# Geometric Models by A. Harry Wheeler and His Student Paul Tracy, Pentagonal Dodecahedra

# Geometric Models by A. Harry Wheeler and His Student Paul Tracy, Pentagonal Dodecahedra

- Description
- These cut, folded, and glued tan paper models are part of A. Harry Wheeler’s examination of extensions of the pentagonal dodecahedron. Included are:
- 1. Model of a regular dodecahedron. No makers marks.
- 2. Model with five-pointed stars on the top and the bottom, and five interpenetrating isosceles triangles for sides. A mark reads: Pentagonal (/) Dodecahedron (/) Nov 7.1935. Another mark reads: E2/E1.
- 3. Model with triangular facets, each having three inward pointing isosceles triangles, on the top and bottom. On the sides are eight additional triangles and six irregular pentagons. A mark reads: Pentagonal Dodecahedron (/) Aug 3, 1936 (/) Aug 5, 1936. Another mark reads Ω 26/21.
- 4. Model composed of the union of three irregular octahedra that are perpendicular to one another. Eight small triangles and four irregular pentagons show on each octagon – pairs of triangles are coplanar. A mark reads: Pentagonal (/) Dodecahedron (/) Aug.12, 1936 (/) Jan 15, 1936. Another mark reads: Model (/) 23. Various sides are labeled with letters of the alphabet.
- 5. Model with triangular facets, each having three inward pointing isosceles triangles, on the top and bottom. The faces of these triangles each serve as the base of an irregular pentagon facing toward the center of the polygon. Each pentagon also adjoins two other pentagons and two triangles that are toward the center. These central triangles are parts of faces of a parallelepiped. A mark on the model reads: Pentagonal (/) Dodecahedron (/) Nov-13-1933.
- 6. Model with triangular facets, each having three inward pointing isosceles triangles, on the top and bottom. Around each of these triangular facets are three additional triangular facets. Three larger isosceles triangles surround both of these groups of facets. Six additional triangles of the same size pass around the middle. A mark on the model reads: Pentagonal (/) Dodecahedron (/) Nov 12, 1935+ [sic].
- 7. Model with two ends that resemble sides of a great dodecahedron. Around the middle are ten isosceles triangles, arranged in pairs. A mark reads: Pentagonal Dodecahedron (/) Nov-7-1935. Another mark reads: Fe12 /) FeH.
- 8. Model with two ends that resemble sides of a great dodecahedron. Around the middle are ten irregular pentagons. A mark on the model reads: Pentagonal (/) Dodecahedron (/) Oct 24-35.
- 9. Model with triangular facets, each having three inward pointing isosceles triangles, on the top and bottom. The edge of each facet connects to an irregular octahedron that faces toward the center of the model. Six small triangles, three facing up and three facing down, complete the model. A mark reads: Pentagonal (/) Dodecahedron (/) Jan 5-6 (/) 1935.
- 10. Model with triangular facets, each having three inward pointing isosceles triangles, on the top and bottom. Six triangles attach to the outer edges of the facets, arranged as in an antiprism. Three sides of an irregular tetrahedron emerge at a base angle of each of the antiprism triangles, producing six points. A mark reads: Pentagonal (/) Dodecahedron (/) Dec-17 1935 (/) Feb-6, 1936.
- 11. Model with triangular facets, each having three inward pointing isosceles triangles, on the top and bottom. The model has numerous other additional triangles and irregular pentagons for sides, many coplanar in interesting ways. A mark reads: Pentagonal (/) Dodecahedron (/) Jan 28 – 1936 (/) Aug 6m 1936.
- 12. Model with rough triangular pyramids on the top and the bottom, with a small coplanar triangle jutting from the edge of each base triangle of both pyramids. Six pairs of triangles around the middle (each coplanar with another) complete the model. A mark reads; Pentagonal Dodecahedron (/) Oct-27-1935.
