Model of a Dual of Archimedean Solid by Richard P. Baker, Baker No. 547 IV

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This metal model painted white was constructed by Richard P. Baker. A mathematics professor at the University of Iowa, Baker believed that models were essential to instruction in many parts of mathematics and physics. Over one hundred of his models are in the NMAH collections.
A typed label taped to the model reads: No. 547 (/) SPACE DUALS OF (/) ARCHIMEDEAN HALF- REGULAR (/) BODIES No. 465, IV, p. 20.
Mathematicians have known since ancient times that there are only five regular convex polyhedra. The faces such a solid are identical regular polygons and the vertices are all alike (each vertex has the same arrangement of polygons). The Hellenistic mathematician Archimedes showed that there are thirteen other polyhedra that have identical vertices, sides of the same length, and faces that are not all the same regular polygons. These came to be called the semi-regular Archimedean solids. There also are two infinite series of semi-regular polyhedra, the prisms (with a regular polygon on the top, the same regular polyhedron on the bottom, and squares around the sides) and the antiprisms (with a regular polygon with an even number of sides on the top, the same polygon on the bottom, and equilateral triangles around the sides). For examples of these polyhedra, made by Michael Berman, see 1978.1065.006 through 1978.1065.20.
In the mid-nineteenth century, the mathematician Eugène Catalan described another set of polyhedra which have identical faces and form regular polygons at a vertex when that vertex is truncated. However, the faces are not regular polygons and the vertices are not identical. These thirteen polyhedra are called duals of Archimedean solids or Catalan solids.
Baker published a catalog of his models in 1931, and included as #465, numbers I through XV, thirteen Archimedean solids plus plus a representative prism and an antiprism. Examples of these do not survive at the Smithsonian. He also made models he called “space duals of Archimedean half-regular bodies,” and might now be described as Catalan solids. These had a general number 547 in Baker’s scheme, and given index numbers I through XV. This is the fourth of them (e.g. IV). Baker’s 1931 catalog includes models assigned numbers as high as 542, suggesting that this model and the other Archimedean duals date from slightly after the catalog.
The thirty-two faces of the model are equal isosceles triangles. Six vertices have four triangles that come together and eight have six. Truncating the model would produce six squares and eight regular pentagons. The polyhedron is sometimes called a tetrakis hexahedron, although Baker did not use that name.
H. M. Cundy and A. P. Rollet, Mathematical Models, Oxford: The Clarendon Press,1961.
R. P. Baker, Mathematical Models, Iowa City, Iowa,1931, p. 20.
Currently not on view
date made
ca. 1932
ca 1932
Baker, Richard P.
Physical Description
metal (overall material)
white (overall color)
soldered (overall production method/technique)
average spatial: 9.8 cm x 9.8 cm x 9.8 cm; 3 27/32 in x 3 27/32 in x 3 27/32 in
ID Number
accession number
catalog number
Credit Line
Gift of Frances E. Baker
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History


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