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You are here: Home / Archives for polyhedra / Platonic Solids

Platonic Solids

GeometryCode bulletin for October 2014

Wednesday, 29 October 2014 by Bruce Rawles

(1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials

Bubble Soccer - toroids and truncated tetrahedra

Follow the bouncing ball: toroidal torsos, tetrahedra and truncated icosahedra

I recently saw a fun video on FaceBook showing soccer players with their torsos enclosed in protective toroidal bubbles, and then found this related Bubble Soccer USA site. Perhaps sport is now imitating what some believe is the shape of the human electromagnetic energy field? Below is a stylized illustration I did some years ago of nested rainbow colored toroids surrounding a meditator in lotus position.

Toroid Fractal Nest Rainbow

Of course, the shape of a traditional soccer ball is roughly the projection of a truncated icosahedron onto a sphere. Since inflated bubbles provide superb cushioning, they are also found on this NASA Mars lander video; note the tetrahedral cushioning balloons (with 6 quasi-spherical balloons on each face) about 3.5 minutes into the video.

NASA - Mars landing - tetrahedral cushion

Solar System Geometry Calendars for 2015

I just updated the popular Martineau Solar System Series calendar for 2015. The models depicting averaged (circular rather than elliptical) orbit relationships are astonishingly accurate … and simple! Enjoy! :-)

MartineauCalendarCover644w

Spiral shell sculptures

Sculptor, fellow artist, geometer and student of metaphysics, Stefán Geir Karlsson recently sent me some interesting conceptual images and commentary about making some really large spiral shell sculptures. His virtual vortices would be fun to explore as full size realized art forms. I’ve long had similar ideas for making huge models of polyhedra with mirrored interiors that we could walk inside, see the labyrinthine reflections and hear the equally fractal echoes; all metaphors of our projections mirrored back to us! :-) Colleague Sara Frucht of Berkeley, Calif. has some excellent smaller models she calls ‘Kaleidoscapes‘ with wonderful interior mirror reflections.

(2) Websites, Books, Videos, Imagery, Music and Quotes

  • Golden Ratio and sound – John Chowning audio
  • A site featuring the work of noted geometer and scholar Tons Brunés and classic sacred geometry constructions
  • 22 maps and charts that will surprise you; some interesting images for map enthusiasts; the last one (#22) about Laniakea and the Milky Way; is particularly impressive to keep our tiny earth-bound issues in perspective! :-)
  • a related, linked video about supercluster Laniakea … staggering!
  • a lovely photo of newly-discovered galaxy SMM J2135-0102
  • Golden Ratio For Kids: Pinterest page
  • Werner Vogt’s geometrically inspired architecture
  • Lissajous figures (I used to make wild animations with an analog oscilloscope and a bank of oscillators in high school) and Hans Jenny’s Cymatics are kindred art forms. … John Martineau has a great little book on the Harmonograph (among his generous assortment of gems in his Wooden Books series; scroll down to the Wooden Books section on our Sacred Geometry books page. … Steven K. Roberts: “here was my childhood harmonograph with adjustable pendulums and U-joints to the drawing tool, with rack-and-pinion pickoff via servos to a second platform above.

(3) Request for Submissions

As always, please let me know how I might support you. Please send me any interesting items about sacred geometry or related interests … since everything is inter-related!If you would like to stay connected and network with kindred souls online, check out my pages on Facebook, YouTube, Twitter, Pinterest and LinkedIn. I always enjoy connecting with both recent and long-time friends and colleagues and discovering new friends of friends :-)Thanks for your interest & support! :-) BTW, I always appreciate enthusiastic reviews on the Amazon SGDS book page, and the newer Amazon book page for The Geometry Code. It’s a good “win-win” way to cross-promote your work as well.

