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Cat Coasters 05

by pmoews, published

Cat Coasters 05 by pmoews Mar 13, 2013
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2117Views 1097Downloads Found in Math Art
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Summary

Here is the 17th and final cat coaster. It is based on the plane group p6m. The other 16 coasters are described in things 54736, 56813, 58639, and 60958.

P6m is the plane group with the most symmetry elements. It has 2 fold, 3 fold and 6 fold rotation axes and numerous lines of reflection and glide reflection. In order to show all the symmetry elements approximately 96 cat images appear on the coaster. Individual images are not noticeable from a distance but are apparent on closer study.

Two stl files are available:

cat_coasters_p6m.stl and cat_decorations_p6m.stl

Cat_coasters_05 scad created the stl files and various images are in coasters_dxf_05.zip

Instructions

The coaster is 110 mm in diameter and should be constructed directly on the build surface. I used one shell and ten percent infill and the coaster printed in about two hours.

Two additional OPENscad programs are included for those who are interested in how the cat coasters were created. The first program, used to produce a large sample of the plane group p6m, is gen_p6m_array.scad. Its input is a single cat image, xcat.dxf. Its output is p6m_cat_cell_13.dxf, an array of 208 cats with p6m symmetry. Some additional information about the generation of the other plane groups is provided as comments in the openscad code.

The second program is gen_p6m_circle.scad. It picks out a circular portion of the large sample of the plane group to be placed on the coaster. Its output, p6m.dxf, is the input to cat_coasters_05.scad.

A pdf files that show some of the symmetry elements of p6m is included in coasters_dxf_05.zip. Reflection lines are shown in red and glide reflection lines in blue. Other pdf files illustrate the included dxf files.

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License

Cat Coasters 05 by pmoews is licensed under the Creative Commons - Attribution license.

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