Johnson Polyhedron-Dual Compounds

by pmoews, published

Johnson Polyhedron-Dual Compounds by pmoews Oct 15, 2012


Here are the 92 Johnson Polyhedron-Dual Compounds. The openSCAD files are collected in Johnson_Compounds_Scad.zip and a selection of the stl files is in Johnson_Compounds_Stl.zip.

The dual stl files described in thing:32101 were converted to polyhedron commands to speed computation.

The Johnson polyhedra are varied, some are not very symmetric, and in fact some of the compounds are ugly. However 8 of the Johnson polyhedra have vertices which are equidistant from the origin, (J27, J34, J37, J72, J73, J74, J75, and J80), and their compounds resemble the Archimedean-Catalan compounds.

Elongated Johnson polyhedral compounds often have interesting belts or end caps. Attractive ones are: J35, J38, J42, J43, J46, and J48. The truncated cubes and dodecahedrons, J66, J67, J68, and J69 are fairly attractive and should make nice 2 color prints. The rhombicosidodecahedrons, J76, J77, J78, and J79 are interesting compounds with a single downward spike.

Sample stl files are:

compound_J27.stl compound_j34.stl compound_J37.stl compound_J74.stl compound_j35.stl compound_j38.stl compound_j67.stl compound_j68.stl

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Compounds J27, J34, J37, J74, and J38 need to be printed with external support. They are well handled by my Replicator. Compounds J35, J67, and j68 have clear flat faces. They can be printed directly on the build platform.

OpenSCAD has two commands which are useful for a study of these compounds; color and animate. All of the openSCAD files use color to distinguish the polyhedron from its dual. Color works in compile mode.

One parameter that needs to be set for constructing a compound is the scale between the polyhedron and its dual. The animate command in the view menu can help with this. A scale factor can be varied over a range with the animate command. Compound_j35_animate.scad contains an example of this feature. Load it in openSCAD, invoke animate and enter 16 in FPS and 250 in Steps. The polyhedron will swell to subsume the dual.