Geometric toys, puzzles, and amusements have been around for who-knows-how-many millennia but in the last few decades, a convergence of technologies and mathematical understanding and explorations has exploded the possibilities and offerings. While there are countless potential geometric toy concepts, we’ll focus (at least at the end of the post) on the permutations of the Platonic Solids. If one wants to have a huge range of options (including – but hardly limited to – the famous fave five Platonic Solids), my first recommendation is Zometool – the virtues of this versatile construction syste ..read more

The Introduction to this website (Sacred Geometry Introductory Tutorial) begins with a geometric symbol that is perhaps the simplest and yet most profound – the circle. Circular patterns and archetypes appear in countless variations in nature, art, architecture, engineering, and just about every area of life we can imagine. Here are a few familiar examples; I’m sure you can think of countless others, both microscopic, macroscopic (telescopic) and in between, in all dimensions of space, time, metaphor, and thought. We touched on the sphere (Music of the Spheres – The Planets) in a recent post ..read more

Here’s an invitation to geometric artists (and enthusiasts) to share their creativity, explorations, and discoveries. My wife Nancy – an artist who for years has worked mostly in acrylics – has recently been making some lovely (ceramic/clay) art while taking a variety of classes since we moved to Arizona last summer and is finding lots of great tutorials for her newfound media on YouTube and elsewhere online – alerted me to this carved (presumably clay) dodecahedron by Debi Stoliar. It has 4 faces with a radial starburst pattern and 1 face with a spiral twirled starburst. Way cool! Over the p ..read more

The Small Stellated Dodecahedron – a classic three-dimensional (pentagram-faced) “star” – makes a wonderful fractal seed. It is a stellation of a dodecahedron where each pentagonal face is capped with a pentagonal pyramid composed of 5 golden triangles, a you could call it a 3-dimensional 5-pointed star. Some years ago when I was dabbling with POV-Ray, I made this primitive, rough study (with low resolution and lighting that didn’t quite do it justice) of a Small Stellated Dodecahedron fractal which is made by replicating smaller versions of itself and overlaying them on each of the 12 “arms ..read more

charcoal sketch of a sphere by Nancy Bolton-Rawles The sphere is such a primal shape at the foundation of matter and so many realms and disciplines, arts, sciences, and much more that it seems overlooked sometimes in favor of more peculiar and/or complex shapes and geometries. Can you imagine just about any facet of any subject or topic that wouldn’t be radically different (if not impossible) without spheres (or circles in 2D) of one sort or another, microscopically, macroscopically, or anywhere in between? Inseparable from any mathematical consideration about circles and spheres is the ubiqui ..read more

In a recent metaphysical Zoom meeting, a friend mentioned a story about 2-dimensional creatures which I recognized as the classic book: “Flatland: A Romance of Many Dimensions by Edwin A. Abbott” first published in 1884 – note the very archaic labels on the cover illustration. (We’ve made several other references to flatland before on the GeometryCode website.) We got into a fun and mind-stretching conversation about how we believe we’re 3-dimensional creatures almost completely oblivious about higher dimensions and probably just as mindless about 1-dimensional and 2-dimensional realms. And of ..read more

Since 2023 was a breakthrough year for AI, it will be interesting to follow how Artificial Intelligence tools will help geometers with a wide variety of interests leverage this mushrooming technology. I made a few preliminary “mixed bag” tests earlier this year with Dall-E 2. Here are a few more recent AI-generated geometric examples by others. I was prepared to search for additional examples when I “switched gears” and thought I’d ask my friend and fellow geometer Dave Van Dyke if we could collaborate on some experiments with Dall-E 3 (since he has been using it a lot more than I have lately ..read more

Thanks to all of you for your continued and ongoing support of this labor of love website! It has been quite a while since we’ve had a reader survey or poll! Here are the results of the last one from a couple of decades ago:   Here’s an opportunity to share your geometric interests, passions, curiosities, favorite topics, and whatever you think will be helpful, useful, and fun! We’ll replicate this survey each year, provide results annually, and hopefully guide our content to where you find existing and unexplored subjects! Please enable JavaScript in your browser to complete this form ..read more

I was looking through prior posts – I’ve been sharing items of interest about geometry and interconnectedness since 2007! – and realized that there is a lot of content that is still every bit as relevant today as when originally published … Since geometrical principles, archetypes, and so many more topics aren’t seasonal or slaves to style… at least as far as I can tell! So, I’m going to pull a couple of images with links to older posts to encourage exploration of the archives. Here’s one about Intention and Symbols and when I followed the link about Villarceau circles I found an interesting a ..read more

Once again this perennial calendar is available! These timeless images portray amazingly accurate geometric representations of the planetary orbits in our very own solar system – now available in printed calendar form with dates for 2024!! Martineau Solar System Calendars These 12 images are highly accurate geometric models of our solar system; details are here. 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 orbi ..read more