Geometric Model of A. Harry Wheeler, Immersion of a Moebius Band (One-Sided Polyhedron)
name: label: maker
content: Wheeler, Albert Harry
notes: label: Description
content: This green translucent plastic model is an immersion of a Moebius band into three-dimensional space. That is, the surface passes through itself along certain lines. The model is dissected into three triangles and three four-sided figures (quadrilaterals). The triangles have angles of 36, 72, and 72 degrees. The pass-through lines of the immersion meet the triangles only at their vertices. The quadrilaterals are in the shape of isosceles trapezoids, and the diagonals of the trapezoids are the pass-through lines of the immersion.
label: Description
content: Wheeler described this model as: "six planes of the heptahedron forming an element to be repeated to form one-sided polyhedra." He stated that it has six vertices, twelve edges, and six faces, for an Euler characteristic of e -k +f = 0. He assigned the model number 708 or M67.
label: Description
content: Compare 1979.0102.416 (which has a full discussion of the surface), 1979.0102.197, 1979.0102.198, 1979.0102.199, 1079.0102.200, and MA.304723.718.
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
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.304723.718
label: accession number
content: 304723
label: catalog number
content: 304723.718
objectType: label: Object Name
content: Geometric Model
physicalDescription: label: Physical Description
content: green (overall color)
label: Physical Description
content: plastic (overall material)
label: Physical Description
content: cut and glued (overall production method/technique)
label: Measurements
content: average spatial: 2 cm x 7.7 cm x 6.7 cm; 25/32 in x 3 1/32 in x 2 5/8 in