Pythagorean Symbolic Dodecahedra
Pythagorean hypotheticals in a PDF/ 16 MB +
(2025 Rewritten Versions)
Computer files based on this continuing, analytical work are provided below, cost free for personal–study. A print shop service did produce pretty good print alignment for inside and outside of this dodecahedron , printed on 2X letter card stock, (11” X 17” sheet approximates 279mm X 432mm sheet sheet.) My proofed version was then roughly cut with scissors and blade. A computer-controlled cutting-machine-service was not found locally, but potentially available tools or machines might be tried for smoother cutting than shown here.
2d AlignedPrinting From JPGS:
Twice the letter size images are provided below for printing. Click on the displayed “unfolded dodecahedra images”. The first one is the outward face and the second one is the inward face for printing both on one sheet. Card stock is recommended and the print shop aligned both sides adequately during my trial.
outwardChecked.jpg
Note that tiny dots appear at circle centers, in full sized display of these images and full sized prints, to center a manual circle cutter. Use of scissors was adequate in several trials.
A variety of 3d file formats were modeled, and still deserve further formating, which could then suit an ever improving 3d services which are available online. The commercial world does strive to satisfy customers who upload 3d files for printing.
Sharing 3d files between users of different hardware and software versions has often needed individual adaptions by users, to fit individual software and hardware. This is considered normal.
If a large projection display of some kind appeals to supporters, then physically surrounding presentation installations might serve a public interest. In a non institutional, non sectarian, harmless setting it may well provide for unbiased meditation, as in private or public spaces, with autistically finished qualities, or even as an experimental project. Non-intrusive, dodecahedral installations or architecture in a garden setting like a "dodecahedral gazebo" is attractive. Virtual-Reality apps might be tried. Another form might be a tailored, fabric tent-work to fit anywhere, even indoors. Both individual and group use is considered tenable.
An example of 3d modeling is offered for download, click here, however the inside engraving was not included for lack of time, and because other means of imprinting 3d products is likely to simplify production of 3d prints, with expected updates in my software. Better adapted software and hardware is likely to call for much better models than these offered examples. (Commercially fabricated and sold knob attachments can be modeled, printed or found ready-made.)
A 3d physical printing file was modeled, (which opened in Rhino 7 as a test of transferability, meaning that a 3d print shop might print it for an individual customer). It has recessed labels on the solid dodecahedron shell and is an elaborate test idea to try out versions, even with knobs added.
Based on decades of my following pro-user-forum discussions, 3d formats may need tweaking when exporting and importing 3d files between differing brands of software and hardware. I’ve not afforded solid 3d printing or router-engraving as yet. My files and discussion are centered here for time being.
All of these 3d models were done in formZ 10 and checked with Rhino 7, (to verify export compatibility). Downloads are posted here for as long as bandwidth costs remain affordable on my currently used server. Cloud servers are not as yet sufficiently understood or familiar, and other priorities demand my time.
TwelveEssentialQualities-VR-sm.wrl, a 402 KB format is available by email request. The wrl format is an almost abandoned 3d format of the early 3d-modeling era, intended for simple, navigational, 3d-model viewing of generic 3d files, and 3d CAD brands should support it. Small, generic computer files are compact.
A larger, 12EssentialQualities-in-out-VRML.wrl, a 794 KB format is available by email request. It includes attempts to provide inside and outside inscriptions, but as of the early 2020s there are universality-issues with surface-solidity encoding, because of surface model efficiencies to reduce file size, and because of universal standards for rendering. All are all still in development for improving universal qualities of rendering and supporting technological updates.
International-language version-collaborators are welcomed if good translation possibilities are offered first. My collaboration is offered when time permits. My 3d modeling work can require refreshing memories of modeling issues, and the author here is currently using formZ-10 alone, while Rhino-7 is currently on an older, unused PC machine. However, sincere inquiries will stimulate renewed efforts in dodecahedral work, and are therefore always welcomed!
©Bo Atkinson Last Corrections: December, 2025. All works are based on continued studies, on hypothetical understandings, and the ever changing digital standards. Hylozoic knowledge is available from laurency.com, free of cost.