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Highlights from the January Post Archives on GeometryCode.com

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I occasionally encounter ICYMI (In Case You Missed It) anthologies of archives from publications that have been around a while. Since that’s true for GeometryCode.com, I thought I would do the same for this site. I’m sure there are plenty of new (or newish) visitors who have probably never seen many of the prior posts from this website, as well as seasoned readers who may have missed or perhaps forgotten some of the content we’ve featured over the years… since 2009 (and before that for a decade or so on other websites such as our former online home, intent.com. (Thanks to the “Wayback Machine” for maintaining archives of our original, primitive (embarrassing by today’s standards) work in our early web explorations. The format and underlying architecture have changed significantly, but the content of “Sacred Geometry Home Page” hasn’t changed much since this snapshot from Jan. 15, 1998!)

With a bit of clerical assistance from AI, I’m presenting a retrospective (by month, starting with January) of some of the 222 prior posts from GeometryCode that might merit revisiting. However, I will still add new finds as they cross my path, so this quasi-sabbatical won’t be devoid of new content. If you (or someone you know) has something that would enhance this website, please let me know! Thanks for your many years of support while I spend a few months (probably a dozen) re-exploring perennial topics via prior posts with evergreen concepts, ideas, and imagery.

I am using chronological order (rather than the more conventional reverse chronological order), putting recent posts at the bottom to give buried content some breathing room for new or renewed exposure.

Welcome to our curated recap of some of the blog posts published in January across recent years on GeometryCode.com. Each entry below includes the post title, published date, and a graphic image from its content, presented as enticements for the curious to review prior content.

GeometryCode.com — Highlights from January Posts (from 2009 through 2025)

These last few summaries are courtesy of ChatGPT. Each entry below includes the post title, published date, and a multi-paragraph summary of its content.

  • Cedar Sprig Symbolism: Freedom or Fragmentation?
    Published January 2023

    In this thoughtful January post, Bruce Rawles reflects on participating in a local New Year’s Day Peace Hike in Yachats, Oregon. He uses the symbolism of cedar sprigs as a metaphor for both individual and collective identity. He connects the fractal geometry of the cedar — with its self-similar branching patterns — to how we might view unity and fragmentation in human thought and social life.

    The post weaves imagery from the hike with contemplative commentary on how symbol and form interact: the geometric complexity of cedar sprigs becomes a lens to examine inclusion, peace, and the fractal nature of experience. Rawles draws philosophical connections between natural patterns and inner psychological landscapes, prompting readers to consider whether they view life through lenses of separation or wholeness. This piece blends personal narrative with meditative geometry, exemplifying the blog’s broader mission of uniting mathematical form with lived experience.

  • 2024 Martineau Solar System Calendars Available Now
    Published January 2024 (note that calendars are available again for 2026!)

    This post announces the release of the 2024 Martineau Solar System Geometry wall calendars — a perennial favorite among readers interested in precise geometric representations of planetary orbit relationships. The calendar series is built from ray-traced images that model the intricate spatial relationships among the planets, combining astronomical accuracy with sacred geometry aesthetics. These calendars serve both as functional datekeepers and as contemplative art pieces that invite reflection on the harmony of celestial mechanics.

    Beyond simply promoting the calendar’s availability, the post elaborates on how each month’s artwork is grounded in long-observed geometric patterns linking planetary motion to geometric forms. It draws a line from scientific modeling to artistic expression, inviting readers to contemplate how geometry underlies both the heavens and artistic representation. The narrative suggests that such resources — whether calendars, prints, or patterns — function as mirrors to natural law and can enrich both intellectual and aesthetic appreciation.

    Martineau solar system calendar -12 months

  • M. C. Escher’s Geometry and Illusory Perspectives Revisited
    Published January 2025

    This engaging post reflects on the work of Dutch graphic artist M. C. Escher and the ways that his art embodies rich geometric ideas. The author revisits classic Escher works — including impossible constructions, symmetry patterns, tessellations, and recursive spaces — and ties them into broader themes about how the human mind perceives space and structure. Escher’s art serves as a springboard for discussing how geometry, often thought of as abstract and formal, can be visually vibrant and conceptually playful.

