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3D Geometries

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

GeometryCode bulletin for May 2014

Saturday, 31 May 2014 by Bruce Rawles

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

Article: Physicists discover ‘clearest evidence yet’ that the Universe is a hologram

Here’s an interesting article that suggests “the three dimensions we perceive are actually just ‘painted’ onto the cosmological horizon.” … It’s always fun to see physics confirm what contemporary non-dual metaphysics – and undoubtedly countless other mystical teachings – have been informing us all along. This is a helpful reminder of the realization that shook the scientific community not too many decades ago when luminaries like Einstein, Bohr, Planck and other met in Copenhagen; their work evolved into the quantum physics we know today … but we all conveniently forget the foundational premise of this ‘new paradigm’ which suggests that the mechanism painting on the cosmological horizon – the primary agency responsible for our material world isn’t material at all. It …. is our mind! :-)

Martineau Solar System Geometries art exhibit still in Castle Rock, CO

An 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 are STILL on display until (about) June 16, 2014 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 last month’s bulletin. Enjoy! :-)

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

TwinCitySprinkler-TetrahedralSculpture
Photos of sculpture the models taken in Corpening Plaza, Winston-Salem NC
  • Timely art news: Colleague VanDorn Hinnant has a new sculpture featuring stacked tetrahedra, with this commentary: “Many of you know that my designs for sculptures to commemorate the 1913 merger of the cities of Salem and Winston have been selected for the city’s first public art commission. Most do not know that the title I chose for the sculptures was inspired by Maya Angelou’s poem titled “Still I Rise”. When I first read the RFP (request for proposals) that the City of Winston-Salem published last year a poem immediately began to emerge. About six weeks ago I was driving to work at Diggs Gallery and a truck passed me with the words on the vehicle “Twin City Sprinklers” and the idea came to me to invite Dr Angelou to co-write the poem with me to commemorate the merger of the two cities. Since beginning this poem I have continued to receive occasional inspirations and added them to the draft. Upon hearing of Dr Angelou’s passing, several new lines for the poem came to me. The two sculpture designs depicted in the photos of the half-sized models below are fast approaching completion, and the bases are ready to be fabricated. Here’s a link where you can assist with your support for this work.
  • Mark Lundin’s interactive 3D online Rubik’s cube; thanks to colleague Liberty McGeo of SunWheel Productions for pointing this out via a post on her FB page.
  • A giant Flower of Life pattern made on a beach in Santa Cruz, Calif.
  • An upcoming sacred geometry workshop in Barcelona and Madrid, Spain by Dr. Santiago Cordoba Rojas

(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, Platonic Solids, polyhedra, sacred geometry art, sacred geometry news

GeometryCode bulletin for April 2014

Monday, 12 May 2014 by Bruce Rawles

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

Martineau Solar System Geometries art exhibit in Castle Rock, CO

An 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 are now on display between May 7 and June 16, 2014 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. Enjoy! :-)

About the Martineau Solar System Geometries art and the Astronomical Geometry It Is Based On

The 12 images were inspired by the remarkable work of John Martineau, in his highly recommended book: “A Little Book of Coincidence.” The accuracy of his models is truly astonishing, typically 99.8 to 99.9% accurate. Johannes Kepler, who was fascinated with the idea of simple geometric models defining the planetary orbits, was on the right track, he just didn’t explore far enough… His original woodcuts appear below, showing the outer and inner solar system. He would have been thrilled to learn of Martineau’s models! I think John Martineau’s name will (some day, hopefully soon) be heralded among Kepler, Galileo, Newton and Einstein for the astronomical discoveries he’s made.

Kepler's solar system models - outer and inner

Here’s my image paying homage to Kepler’s elegant, though not particularly accurate models of the solar system.

Homage To Kepler's model of the solar system

All images in my “Martineau Solar System” series were created with the freeware ray tracing application, POV-Ray;  I’ve been using MegaPOV more recently. Here is an online gallery of this art (available as posters, greeting cards or apparel), plus other related images & photography.

