Polyhedral Nerds Assemble!

When: Wednesday, June 3rd
Time: 7:30pm EST
Re: Polyhedral Design w/ Mike

Thank to all that participated. Here are the promised files, including STEP files for both the session and the completed shape, printable STL files, original shape STL, and the saved Stella4D file.
Truncated Cuboctahedron Files.zip (296.3 KB)

Original Post

The option on the left uses 3D printed connectors that are hidden inside and use screws to connect faces. The second one uses 3D printed borders that attach to each other without screws. I’m using these shapes as an example, and the one we do will be different. Which method would the group like to learn?

  • Internal connectors with screws
  • Border style
0 voters
19 Likes

I voted for one but I’d love to see an overview of whichever one we don’t do the deep dive into.

13 Likes

What shape shall we make? Here are a few choices.

Truncated Cuboctahedron
Icosidodecahedron
Pentagonal Hexecontahedron

  • Truncated Cuboctahedron
  • Icosidodecahedron
  • Pentagonal Hexecontahedron
0 voters

The Truncated Cuboctahedron requires modeling 3 shapes, the Icosidodecahedron 2, and the Pentagonal Hexecontahedron has 1. However, the Pentagonal Hexecontahedron requires printing 60 face connectors and is probably the trickiest to assemble.

8 Likes

Based on the scheduled time, it looks as though I will probably not be able to attend as I will still be driving home from work (7:30pm EST = 4:30pm Arizona) and I will not get home until ~6pm. Will this event be recorded (i.e. audio/video) and available to play at a later time?

4 Likes

I’ll record it and post it here.

8 Likes

Looking forward to the meet. Thanks @pubultrastar!

5 Likes

Thank you so much!

5 Likes

Thank you @pubultrastar for sharing your knowledge and experience. We thorougly enyoyed learning from you. today. :ok_hand:

8 Likes

Sorry for being late! I’ve been so busy, I didn’t even realize we’ve reached June. And I had to think about the time zone. Great information though, thanks again!

8 Likes

You really made a few lights come on for me. The biggest one is when in doubt look the construction tab and there is probably a unique way do a construction plane that I hadn’t thought of.

8 Likes

Apologies for being a no-show. I was dealing with an issue for a client, lost track of time, and didn’t excuse myself. Bummed I missed out.

8 Likes

Missed my alarm. I’ll be there next time!

6 Likes

I’ve posted the video from last night along with the files at the top of this thread. Thanks to all who joined in on the session. Please post any questions here if you have any!

10 Likes

What is the difference between Platonic and Archimedean? Is it just that Platonic Polyhedra have congruent sides, and Archimedean have some sides of different shapes?

8 Likes

Platonic and Archimedean solids are highly symmetrical, 3D convex polyhedra. Platonic solids are uniform and made from a single type of regular polygon, while Archimedean solids are made from two or more types of regular polygons, maintaining identical vertex configurations throughout. [1, 2]

Platonic Solids

Named after the ancient Greek philosopher Plato, there are exactly 5 Platonic solids. They are defined by three strict rules: [1, 2]

  1. All faces are congruent (identical in shape and size).
  2. All faces are regular polygons (all sides and angles are equal).
  3. The exact same number of faces meet at every vertex. [1, 2]

The five Platonic solids include:

  • Tetrahedron: 4 faces (triangles)
  • Cube (Hexahedron): 6 faces (squares)
  • Octahedron: 8 faces (triangles)
  • Dodecahedron: 12 faces (pentagons)
  • Icosahedron: 20 faces (triangles) [1, 2, 3, 4, 5]

Archimedean Solids

Named after the ancient mathematician Archimedes, there are exactly 13 Archimedean solids. They drop the strict single-polygon requirement of Platonic solids, allowing combinations of two or more regular polygons, but still follow these rigid rules: [1, 2, 3]

  1. All faces are regular polygons.
  2. The arrangement of polygons is identical around every vertex. [1, 2]

Many of them can be formed by “truncating” (slicing off the corners) of Platonic solids. The 13 Archimedean solids are: [1, 2]

  • Truncated Tetrahedron
  • Cuboctahedron
  • Truncated Cube
  • Truncated Octahedron
  • Rhombicuboctahedron
  • Truncated Cuboctahedron (Great Rhombicuboctahedron)
  • Snub Cube
  • Icosidodecahedron
  • Truncated Dodecahedron
  • Truncated Icosahedron
  • Rhombicosidodecahedron
  • Truncated Icosidodecahedron (Great Rhombicosidodecahedron)
  • Snub Dodecahedron [1, 2, 3]
11 Likes

Wow. The things we don’t know we don’t know. Thanks.

5 Likes