    Throughout the text, readers are encouraged to appreciate how Escher’s imagery not only plays with visual paradoxes but invites a willingness to consider multiple perspectives simultaneously — a theme with deep resonance in non-Euclidean geometry and spatial reasoning. There’s also a conversation about how such visual explorations can inspire geometric creativity and reframe the way we look at patterns, proportion, and dimensionality in both art and mathematics. The author hints that future posts will build on these provocations, particularly around non-Euclidean geometry and related artistic interpretations.

    3 interlocking Escher-inspired reptile tiles

  • Thanks for exploring these highlights from GeometryCode.com’s January archives!

Sacred Geometry Design Sourcebook (SDGS): 29 years and counting…

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(Update August, 2026: This timeless classic has been in print for almost 30 years. The original title for this post was “… SGDS turns 20”, but that was almost a decade ago. Fortunately, geometry doesn’t change much from millennium to millennium, so everything below is basically still current and correct!)

I printed and published the first copies of Sacred Geometry Design Sourcebook (SDGS) in December 1997. It took a year of intensive graphics work using Claris CAD – does anyone remember that Apple application? – to convert and extend numerous hand-drawn geometric illustrations into digital form. My wife (Nancy Bolton-Rawles) took an evening class and I started with an evening a week – while she was in class – learning how to use this early CAD program for something other than video routing switcher control panels and making these geometric archetypes with far more accuracy and resolution than I could possibly achieve by straightedge and compass (the classic geometer’s tools) or any other physical mechanical means. Those evenings quickly overflowed into seemingly every conceivable spare moment. I realized that these CAD drawings (plus a few other unique images such as a stereogram, some unusual tables, charts, spreadsheets, and even a cameo illustration of a sphere by Nancy (who was taking art classes during that time) merited a book. There are over 1300 geometric CAD illustrations, counting all the variations I placed in the margins of many of the larger full-page (8.5″ x 11″) images.

It’s amazing to reflect on the journey of explorations that have branched off (fractals, anyone?) from this first book by countless colleagues. I am profoundly grateful to one and all for the links, shared discoveries, and inestimable support in 2 dimensions, 3 dimensions, 4 dimensions, and beyond over the past two decades … and before and after that, too – since we’re all interconnected beyond time and space! It’s been wonderful fun to get emails, postal mail of unexpected geometrically-inspired gifts, and other correspondence via Facebook (GeometryCode.com and Geometry Code) plus other social media, etc. Thanks, everyone, for your generous and steady contributions and support over the past two decades! :-)

If you are new to this website (or would like to peruse some of these topics again), you might want to start with this introduction to sacred geometry and then explore many years of bulletins, posts, and articles about related geometric coloring books – of which SGDS is a prime example! – and other sacred geometry art, books, calendars, food, audios and interviews, jewelry, music, news, physics, spaces, toys and videos, the golden ratio, Fibonacci numbers, other interesting numbers and proportions, the Platonic Solids and Archimedean Solids, other polyhedra, plus even some interconnections with the ancient, timeless Hermetic Laws and their relationship to modern physics … and metaphysics … which led to my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation.

To commemorate this 20th anniversary month (December 2017) of SGDS, here is an illustration that I added later, but didn’t make it into the book: a fold-up pattern for the Rhombic Triacontahedron, also known as Kepler’s Solid, which is an example of a zonohedron.

Here are the pages and posts on this website that refer to SGDS; enjoy! :-)

Last but not least, I’m copying the content from a personal blog post (from a decade ago) which provides details on many of the images in SGDS, including how to draw many of the 2-D patterns (which took the form of an email Q and A response):

(Question)
Dear Bruce:

I was reading your web pages about your book SACRED GEOMETRY DESIGN SOURCEBOOK and I wondered if you could tell me whether the book provides the reader with details of how to draw the 2-D patterns for themselves or whether they are just templates without such instruction.

