Geometric Model of A. Harry Wheeler, Immersion of a Moebius Band (One-Sided Polyhedron)

Description:

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.

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.

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.

Reference:

A.H. Wheeler, Catalog of Models, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.

Maker: Wheeler, Albert Harry

Location: Currently not on view

Place Made: United States: Massachusetts, Worcester

Subject: Mathematics

Subject:

See more items in: Medicine and Science: Mathematics, Science & Mathematics

Exhibition:

Exhibition Location:

Credit Line: Gift of Helen M. Wheeler

Data Source: National Museum of American History

Id Number: MA.304723.718Accession Number: 304723Catalog Number: 304723.718

Object Name: Geometric Model

Physical Description: green (overall color)plastic (overall material)cut and glued (overall production method/technique)Measurements: 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

Guid: http://n2t.net/ark:/65665/ng49ca746b4-a6d3-704b-e053-15f76fa0b4fa

Record Id: nmah_1073529

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