- 13. Model with the underlying structure of a rhombic parallelepiped. A pentagonal prism juts from each face of the parallelepiped. The prisms are arranged with three around one vertex of the parallelepiped and three around the other edge. Numerous sides are coplanar. A mark on the model reads: Pentagonal (/) Dodecahedron (/) Nov. 27, 1935.
- 14. A model with two intersecting nine-sided structures, each with three two-sided indentations at the outside and three irregular octagons around the sides. Each triangle on the outside is coplanar with another triangle there. A mark reads: Pentagonal (/0 Dodecahedron (/) Dec 18, 1935.
- 15. A two-pointed model that has three irregular quadrilaterals around each point, two rings of six small triangles adjacent to the bases of the quadrilaterals, and six pairs of larger isosceles triangles around the middle. Numerous sides are coplanar. A mark reads: Pentagonal (/) Dodecahedron (/) Nov. 12 – 1935.
- 16. A two-pointed model that has three irregular quadrilaterals around each point, A disjoint irregular pentagon and a small triangle are coplanar with (but separated from) each quadrilateral. Six other small triangles, in pairs, are scattered around the center. A mark reads: Aug.27.1936. Another mark reads: Sep40 / Sep 41.
- 17 The underling structure of this model is a parallelepiped with two vertices that serve as points. An irregular tetrahedron emerges from six of the vertices. One side of each tetrahedron is coplanar with a side of an adjacent parallelepiped. A mark reads: Pentagonal (/) Dodecahedron (/) Dec 25-26, 1935.
- 18. The underlying structure of this model is a parallelepiped with two vertices that serve as points. Around the center are six pentagonal pyramids. Each has two edges along edges of the parallelogram of the parallelepiped below it, coplanar with an adjacent parallelogram. Other faces of the pyramids also are coplanar in pairs. A mark reads: Pentagonal (/) Dodecahedron (/) Nov 8 – 1935.
- 19. The underlying structure of this model is a parallelepiped with two vertices that serve as points. Around the center are three irregular heptagons, each with four small triangles and two irregular pentagons as sides. Each pentagon is coplanar with a small triangle in an adjacent heptagon. The other small triangles are coplanar with sides of the parallelepiped. A mark reads: Pentagonal (/) Dodecahedron (/) Nov 27, 1935 (/) Sept 21, 1936. Another mark reads: Ω10 / Ω9. Compare 19 and 20. They are not identical.
- 20. The underlying structure of this model is a parallelepiped with two vertices that serve as points. Around the center are three irregular heptagons, each with four small triangles and two irregular pentagons as sides. Each pentagon is coplanar with a small triangle in an adjacent heptagon. The other small triangles are coplanar with sides of the parallelepiped. A mark reads: Pentagonal (/) Dodecahedron (/) Nov 27, 1935. Another mark reads: Ω9/ Ω10. Compare 19 and 20. They are not identical.
- 21. The underlying structure of this model is a parallelepiped with two vertices that serve as points. Each side of the parallelepiped has two tetrahedra on it that meet along one edge. This creates a seven-sided structure (plus one side that is on a face of the parallelogram). Numerous sides are coplanar. A mark reads: Pentagonal (/) Dodecahedron (/) Dec 25-26, 1935. Another mark reads: Model Ω5.
- 22. A two-pointed model that has three isosceles triangles around each point. In the middle are three intersecting irregular octahedra like model 4. Above. A mark on the model reads: Paul Tracy (/) Nov. 16, 1936. Another mark reads X11/X12.
- 23. A model that consists of six irregular tetrahedral held together by two wire triangles. Each tetrahedron ha two smaller triangles and two larger triangles and meets an adjacent triangle at a vertex. Every side of each tetrahedron is coplanar with a side of another tetrahedron. A mark reads: Pentagonal (/) Dodecahedron (/) Jan 12-18 (/) 1936.
- 24. A model consisting of six pentagonal pyramids glued together in a ring. Each side of each pyramid is coplanar with two sides of other pyramids. A mark on the model reads: Pentagonal Dodecahedron (/) Dec 5 (/) 1935. Another mark reads: Se17.