More details about the individual images in the Martineau Solar System Geometries art exhibit

Here are early studies (sans NASA or other photographic tiled imagery for the background) for both the inner and outer solar system models, respectively, that John Martineau figured out; note that these highly accurate geometric approximations to planetary orbits averaged as circles (instead of the ellipses they actually are) were accomplished using only 2-dimensional geometric models, and rather simple ones at that! :-)

Outer Solar System per Martineau - POVray study

Outer Solar System per Martineau - POVray study

Outer Solar System: Solar System to Uranus Per Martineau

The background image for this foreground montage of John Martineau’s geometric solar system models is a tiled Kirlian photography image of fingertip corona discharge patterns that I took decades ago using a homebrew adaptation of a kit from Edmund Scientific Company.

Inner Solar System: Solar System to Mars Per Martineau

The background image for this closeup foreground montage of John Martineau’s geometric solar system models is a tiled color-inverted version of the Kirlian photography image used in the Outer Solar System model; the intent being to depict the warmer colors as a metaphor for the proximity to our sun.

Venus And Mars Per Martineau

With tiled planes of solar and lunar motifs in the background, a dodecahedron (12 pentagons, Plato’s symbol for ether or spirit) defines 20 spheres (the metallic looking ones) that exactly touch. Inside these are the orbit of Venus (green) and outside all is the orbit of Mars (faint red). The accuracy of the model (averaging the major and minor axes of the elliptical orbits) is 99.98%

Earth And Mars Per Martineau

With tiled planes of flora (a Hawaiian plant swirled within a honeycomb grid) and fauna (Chambered Nautilus) motifs in the background, an icosahedron (20 triangles, Plato’s symbol for water) defines 12 spheres that exactly touch. The centers of these define the orbit of Earth (blue) and outside all is the orbit of Mars (red). The accuracy of the model (averaging the major and minor axes of the elliptical orbits) is 99.9%

Earth And Venus Per Martineau

This image was inspired by the remarkable work of John Martineau, in A Little Book of Coincidence. Five tiled spiral galactic (NGC300) planes form the background. The perigee and apogee relationship between Earth and Venus is described by a nested pentagram pair. Accuracy is 99.9%

Venus and Earth Orbits Per Martineau

The orbital relationship between Earth and Venus is described by two concentric circles. The inner circle represents the orbit of Venus which passes through the centers of 8 circles that just touch each other. The outer circle represents the orbit of Earth which touches the outer sides of these 8 circles. The accuracy of this relationship is 99.99%

Earth and Mars Cross Per Martineau

This image was inspired by the illustration at the bottom of page 40 of the remarkable work of John Martineau, in A Little Book of Coincidence. A circle (Earth orbit) just touches each of 4 small circles, which in turn, each just touch 4 larger circles, which each touch the largest outer circle (Mars orbit). Spheres are used to represent the circles for artistic effect, and the outermost eight spheres are decorative only. The accuracy of this relationship is 99.9%

Venus And Mercury Per Martineau

Tiled, mirrored images of Mercury’s surface features (colorized three different ways) form the background. Three circles, whose centers are the vertices of an equilateral triangle, define an outer circle which exactly fits around the three (the orbit of Venus) and an inner circle which exactly touches the three vertices (the orbit of Mercury). Accuracy is 99.9%

Jupiter And Mars Per Martineau

This image was inspired by the remarkable work of John Martineau, in A Little Book of Coincidence. Tiled planes of Jupiters surface (top & bottom) and a colorized map of Mars sketched by the astronomer Antoniadi (left & right) form the background. The centers of four circles define the orbit of Jupiter and the orbit of Mars is defined by the red circle. The accuracy of this relationship is 99.99%

Jupiter, Saturn And Uranus Per Martineau

This image was inspired by the remarkable work of John Martineau, in A Little Book of Coincidence. Tiled, mirrored images of Saturns rings (colorized three different ways) form the background. Three concentric circles, define the orbits of Jupiter, Saturn and Uranus. The innermost (Jupiter) touches 8 middle points of an octagram. The outermost octagram points define Saturns orbit. The circle around an equilateral triangle around Saturn defines Uranus. The accuracy of the Jupiter/Saturn relationship is 99.9%

