sacred geometry toys

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 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.

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.

Fractile Fun

Sunday, 17 July 2011 by Bruce Rawles

Fractiles are versatile geometric toys made of magnetic diamond shaped tiles.

I first learned about Fractiles and Zometool in the fall of 1997 at a Sacred Geometry conference in Boulder, Colorado.

While Zometool is primarily a 3D modeling system, Fractiles are generally used in just 2D. Accordingly, they make a great introduction to interesting ‘flat’ geometries with negligible technical background. Since the diamond-shaped tiles are arranged on a flat surface, they take up very little space, which means that they are very portable, even when assembled in any of a gazillion patterns.

What makes the combinations of these 3 diamond shaped patterns so versatile (and unique)? The angles of the rhombic shapes are all multiples of 1/14th of a circle, so one can complete a radially arranged design, and/or make amazing tiling patterns, or just play around with very aesthetically enjoyable possibilities with the permutations.

I’ve enjoyed playing — I’m just a big kid — with Fractiles for many years. I don’t even need the excuse of having younger family members visiting to bring them out and design elegant patterns with these unique magnetic tiles in 3 diamond shapes. Here are a few examples of the endless patterns that can be made in a few minutes.

Here’s a list of features from the Fractiles website:

Award-Winning Fractiles-7 received a Parents’ Choice Award for play and educational value, quality and design.
Versatile: Use these wonderful little diamond-shaped tiles to easily create seven-fold snowflakes, starbursts, spirals, bouquets of flowers, swarms of fireflies, beautiful mandalas, butterflies, spaceships, 3-D illusions, much more.
Elegant Geometry: The versatile elegant geometry allows anyone to create endless varieties of imaginative and beautiful designs. Designs range from very simple to infinitely complex. One can spend tireless hours discovering new levels of play and design.
Infinite Possibilites: Puzzle with millions of solutions — limitless combinations and diverse designs.
Wide Appeal: Fractiles Fans range from young children to seniors, from those with no math background to advanced math researchers.
Easy to Manipulate: The MAGNETIC tiles stay put – yet slide easily on their specially textured board – a helpful feature for anyone with fine motor skill problems. Magnetic Fractiles-7 is a great travel toy!
Builds Pattern Recognition Skills: Pattern recognition skills are key to learning. Lack of pattern recognition skills is linked to learning disabilities Fractiles-7 is so much fun you may not even notice how regular play increases your pattern recognition skills.
“Fractiles is so popular with my first graders, that we have to have a sign up for equal turns!” – teacher Marilyn Bowker
“My 7th and 8th graders live for free time so they can play with Fractiles.” – Sandra Bullard, The Prentice School, “Where Children with Dyslexia Learn to Learn”
Ethical: Production Fractiles is manufactured in the USA with no child labor or exploitation.

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.