polyhedra

Zometool builds models from SGDS

Monday, 28 November 2011 by Bruce Rawles

Zometool, with the addition of green struts, can build many of the designs – both 2 and 3 dimensional – that appear in the pages of Sacred Geometry Design Sourcebook (SGDS) and other 2D and 3D models. Now, more than ever, this superlative modeling system (which is also the coolest toy in the geometric Universe, in my opinion) is a fabulous complement to Sacred Geometry Design Sourcebook.

The green struts allow for square root of 2 proportions relative to blue struts, which allow shapes like tetrahedra, octahedra, star tetrahedra, several more Archimedean Solids and MUCH more to be built. Amazing how adding another proportional system to the prior version seems to add many dimensions to the possibilities. (BTW, the feline model within the model is Cooper, our new kitten.)

Here are examples of some of the Zometool models that appear in the pages of Sacred Geometry Design Sourcebook. I’ll be adding to these as I go on, so look for announcements in the monthly bulletin about updates to this page. This example, from page 236, shows the 2-D projection of icosahedral and dodecahedral cross-sections, and the underlying golden rectangle and golden-ratio-based geometric proportions.

Chrome Zome Jewelry

Monday, 28 November 2011 by Bruce Rawles

Zometool Jewelry – featuring elegant chrome-plated Zome hubs – is now available! Nancy (our resident jeweler) says she can make these earrings with the bottom (Swarovski 6mm) crystal in a variety of colors in addition to the pink (rose) and jet black varieties shown here, including clear, aqua, blue, light blue, midnight blue, teal, green, purple, amethyst purple, and other colors and variations. Each earring features the unique Zometool hub (12 pentagonal holes, 20 triangular holes and 30 golden rectangle holes) with a metallic chrome finish. Chains and earring hooks will vary with styles.

This is just our first offering, so look forward to matching necklaces and other variations coming soon!

Note: These two pairs are now available. We’ll feature more items on GeometryCode.com and NancyBolton.com as they become available.

To buy a pair, specify the stock number, and send a money order or check to Intent Design Studio for $30 a pair plus $5 shipping to US addresses. Colorado residents, please add applicable sales tax.

Stock number CZ1: $30 + $5 shipping to US addresses
1 Pair Chrome-plated Zometool hubs, with Pink Swarovski 6mm crystals, silver hooks and silver chain

Stock number CZ2: $30 + $5 shipping to US addresses
1 Pair Chrome-plated Zometool hubs, with Jet Black Swarovski 6mm crystals, silver hooks and gun-metal plated chain

(The chrome ‘hub’ is about 5/8″ in diameter; the chain is 1″ long; the hook is 1/2″ long; the crystal is about 1/4″ long and the total length or ‘dangle’ of the earrings is about 2 3/8″.)

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 infinite 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.