If you like to color with colored pencils (or other media), make 3-D fold-up geometric art, do stained glass, quilts, geometric arts and/or crafts, or just want an extensive reference/resource of geometric archetypes, patterns and essential line art, you might enjoy a copy of my first book, Sacred Geometry Design Sourcebook: Universal Dimensional Patterns.

If your leanings are more metaphysical … and perhaps whimsical :-) … you might enjoy my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation. It was originally going to have geometry and Hermetic Laws/symbolism as a primary focus, but in 2007, a reawakened interest in the spiritual masterpiece, A Course In Miracles – thanks to Gary Renard – shifted the primary emphasis to an exploration of the two thought fundamental systems we all vacillate between, and how we can gradually shift our mind’s identity to the happy one.

Bruce Rawles
PO Box 192, Castle Rock, Colorado 80104
author of The Geometry Code book; co-author of The Geometry Code screensaver
author of Sacred Geometry Design Sourcebook
Free monthly email bulletin on sacred geometry and related subjects
You might also enjoy my blog which has lots of other fun and info in addition to these bulletins.
BTW, there are TWO different GeometryCode bulletins (and you can subscribe to either or both):
  • a monthly bulletin (which tends to be sent towards the end of the month when I realize I haven’t sent one yet! :-)
  • an update bulletin (you can subscribe on any page from the box in the right sidebar just below the search box) that gets sent any time there’s a new blog post the prior day

Filed Under: 2014 Bulletins, 2D Geometries, 3D Geometries, Bulletins, Platonic Solids, sacred geometry art, sacred geometry calendars

GeometryCode bulletin for September 2014

Tuesday, 30 September 2014 by Bruce Rawles

(1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials

Mutation game – prototype

Inventor Mark White recently sent me a prototype – check out his KickStarter campaign – for his very cool new “Mutation” game which allows 4 white and 4 black ‘knobs’ to traverse the edges of a colorful dodecahedron. You get an intuitive and kinesthetic sense of the shape and its topology by traversing the edges and it has a good ‘feel’ in your hand. The goal of one of many possible games is to be the first to make your 4 knobs (white or black) into a tetrahedral pattern. Here’s a bright youngster at a recent science event I participated in playing with the proto.

girl with Mutation game proto

More fun with Zometool

At the aforementioned educational event (the Castle Rock, Colorado library “Full STEAM Ahead program” Science-Technology-Engineering-Arts-Mathematics) last weekend, I set up a demo showing a recursive video animation I did of the nested Platonic solids on my laptop … along with a 3d model made from ZomeTool which some of the young event participants helped me to add to, making a sort of quasi-partially-truncated inner-stellation (nowhere near mathematically correct jargon, but you kinda get the idea :-) of a cube with green and blue struts which enclosed the outermost octahedron. Fun! :-)

Nested Platonics - Stellation Added

Kindle edition of The Geometry Code turned 2 yesterday

Amazing that it’s already been a couple of years since I released the Kindle edition of the book: The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation … You can read more about this geometric/Hermetic/metaphysical romp here, and download the first chapter for free here. The ‘tree-ware’ version has been around even longer for those that enjoy a ‘real book’ to curl up with.

(2) Websites, Books, Videos, Imagery, Music and Quotes

  • neat article: New Experiment Will Answer Some Mind-Bending Questions On Whether We Live In a Hologram
  • Dream Art Gallery (thanks to Ed Kellogg for this, and numerous other submissions!)

(3) Request for Submissions

As always, please let me know how I might support you. Please send me any interesting items about sacred geometry or related interests … since everything is inter-related!If you would like to stay connected and network with kindred souls online, check out my pages on
Facebook, YouTube, Twitter, Pinterest and LinkedIn. I always enjoy connecting with both recent and long-time friends and colleagues and discovering new friends of friends :-)Thanks for your interest & support! :-) BTW, I always appreciate enthusiastic reviews on the Amazon SGDS book page, and the newer Amazon book page for The Geometry Code. It’s a good “win-win” way to cross-promote your work as well.

