Spherical Icosahedral Ornaments

by pmoews, published

Spherical Icosahedral Ornaments by pmoews Jan 1, 2013

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3207Views 1348Downloads Found in Math Art
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Here are 4 icoshedral spherical ornaments constructed using the method described in thing:39818 - Icosahedral Symmetry on a Sphere. The ornaments are 70 mm in diameter and have an opening in the bottom so that they can be displayed on a lighted turntable. The image at the lower left shows them internally illuminated.

The icosahedral symmetry elements, (six 5 fold axes, ten 3 fold axes, and fifteen 2 fold axes), are easily identified in 3 of the ornaments. One ornament(04), is composed of 60 triangles and 30 circles. It has the correct symmetry but the elements are slightly more difficult to locate. It is a small version of the Times Square New Years ball.

Stl files are:

Icosahedral_ornament_01.stl - Pattern used was a rosette of 10 rays each ray bearing 2 circles

Icosahedral_ornament_02.stl - Pattern used was a rosette of 20 rays

Icosahedral_ornament_03.stl - Pattern used was the three fold array of Sierpinski triangles from thing:39424

Icosahedral_ornament_04.stl - Pattern used was a mapping of an icosahedron and a dodecahedron on to a sphere with the addition of circles at the two fold axes.

The patterns used are dxf files; they are included in dxf_files.zip. The openSCAD code is gen_icosahedral_ornament.scad.


The ornaments can be printed directly on the build platform. On my Replicator they print in under 3 hours.

The file dxf_files.zip needs to be expanded to dxf_files and held in the directory where the openSCAD code is executed.

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