(Answer)
The simplest answer is “yes and no”, depending on which of the 1300+ images you’re referring to.

The detailed answer is (here goes!) that I cover some of the philosophy and underlying math, concepts and archetypal ideas in the beginning of the book, and provide a generous assortment of references in the back of the book. For the remainder (majority of the 256 pages), I give the images as much room as possible so that not only can the patterns be photocopied easily (I went with spiral binding just for that reason), the image quality would be as high as possible for an 8.5″ by 11″ format.

Some of the illustrations give step-by-step procedures (in graphical form, assuming some basic familiarity with how to use a compass and straightedge), such as:

page 44 (showing how “unit cells” for the tiling patterns can be used to create an enormously expanded variety of additional patterns by recognizing how the space-filling shapes can be varied; this applies to the “unit cell” examples on pages 16-43,

page 45 (showing how each of the patterns on pages 16-43 can embellished with fractal or other inscribed detail for each of the polygons for an infinite (literally!) variety of possible variations, (which actually also applies to the majority of the remaining images in the book; page 237 gives a 3D example of this),

pages 46-84 have either explicit (most of these pages) or simple to observe implicit “unit cells” which show how these can be created in a great variety of ways,

page 84 (Pentagon Rotation Grid) gives the 73.2% proportion crucial to the exact construction of this pattern,

page 85 (Genesis of the Seed of Life) shows the step-by-step “compass only” construction of this important and universal pattern,

page 86-95 (variations on Seed of Life and Flower of Life) show how once the Seed of Life is constructed, so many other patterns can be easily derived – Flower of Life, Hexagonal Grid, 2nd Harmonic Overlay (which is used in Mika Feinberg’s beautiful LightSOURCE screensaver animation; see my Resources page, Tree of Life, Fruit of Life, Heart and Ankh matrices, recursions, Metatron’s Cube, etc.),

page 95: since the Dodecahedron is the most complicated shape to derive from Metatron’s cube, the top center illustration on this page shows which vertices are used to create the “dodecahedron 2D shadow” with small circles highlighted in the larger image,

page 96: The general instructions for creating Nested Inscribed Polygons appear on this page,

page 100-102: other examples of the crucial proportions needed to create these image either by hand or with a computer graphics program; numerous pages provide these instructions in the text without detracting from the space given to the images,

pages 104-105, 110-113, 123-124, 128, 130, 138-139, 144-145, 155, 163, 166, 171, 176-180, 182-187: all have instructions and details on how to create the images,

page 146: very detailed step-by-step instructions for inscribing a pentagon within a circle,

page 147: very detailed step-by-step instructions for inscribing a pentagon starting from one side of a given length,

page 156: very detailed step-by-step instructions for creating a golden rectangle (including “whirling squares and more),

page 156: very detailed step-by-step instructions for dividing a line by the golden ratio,

page 157: very detailed mathematical information about golden ratio progressions and powers, illustrated graphically,

page 188: shows how the Parthenon at the Acropolis in Athens, Greece incorporates the golden ratio

page 189: an amazing amount of data on this page about the Great Pyramid at Giza, Egypt showing phi (golden ratio) and pi proportions, and the proportions of the so-called “King’s Chamber” although the so-called “sarcophagus” (granite box) within is too large to fit through the only passage leading into that chamber, which violates the generally accepted funerary rite theory,

page 190: the classic “Measure of Man” (Vitruvian Man) by Leonardo daVinci, copied around the world, showing the golden ratio proportions in the human body,

page 191: the only known CAD drawing adaptation (to my knowledge) of Leonardo’s “Ideal Church” sketch,

page 192: detailed specifics about the Shoemaker’s Knife of Archimedes, giving several variations all showing the mathematical principle,

page 194: details of the geometry of the classic 1991 Barbury Castle, England crop circle formation,

page 195 and page 52: the details of the geometry encoded in the Sri Yantra (a classic Hindu mandala) and the cross section of the Great Pyramid at Giza, Egypt (also the “squaring the circle” conundrum), both with a 1-Phi-Square Root of Phi triangle which has a 51 degree, 51 minute slope,

