Johnson Polyhedra

by pmoews, published

Johnson Polyhedra by pmoews Jan 25, 2012

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Johnson polyhedra have faces composed of regular polygons: triangles, squares, pentagons,hexagons, octagons and decagons. There are only 92 such polyhedra. Instructions for making paper models are available, but with stl files one could print more durable examples.
I recently came across the netlib library of polyhedra at
which includes the Johnson polyhedra. I was pleased to see that it would be easy to convert the files to openSCAD polyhedron comands. Polyhedron commands are
a compact way of describing a polyhedron and, when executed, output an stl file.
I wrote a fortran program to convert the files; however a few files had errors. I had corrected most errors with openSCAD's unusual, but marvelous, "thrown together" mode when I was informed that the errors had already been noticed and corrected by George Hart
There is a link on the George Hart page to a set of VRML files which display the Johnson polyhedra with color coded faces. References are also given.
Using the corrected files I was able to finish the conversion. You will find the 92 scad files in Johnson_Scad_Files.zip and the 92 stl files in Johnson_Stl_Files.zip.
To get a large version of the polyhedra it is best to print a hollow structure. Five examples of hollow polyhedra stl files are included here together with a sample openSCAD file, hollow_j03.scad.


The stl files can be printed directly, or slightly scaled up, to produced a small model. Note that the z axis in the stl files is not at right angles to the largest face which would have been ideal for the printer. Rotate the model so that a face is nearly parallel to the build surface and use the "lay flat" command, in the rotate menu, and the "put on platform" command, in the move menu, to properly position the model for printing.
Instructions for making hollow Johnson polyhedra are included as comments in hollow_j03.scad. All samples were printed with a raft and without support.
Included hollow Johnson Polyhedra
J03 triangular cupola
J26 gyrobifastigium (only Johnson polyhedra that fills space)
J37 elongated square gyrobicupola
J60 metabiaugmented dodecahedron
J79 bigyrate diminished rhombicosidodecahedron

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Johnson Polyhedra by pmoews is licensed under the Creative Commons - Attribution license.

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Please i am a hobbyist...

can anyone tell me how i can "print" the nets of these objects with my "normal" computer programs (i have a Mac!)?

I am not an expert, but would like to have somemodells of paer...

Thanks for help!

You would need a 3d printer, first.

After you have that, you can find tutorials online to print using replicatorg and a stl file.

I stand in awe... this is an amazing collection of solids.

I plan on printing these for my students for practice with point group.

Will you be doing the 230 unique space groups next?

I'm trying to print the metabiaugmented dodecahedron - I set 0% fill 2 walls and every few layers it strings across a - flat layer across the inside. What Skienforge settings should be used to get hollow?

Under Fill change Diaphragm Period to 99999. It crates a solid layer every 100 layers by default.

Nevermind...I think it has to do with the wall thickness...If I made it hollower then it would print as I expected it to. Pretty thick walls.