If you like to color with colored pencils (or other media), make 3-D fold-up geometric art, do stained glass, quilts, geometric arts and/or crafts, or just want an extensive reference/resource of geometric archetypes, patterns and essential line art, you might enjoy a copy of my first book, Sacred Geometry Design Sourcebook: Universal Dimensional Patterns.

If your leanings are more metaphysical … and perhaps whimsical :-) … you might enjoy my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation. It was originally going to have geometry and Hermetic Laws/symbolism as a primary focus, but in 2007, a reawakened interest in the spiritual masterpiece, A Course In Miracles – thanks to Gary Renard – shifted the primary emphasis to an exploration of the two thought fundamental systems we all vacillate between, and how we can gradually shift our mind’s identity to the happy one.

Bruce Rawles
PO Box 192, Castle Rock, Colorado 80104
author of The Geometry Code book; co-author of The Geometry Code screensaver
author of Sacred Geometry Design Sourcebook
Free monthly email bulletin on sacred geometry and related subjects
You might also enjoy my blog which has lots of other fun and info in addition to these bulletins.

Filed Under: 2014 Bulletins, 3D Geometries, Bulletins, Platonic Solids, polyhedra, sacred geometry toys

LA Talk Radio Interview with Dave Cohen

Monday, 22 September 2014 by Bruce Rawles

Dave Cohen - Good Vibration Station-LA talk Radio

Hermetic Laws (such as Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause&Effect, Gender), Geometric symbolism, the Great Pyramid, intrinsic Oneness reflected in the principle of interconnectedness, UFOs, Atlantis, holographic projections, Fibonacci spirals, the Golden Ratio in nature, modern physics, architectural acoustics, flying, resonant toning, geological dating, Chambered Nautilus shells, galactic spirals, and DNA helices were just few of the topics we touched on in this initial interview – more to follow – with the exuberant Dave Cohen on his “Good Vibration Station” radio show on LA Talk Radio. We’ll just have to talk about Plato’s allegory of the cave (and his famous solids) … plus many other subjects in greater detail on a subsequent show – which we intended to get to, but ran out of time! BTW, I mentioned Dave’s very cool sacred geometry inspired shirts on a prior FaceBook post, but his elegant designs deserve mention here again.

https://geometrycode.com/audio/DaveCohen-LAtalkRadio-21Sep2014.mp3

Filed Under: 2D Geometries, 3D Geometries, Fractal Geometry, Platonic Solids, sacred geometry art, sacred geometry books, sacred geometry interviews

GeometryCode bulletin for June 2014

Monday, 30 June 2014 by Bruce Rawles

 

(1) News, Events, Interviews, Workshops, Classes, Exhibits, Products, Articles, Tutorials

torus In warp drive conceptual model

Toroids make cameo appearance in warp drive prototype

Ready to travel at warp speed? It looks like the familiar geometry of our friendly (galactic) neighborhood torus might factor into future warp drives. Here’s an interesting article and a related one: NASA Reveals Latest Warp-Drive Ship Designs – that – once again – suggests that Gene Roddenberry was on the right track. NASA’s Advanced Propulsion Lead, Dr. Harold White gives a talk about how Faster-Than-Light (FTL) travel might actually work – thanks to Dave Van Dyke of Z-Axis Graphics for this link.

… and in the ‘closer to home’ appropriate technology arena, another geometric icon, the spiral shows up in home energy systems…

Archimedes spiral wind generator

Archimedes: a new efficient wind generator design uses a spiral form

How about an 80% efficiency ratio for a home power wind turbine design? This new wind power capturing technology leverages the intrinsic efficiency of the spiral form to harness wind energy for small homes and apartments … or perhaps an array for larger systems? I sure saw a lot of larger wind turbines on my recent trip to California; wind farms in Wyoming, and in California east of Livermore over Altamont Pass, near Tehachapi, Palm Springs, and San Gorgino Pass. Why not combine solar and wind.