page 196: numerous details common to the 5 Platonic and 13 Archimedean Solids,

pages 197-214; numerous details specific to the 5 Platonic and 13 Archimedean Solids, including how the insphere/intersphere/circumsphere/side length proportions are calculated,

pages 215-224: similar details specific to the 4 Kepler-Poinsot solids, the Star Tetrahedron (a.k.a. Stella Octangula) and related polyhedra,

pages 225-229: numerous graphics showing how the Platonic Solids relate to each other in a myriad of fascinating – awe-inspiring, really! – ways,

pages 230-235: numerous relationships between 3D polyhedra with 5-sided symmetry and the “shadow” they cast on a decagon (10-sided polygon), with construction details,

page 236: step-by-step instructions on creating an accurate drawing of the Icosahedron and Dodecahedron starting from a Golden Rectangle,

pages 237-255: generous appendices for hands-on explorers of all ages and levels of experience, including tables and charts of regular polygon angles, apothem, radius and side ratios and areas, radius ratios by coordination number for Ionic Chemical Bonding (which relates to properties of materials at the molecular and planetary levels), Fibonacci Numbers, Perfect Right Triangles (when I put the book together, I wasn’t aware of the Phi-1/Phi-Square Root of 3 Right Triangle that Mike Green of British Columbia introduced me to), Prime Numbers, extensive tables with all sorts of data on the Platonic and Archimedean Solids (useful for a variety of purposes, including model construction and computer simulation and animation, a map of planet Earth showing superimposed Platonic Solid Vertex Latitudes and (example) Longitudes, a fun stereogram with 6 Small Stellated Dodecahedra (there, I gave the clue away Happy, a short bio of myself, 3 pages of bibliography (more on my links pages and blog), and unique graphical index to all the illustrations in the book. Whew! I’d almost forgotten how much I packed into this labor of love over a decade ago!

Many of the 1300+ images are somewhat self-explanatory graphically (especially if you have created the basic shapes like the Seed of Life, Golden Rectangle and a few others by hand with compass and straight-edge, which I highly recommend for anyone as mentor Keith Critchlow so aptly reminded me when reviewing my original manuscript)…

… and of course, if you are finding re-creating one of the patterns challenging, I’d be happy to answer other questions via email that I can share with other enthusiasts on my blog (which I’ll do with this reply; thanks for asking! :-)

I’m also working on a number of related projects that will complement the book with video “hands on” procedures, etc. Stay tuned!

Interesting geometric links to wrap up 2015

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Aerial photography shadows reveal 8-sided geometry of the Great Pyramid at Giza, Egypt

Hi all:

Here’s a fun and interesting collection of sacred geometry links you might enjoy:

Every year I update this sacred geometry calendar which has images from the Martineau Solar System. Here are details about the 12 images which are highly accurate geometric models of pairs of planetary orbits in our solar system. They were inspired by the remarkable work of John Martineau (publisher of Wooden Books), who wrote “A Little Book of Coincidence.” Tiled images of planetary surfaces and related images form the backgrounds. Images are two or more orbits defined by simple 2D (circles, triangles, squares, pentagons, hexagons, octagons) or 3D geometries (e.g. tetrahedron, icosahedron, dodecahedron) typically with 99.9% or greater accuracy. The work picks up where Johannes Kepler’s mystical exploration left off.

Martineau solar system calendar -12 months

GeometryCode Bulletin – September/October 2015

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

Vibration Station Conversation – The Geometry Code Book: Chapter 2

Great Pyramid - Sphinx - Compass - InfinityDave Cohen (a.k.a. Davie Crockett) and I shared this conversation about “Take Home Lessons from Modern Physics” which is Chapter 2 from the book The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation on 11 October 2015, on his LA Talk Radio show.

