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Johnson Compounds as Ornament

by pmoews, published

Johnson Compounds as Ornament by pmoews Nov 29, 2012

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7854Views 1730Downloads Found in Math Art
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Summary

Some of the Johnson Compounds (see thing:32445, Johnson Polyhedron_Dual Compounds) make interesting two color ornaments. As they are a combination of two polyhedra they are easy to construct, one polyhedron per color. One limitation, due to the current two color software in ReplicatorG, is that we need compound polyhedra which have flat bases. Fortunately there are a number available.

Here are three examples of two color prints where a connector has been added to the top.

Compound_J18_color_1.stl and Compound_J18_color_2.stl
Compound_J42_color_1.stl and Compound_J42_color_2.stl
Compound_J68_color_1.stl and Compound_J68_color_2.stl

The openSCAD code that produced the above files is collected in Compound_Johnson_color_scad.zip.

Instructions

The ornaments were printed on a Replicator using 3 shells and 5% infill.

The compound of J18 was chosen because J18 has only 14 faces and all are at least partially visible in the compound. The connector is attached to a vertex of the dual which protrudes through the large hexagonal face of J18. All but one of the vertices of the dual are visible which makes the compound relationships easier to see. The base does suffer some overhang which roughens some of the lower faces.

In the compound of J42 the dual forms a band around the middle of the J42 polyhedra. J68 has 11 decagonal faces, one forms its base, and the other ten are pierced by its dual.

Other Johnson compound from thing:32445 which are easily converted for two color printing are: J7, J35, J43, J44, J48, J65, J66, J67, and J69.

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At first glance I thought these were Ultraman ornaments. 

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