3D Geometries

Nanodot Newbie

Sunday, 27 November 2011 by Bruce Rawles

I recently started experimenting with Nanodots Magnetic Constructors (a 216 magnet set of remarkably strong (and fun!) little spherical (NdFeB) magnets. They are enjoyable to play with just from a tactile, sensory perspective, since they are like a set of high-tech micro-planets you can squeeze and morph in your hand like modeling clay … and the next moment, when you pull the amorphous mass apart, you get dynamic strings of metallic pearls that have amazing tenacity to maintain the connection to the whole. I’m just getting started in using Nanodots to explore my primary interest in geometric shapes.

Here are a few photos of Nanodots in 2D (flat shapes in a plane).

As you might imagine, if you make two shapes and put them close together on a flat surface, suddenly you find yourself with one shape! Symbolically, the magnetic principle abhors duality! :-) When you have smallish shapes in close proximity, but not so close that they join, you can rotate one and the neighboring shapes will rotate in tandem, almost like invisible gears; cool! :-)

I’ve made a few simple 3D geometries with Nanodots, but will need to spend more time and try a variety of polyhedra and other shapes. Interestingly, a few of the shapes (like the tetrahedron which moves immediately into a square and the octahedron which jumps into a more space-filling arrangement) are a bit tricky to hold (without some external constraint), since their geometries when made of magnetic spheres tend to fly apart and rearrange into more stable magnetic alliances. I think I see why the seasoned users make stable clusters and then make the larger shapes out of these smaller clusters.

Since their magnetic properties lend toward modeling with larger clusters that aren’t as influenced by smaller numbers of spheres, I’ll explore further with larger sets. Here are some excellent examples that others (mostly with larger sets than 216) have made.

Dotpedia

Squishy Icosahedron Frame – YouTube

There are LOTS of great examples (both videos and static images) of polyhedra and other geometric shapes that are superb uses of Nanodots here; enjoy!

Hands-on sacred geometry workshop Oct. 8, 2011 in Castle Rock, CO

Wednesday, 28 September 2011 by Bruce Rawles

I’m giving a day-long, hands-on* sacred geometry workshop from 10AM-5PM on Saturday, October 8, 2011, here at our new home in Castle Rock, Colorado. We’re about 20-60 minutes south of Denver, depending on what part of the metropolitan area you might be driving from. Cost is on a sliding scale from $25-$75 based on need. Pre-registration is required, due to limited space around our dining room table! :-) Please contact Bruce via GeometryCode.com to register. I’ll be happy to phone or Skype with even more details. Please bring a geometer’s compass, straight-edge, scissors and cellophane tape; I will supply lots of 2D and 3D handouts including platonic solid fold-up patterns, plus LOTS of visual multimedia imagery, animation and more, along with plenty of theory on the mystical underpinnings of sacred geometry! :-) I typically bring most of my extensive library on the subject out for everyone to peruse; you can see most of them (except some of the rare and obscure titles) on the GeometryCode Amazon aStore. Here is a full resolution printable flyer for the event.

Infinite Recursive Zoom In of Nested Platonic Solids

Thursday, 4 August 2011 by Bruce Rawles

Infinite Nested Platonic Solid Recursion

This continuous loop rotates around a nest of the five Platonic Solids: Cube (red), Tetrahedron (yellow), Octahedron (green), Icosahedron (blue) and Dodecahedron (purple), returning to a cube oriented along the same x-y-z axes one third the size in each dimension as the outer cube. The transparency of the inner cube changes from 100% opaque to 100% transparent as the animation proceeds, which allows playing as an infinte recursive loop. Each “new cube” (as one loop of the animation completes) has 1/27th the volume of the original, since the side length is 1/3 of the starting cube.

This is a higher resolution version of the clip originally uploaded to YouTube on March 31,2007.