We talked – among MANY other things – about specific topics that shook the scientific worldview several decades ago such as the Copenhagen Interpretation of the wave/particle duality, and subsequent discoveries such as quantum entanglement, and how these continue to affirm the idea that mind was no longer the ‘ghost in the machine’ after quantum physics became the superset of scientific thinking after the era of Newtonian physics that now incorporated (inclusively) both the mechanical and mental paradigms.

This interview is part of an ongoing series where we discuss one chapter (about one per month) from The Geometry Code book until we’ve gone through all 10 chapters, including the 7 Hermetic Laws from the Kybalion and related geometric symbols.

If this conversation piqued your interest, you can listen to the prior conversation about the first chapter here, and also read the first chapter of The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation for free by (also free) subscribing to the GeometryCode.com monthly bulletin. Enjoy!

NCCU Art Museum: “Vandorn Hinnant: Explorer of Form and the Beauty of Number”

Geometer colleague Vandorn Hinnant has a new exhibit of 3D Geometric art in North Carolina – see images below.

VandornHinnantNC2015Exhibit

VandornHinnant-NC2015Exhibit

Here’s Vandorn’s writeup about the exhibit:

The best day for visiting the exhibition is on a Sunday: 2pm – 4pm. The parking is free. Traveling South on Fayetteville Street from Downtown Durham at the intersection of Durham expressway 147 and Fayettville Street you will come to an intersection with Lawson Street. Go through this intersection to the 1st left turn into campus. There will be a Guard Booth (a small brick kiosk) as you enter this small side street. You can park anywhere in this area and the adjoining two parking lots. The NCCU Art Museum will be in the same building that houses the Edward Riddick Music Building which is connected to the Fine Arts Building. These buildings are on the perimeter of the above referenced parking lots.

Address:
North Carolina Central University
NCCU Art Museum
580 East Lawson Street
Durham NC 27707
919-530-6211 Art Museum

Please join us for an exhibition opening reception at the NCCU Art Museum on Sunday, 13 September 2015 from 2:00 pm to 4:00 pm “VANDORN HINNANT: Explorer of Form and the Beauty of Number” an exhibition of forty works of art created between 1980 and 2015

What we experience as visual art can be viewed as the result of individual responses to a myriad of experiences; psychological / emotional / physical and metaphysical. Some art can be viewed as statements about responses to, and expressions of Soul’s human conditions. This inclination to visually record or to document an experience is, in part, an answer to the question: “What is the driving force behind the need we have to share and to communicate our experiences with others?” The artist’s creative response is a need to and/or willingness to leave behind some form of a record of their experiences.

New format for monthly bulletins

To provide me with more time to generate and gather material for new posts, I’m automating the monthly bulletins, starting November 1, 2015. You will still get the same content, but the format will be slightly different, with a compilation of all posts made during the past month. This will provide an additional benefit of automatically delivering a bulletin each month more consistently, regardless of how crazy my schedule happens to be – which was definitely the case last monthy – thanks for your patience! :-) BTW, if there’s enough interest for a WEEKLY bulletin digest (in addition to this monthly digest and the newer daily digest, let me know and I’ll add that third option.

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

(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
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.

GeometryCode Bulletin – August 2015

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

Fibonacci- Icosahedron by Rafael Araujo

Vibration Station Conversation – The Geometry Code Book: Chapter 1

Great Pyramid - Sphinx - Compass - InfinityDave Cohen (a.k.a. Davie Crockett) and I shared this conversation about “The Question of Identity: Two Thought Systems” which is Chapter 1 from the book The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation on 23 August 2015, on his LA Talk Radio show.

We talked about how examining the contents of our mind reveals two mutually exclusive thought systems: the kind, all-inclusive, 100% sane transpersonal thought system that make use of all symbols (including geometric ones) for the benefit of all … and the 100% insane ‘me first’ we/they personal thought system of ego, which denies shared interests in favor of special, separate interests.

This interview is part of an ongoing series where we discuss one chapter (about one per month) from The Geometry Code book until we’ve gone through all 10 chapters, including the 7 Hermetic Laws from the Kybalion and related geometric symbols.

Dave Cohen - Good Vibration Station-LA talk Radio

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

(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.