Jupiter And Earth Per Martineau

This image was inspired by the remarkable work of John Martineau, in A Little Book of Coincidence. Tiled colorized planes of the Great Red Spot of Jupiter (shifted +/- 120 degrees of hue, too!) form the background. The hexagon within a triple nested hexagram defines the orbit of Earth. The orbit of Jupiter is defined by the outer circle, and astonishingly, two clusters of asteroids (the Trojans) occupy Laplace Points, which are also defined by the + and – 60 degree positions in Jupiters orbit as shown on the diagram below. Accuracy of the Earth/Jupiter orbital relationship is 99.8%

Neptune And Uranus Per Martineau

This image was inspired by the remarkable work of John Martineau, after he wrote A Little Book of Coincidence (hence the model does not appear in that book.) Tiled images of Neptune’s surface line the union of two vesical tubes to form the background. A tetrahedron and its truncation define the orbits of Neptune and Uranus, respectively, with 99.93% accuracy. Here’s an early study (sans NASA tiled imagery for the background):

Neptune and Uranus Per Martineau - POVray study

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

Here are a couple of geometric websites this month, with lots of interesting content for geometry enthusiasts:

  • Geometric – a Pinterest site
  • Sacred Geometries and Their Scientific Meanings – The Interface between Science and the Transcendental

(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, Archimedean Solids, Bulletins, Platonic Solids, polyhedra, sacred geometry art, sacred geometry news

GeometryCode bulletin for March 2014

Sunday, 30 March 2014 by Bruce Rawles

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

Cube of One Way Mirrors

a Cube of One Way Mirrors

Reminiscent of Sara Frucht’s Kaliedoscapes which also explore the interplay of light reflected on the interior surfaces of polyhedra, both Platonic and Archimedean – see this recent related post about her reVERB™ Casual Music Game – this article about a cube with flexible walls made of one-way mirrors has a neat video showing what happens when the attached bellows change the geometry from flat planar surfaces. I’d like to see a ‘walk-through’ gallery of Kaleidoscapes that allow visual and acoustical interaction with all the Archimedean and Platonic solids as an interior participant.

New York City Sacred Geometry Fest

We already mentioned this event in the January 2014 bulletin, but there’s still time left (as far as I know) to attend a conference about sacred geometry – and these don’t happen that often – in New York next month. If anyone attends (I would, but have prior commitments) please feel free to send me any interesting links or reports from this fest … and say hi to our colleagues! Here’s a page of links from their site, and an example of one of the many workshops at this event: Leonardo’s Mind: The Geometry of the Renaissance.
Sacred Geometry Fest 2014 NYC

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

Here are a few websites and links of interest to sacred geometry enthusiasts:

  • Romanesco broccoli based-design anyone? This article explores shapes that may assist ecology, aesthetics and design.
  • A fun video: Mathemusician Vi Hart Explains Space-Time with a Music Box and a Möbius Strip
  • Thanks to my Mom for sending me this link with a lovely acoustic recording of cylindrical resonances: Singing Bowls for World Peace and Healing
  • Organically geometric, this page of rock sculpture photography was from new age musician Iasos’ most recent bulletin.
  • An interesting LinkedIn conversation (you can see where I chimed in) addressing “Do you know/use/ sacred geometry/golden ratio in your works?”
  • Designer’s guide to the Golden Ratio
  • “… I am trying to give people a sense of unity rather than build even more barriers.” says Mariam Nihal, author of an article entitled: Geometry key to Islamic art: Dana Awartani
  • Ripples from the big bang? … Synchronistically, my niece is studying gravitational waves in space using laser interferometry.
  • A Pinterest page: Geometric Inspired
  • This designer uses a stellated octahedron a.k.a. star tetrahedron a.k.a. daVinci’s ‘stella octangula’ in her logo
  • An article that explores Sacred Geometry and Unified Fields by MonkeyBuddha
  • … and although it was a couple weeks ago (March 14), here’s a bit about The True Meaning of Pi Day … for fun

(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, Archimedean Solids, Bulletins, Platonic Solids, polyhedra, sacred geometry art, sacred geometry news

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ZomeTool Zometool - my favorite 3D creative tool/toy system. I use mine for demos and exploration.
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Fibonacci Quarterly - Official Publication of the Fibonacci Association (since 1963)

Recent GeometryCode Posts

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