Dodecadodecahedron screen saver

Friday, 17 June 2011 by Bruce Rawles

Dave Van Dyke of Z Axis Graphics, who generated this lovely Dodecadodecahedron animation video, just generously contributed a free companion Dodecadodecahedron screen saver (Windows only; In Windows it wants to install in C:\Windows\system32\); enjoy!!! Dave’s comment about the screen saver gift: “…just thought it would be fun.” Thanks, Dave!!!

Notes from the animator (Dave Van Dyke):
The dodecahedron was created and animated using 3DS Max. If you intend to animate the “P” and “Q” parameters of the Hedra you must use the Edit Mesh modifier. The Edit Poly modifier will not work. The nice Glow effect is an option in the Mental Ray renderer found under the Renderer Tab. The frame is formed by making a copy of the dodecahedron and applying the Lattice modifier. The material assigned to the dodecahedron is a Multi/subObject material. The material for the star faces and the remainder of the dodecadodecahedron are the same. Having two materials that are the same allows you to take control of the transparency of one selection set of polygons leaving the others unaffected.

Update (16July2011): Dave has again contributed another interesting screensaver. This one is an organic-looking simulation of magnetic particles streaming around the magnetic lines of force defined by a torus. Thanks again, Dave!

Zometool Inspiration

Saturday, 28 May 2011 by Bruce Rawles

Carlos Neumann zometool microdo — Carlos Neumann with a Zometool ‘microdo’ model

Recently we had lunch in Denver, Colorado with Carlos Neumann of Zometool, the maker of my favorite geometric modeling tool/toy. It’s really both a fabulous design and 3D visualization modeling environment AND a fun toy for any age – even those who don’t think they like geometry. He brought along a Zometool model of the “Microdo.” See the close up photograph below:

zometool microdo photo — Zometool “microdo” model

and a screen snap of it using the new Zomepad software, a VERY cool 3D modeling app that lets one rotate, modify, translate, zoom, etc. Zometool models in real time. The screen snaps just give a hint of how fun this app is!

Zomepad Microdo model — Zomepad image of Microdo model

Here’s a chrome plated (dare we say “Chrome Zome”? :-) hub. Notice that the polygons that make up the hub are equilateral triangles, regular pentagons and golden rectangles, which provide phenomenal versatility in creating Platonic and Archimedean Solids, as well as a staggering array of amazing shapes that use these foundational geometries and their 3-fold and 5-fold rotational symmetries and much more. Stay tuned for fun and decorative developments with these shiny orb-like gems! :-)

ZomeTool Chrome plated hub — Chrome plated Zometool hub

Another thing to notice about the Zomepad models is that there are background dots: red (pentagonal), yellow (triangular) and blue (golden rectangular) that are aligned behind the model as it rotates around so that you can see when you’re lined up with an axis of rotation and/or symmetry. Pretty neat!

Here are the default models that you can explore with the current pre-release version of the ZomePad app:

ZomePad model - pentagram/pentagon fractal — ZomePad model – pentagram/pentagon fractal

ZomePad Hypercube (Tesseract) model — ZomePad Hypercube (Tesseract) – 3D ‘shadow’ of a 4D polytope

ZomePad 3D Hexagonal (honey comb) grid model

Here are some Zometool models I put together years ago:

zometool stellated dodecahedron — Zometool stellated dodecahedron

The stellated dodecahedron model hung above my office cubicle at Grass Valley Group in northern California for several years; sure made a great landmark to direct folks to my desk! :-)

Here’s another of the countless topologies and geometric variations that one can make with Zometool hubs and struts. If you enjoyed Tinkertoys (or perhaps Erector sets, etc.) when you were a kid, check out Zometool. There really isn’t anything else like it. The engineering and precision design of the hub alone is an amazing story in itself that Marc Pelletier gave us a quick tour of when I was at a sacred geometry conference in Boulder, Colorado years ago, where I met lots of wonderful geometer colleagues I’m still mostly in touch with.