Martineau Solar System Geometries art reception and end of exhibit in Castle Rock, CO

I will be appearing at a “Meet the Artists” reception in the CR Bank Room East at the Castle Rock library on July 8, 2014 from 7-8PM. This will conclude the multi-month exhibit of all 12 of my “Martineau Solar System” series framed giclées prints, plus 24 framed acrylic, collage and mixed media art images by Nancy Bolton-Rawles  on display at the Philip S. Miller Public Library, 100 S. Wilcox St., Castle Rock, Colorado 80104 during regular library hours. This is the first public exhibit for either of us since we moved to Colorado almost 3 years ago… You can find upcoming, ongoing and past exhibits, classes and other events here. LOTS more details about the individual images are in the April 2014 bulletin.

Find Your Geometry Name

In case you missed it, here’s a quick, fun diversion to help you find your ‘geometry name‘ using the first letter of your first and last name. Enjoy! :-)

(2) Websites, Books, Videos, Imagery, Music and Quotes

  • Where do a morphing tesseract, a walking ostrich and a vintage black and white photo of a nun converge? In this endlessly looping video! Thanks to Ed Kellogg for sending this link.
  • DaVinci’s “stella octangula” a.k.a. stellated octahedron a.k.a. star tetrahedron makes an appearance in my home town (Livermore, California) in the microscopic geometry of this new ultralight, ultrastiff material.
  • Flaming Lotus Girls use dodecahedral hubs in their fiery Burning Man sculpture.
  • Quantum biology in the plant kingdom?
  • Geometric tattoos, anyone?

(3) Request for Submissions

As always, please let me know how I might support you. Please send me any interesting items about sacred geometry or related interests … since everything is inter-related!If you would like to stay connected and network with kindred souls online, check out my pages on
Facebook, YouTube, Twitter, Pinterest and LinkedIn. I always enjoy connecting with both recent and long-time friends and colleagues and discovering new friends of friends :-)Thanks for your interest & support! :-) BTW, I always appreciate enthusiastic reviews on the Amazon SGDS book page, and the newer Amazon book page for The Geometry Code. It’s a good “win-win” way to cross-promote your work as well.

If you like to color with colored pencils (or other media), make 3-D fold-up geometric art, do stained glass, quilts, geometric arts and/or crafts, or just want an extensive reference/resource of geometric archetypes, patterns and essential line art, you might enjoy a copy of my first book, Sacred Geometry Design Sourcebook: Universal Dimensional Patterns.

If your leanings are more metaphysical … and perhaps whimsical :-) … you might enjoy my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation. It was originally going to have geometry and Hermetic Laws/symbolism as a primary focus, but in 2007, a reawakened interest in the spiritual masterpiece, A Course In Miracles – thanks to Gary Renard – shifted the primary emphasis to an exploration of the two thought fundamental systems we all vacillate between, and how we can gradually shift our mind’s identity to the happy one.

Bruce Rawles
PO Box 192, Castle Rock, Colorado 80104
author of The Geometry Code book; co-author of The Geometry Code screensaver
author of Sacred Geometry Design Sourcebook
Free monthly email bulletin on sacred geometry and related subjects
You might also enjoy my blog which has lots of other fun and info in addition to these bulletins.

Filed Under: 2014 Bulletins, 2D Geometries, 3D Geometries, 4D Geometries, Bulletins, Platonic Solids, sacred geometry art, sacred geometry news, sacred geometry videos

Find Your Geometry Name

Sunday, 15 June 2014 by Bruce Rawles

Find Your Geometry Name
Mine would be Bisected Rhombicosidodecahedron… What’s yours? :-)

Filed Under: 2D Geometries, 3D Geometries, 4D Geometries, Archimedean Solids, Fractal Geometry, Numbers and Proportions, Platonic Solids, polyhedra, sacred geometry art

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