- 25. A model with a ring of six regular pentagons on the inside, Three congruent irregular heptagons on the top, and three more of these heptagons on the bottom. A mark reads: Pentagonal (/) Dodecahedron (/) Dec 8 1935. Another mark reads: Se18.
- 26. A model with a ring of six pentahedra. Each has two isosceles triangles and an irregular quadrilateral around a point and two smaller isosceles triangles below. The pentahedra are glued together so that alternating points face up and down. A mark reads: Pentagonal (/) Dodecahedron (/) Nov-15-1935. Another mark reads: Se13.
- 27. A model in two identical parts, held together with wires to leave an opening at the center. Each part has twelve sides – three pairs of isosceles triangles on the top and bottom, three larger isosceles triangles around the outside, and three isosceles triangles on the inside. It appears that the top triangle and the bottom triangles have a common vertex at the center, so that numerous sides are coplanar. A mark reads: Pentagonal (/) Dodecahedron (/) Jan 2-18, 1936. Another mark reads: Model (/) S.
- 28. The top and bottom of this hollow model have triangular facets, surrounded by three isosceles triangles, with six smaller triangles on the inside, arranged in pairs. The outside isosceles triangles join to alternate pentagonal pyramids arranged in a ring (the ring of pyramids is like 24). Numerous sides are coplanar. A mark on the model reads: Pentagonal (/) Dodecahedron (/) Dec 9, 1935. Another mark reads: Σ 9.
- 29. The top and bottom of this hollow model have triangular facets, surrounded by three isosceles triangles, with six smaller triangles on the inside, arranged in pairs. The outside isosceles triangles join alternate pentahedra which have three triangles of one size and two of a smaller size. The pentahedra also are joined, with points facing alternate directions. A mark reads: Pentagonal (/) Dodecahedron (/) Dec 15, 1935. Another mark reads: 27. Another mark reads: Ω 17/16. Numerous sides are coplanar.
- 30. The top and bottom of this hollow model have triangular facets, surrounded by three isosceles triangles, with six smaller triangles on the inside, arranged in pairs. Around the center are three hexahedra, each having two irregular pentagons, two isosceles triangles, and two irregular quadrilaterals as sides. Several sides are coplanar. A mark on the model reads: Se 14/15. Another mark reads: Paul Tracy (/) Dec 15-27-1935 9/0 Nov 2,1936. For the underlying ring, see.31.
- 31. This hollow model consists of three irregular hexahedra, each having two irregular pentagons, two isosceles triangles, and two irregular quadrilaterals as sides. The hexahedra are joined along part of edges of triangles. A mark on the model reads: Pentagonal (/) Dodecahedron (/) Dec. 15, 1935. Another mark reads: NO.63. Another mark reads: Ω15/14.
- 32.This hollow model is a ring of six irregular pentahedra. Each has two relatively large isosceles triangles, two smaller isosceles triangles, and an irregular quadrilateral as sides. The quadrilaterals or on the inside, with points in alternating directions. A mark on the model reads: Pentagonal (/) Dodecahedron (/) Dec. 28, 1935. Another mark reads: Model (/) 30. The “3” is very faint.
- Location
- Currently not on view

- Object Name
- Geometric Models

- date made
- 1935-1936
- associated dates
- 1935 10 27 / 1935 10 27, 1936 11 16 / 1936 11 16

- maker
- Wheeler, Albert Harry
- Tracy, Paul

- associated place
- United States: Massachusetts, Worcester

- Physical Description
- paper (overall material)
- metal (overall material)
- tan (overall color)
- cut & folded;cut and glued (overall production method/technique)
- Measurements
- average spatial: 8 cm x 53 cm x 43 cm; 3 5/32 in x 20 7/8 in x 16 15/16 in

- ID Number
- 1979.3002.003
- catalog number
- 1979.3002.003
- nonaccession number
- 1979.3002

- Credit Line
- Gift of Louise D. Campbell

- subject
- Mathematics

- See more items in
- Medicine and Science: Mathematics

- Data Source
- National Museum of American History

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