Johnson Polyhedra Duals

thingiverse

The 92 Duals of Johnson Polyhedra are available for download as STL files, with details on their construction provided by the method described in thing:30958. To learn more about duals and view examples, visit Wikipedia or George Hart's Virtual Polyhedra Site at http://www.georgehart.com/virtual-polyhedra/duality.html. In simple terms, if an object A transforms into B via a process and B returns to A using the same process, they are considered duals where their vertices and faces exchange roles. While there are 92 polyhedra, this text presents select examples with their duals and compounds to demonstrate the process. These compressed files contain the STL files for these examples: J9.stl, J9_dual.stl (compound_j9.stl), J12.stl, J12_dual.stl (compound_j12.stl), and J16.stl, J16_dual.stl (compound_j16.stl). The program that produces openSCAD programs for the duals is also included in johnson_duals_scad.zip, with all the STL files of the duals found in johnson_duals_stl.zip. Four STL files require external support during printing: compound_j9.stl, J12.stl, compound_j12.stl, and compound_j16.stl. In examples 1, 2, and 3, J9.stl is an elongated pentagonal pyramid with specific face types and 11 vertices; its dual, J9_dual.stl, has a regular pentagonal face and both share vertices in the compound. J12 is a triangular dipyramid of equilateral triangles with five vertices, while its dual is a triangular prism with six vertices; the 5 vertices of J12 protrude from the dual in the compound. Lastly, J16 is an elongated pentagonal dipyramid with 10 triangular faces and 12 vertices, whereas its dual is an elongated pentagonal prism featuring a regular pentagonal face, 15 vertices, and the 12 vertices of J16 protrude from the dual in the compound.