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Geometric Model by A. Harry Wheeler, One-Sided Polyhedron

Geometric Model by A. Harry Wheeler, One-Sided Polyhedron

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This pink plastic model has tetrahedral symmetry. It is the union of four congruent heptahedra. Each heptahedron has one equilateral triangle, three small triangles (with hypotenuses along the edges of the equilateral triangle), and three irregular quadrilaterals for sides. Each of the quadrilaterals is coplanar with a quadrilateral in another heptahedron. A mark on the model reads: 658.
According to Wheeler, the model has eighteen vertices (e), thirty-six edges, and nineteen faces. This gives an Euler characteristic of e – k + f = -1. Wheeler also says that the model can be derived from a regular icosahedron by removing alternate octants. He attributes the construction to K. Merz of Chur, Switzerland.
A.H. Wheeler, Catalog of Models, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.
Currently not on view
Object Name
Geometric Model
Wheeler, Albert Harry
place made
United States: Massachusetts, Worcester
Physical Description
plastic (overall material)
pink (overall color)
cut and glued (overall production method/technique)
average spatial: 5 cm x 6.5 cm x 6 cm; 1 31/32 in x 2 9/16 in x 2 3/8 in
ID Number
accession number
catalog number
Credit Line
Gift of Helen M. Wheeler
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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