Geometric Model by A. Harry Wheeler, One-Sided Polyhedron
date: label: date made
content: ca 1940
name: label: maker
content: Wheeler, Albert Harry
notes: label: Description
content: This self-intersecting polyhedron has twelve trapezoidal faces (made out of light turquoise plastic) and twelve triangular faces (made out of dark turquoise plastic). It has twelve vertices at which two trapezoids and two triangles meet and four vertices at which six trapezoids and three triangles meet. The polyhedron has a total of 42 edges. A mark on one face of the polyhedron reads: 710 (/) e = 16 (/) k = 42 (/) f = 24 (/) e – k + f = -2. The number 710 is that Wheeler assigned to the model. The other marks refer to the Euler characteristic of the polyhedron, which equals the number of vertices, minus the number of edges, plus the number of faces. Hence: 16 – 42 + 24 = -2.
label: Description
content: Speaking more mathematically, this model consists of four copies of Wheeler’s model #708 (MA.304723.416) glued together in the pattern of a regular tetrahedron. It is a closed, non-orientable surface; that is to say it has neither inside nor outside. It has 4 x 6 = 24 faces. At first glance, there are 4 x 12 = 48 edges, but six are identified along the edges of the tetrahedron, leaving 42. At first glance, there are 4 x 6 = 24 vertices, Twelve of these (those like v4 – v6 in Figure 1) remain unidentified, but the others are amalgamated into the four vertices of the tetrahedron, for a total of 16 vertices. The Euler characteristic of the model is thus 16 – 42 + 24 = -2.
label: Description
content: For a pattern related to this model, which is dated March 1945, see 1979.3002.104.
label: Description
content: Reference:
label: Description
content: A. H. Wheeler, <I>Catalog of Models</I>, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.
label: Location
content: Currently not on view
place: label: place made
content: United States: Massachusetts, Worcester
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
label: See more items in
content: Science & Mathematics
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content: Mathematical Association of America Objects
publisher: label: Related Publication
content: Wheeler, A.H.. List of Wheeler Models
creditLine: label: Credit Line
content: Gift of Helen M. Wheeler
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: MA.304723.410
label: accession number
content: 304723
label: catalog number
content: 304723.410
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: plastic (overall material)
label: Physical Description
content: blue (overall color)
label: Physical Description
content: blue, light (overall color)
label: Physical Description
content: cut and glued (overall production method/technique)
label: Measurements
content: average spatial: 12 cm x 16 cm x 16 cm; 4 23/32 in x 6 5/16 in x 6 5/16 in