematical Society, vol. 60 #3, 1954, pp. 264-265.

David E. Zitarrelli, “Connected Sets and the AMS, 1901-1921,” Notices of the American Mathematical Society, vol. 56 #4, April, 2009, pp. 450-458.

Currently not on view