Search Results for: dodecahedra

Geometric art in multiple media; what have you made or found of interest?

Sunday, 28 April 2024 by Bruce Rawles

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 past few decades, I’ve seen lots of great geometric art, imagery, and more in numerous media, yet occasionally new media forms cross my path in delightful ways. If you search for your favorite geometric form using the search function at the top of the sidebar of this website, you’ll likely find lots of examples. I enjoy learning and discovering new and unique ways artists are transforming geometric ideas into physical and virtual art.

If you have some geometric art (2D, 3D, or otherwise) that we haven’t featured (or haven’t for quite a while) especially if you are using unconventional media, please use our contact form with a link to your art for consideration in the next monthly post on this website and/or our social media (Facebook, YouTube, Twitter a.k.a. X, Pinterest, Instagram, or perhaps another platform we haven’t explored yet! THANKS!

Here are a few dodecahedra (and related shapes) on this website:

$fractal dodecahedron$

Small Stellated Dodecahedron animation

Tuesday, 19 March 2024 by Bruce Rawles

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” of the original, then doing this recursively as many times as your patience, resolution, etc. allows!

Here is a link (Math Monday: Fractal polyhedra clusters) to a rotating animation of a Small Stellated Dodecahedron fractal, which is one of the four Kepler-Poinsot Solids (all of which are featured with fold-up patterns (and more examples) in Sacred Geometry Design Sourcebook (SGDS):

Math Monday: fractal polyhedra cluster (small-stellated dodecahedra)

AI generated geometry – revisited a few months later

Sunday, 31 December 2023 by Bruce Rawles

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 with fun and impressive results) and here’s what he generated (in less than an hour on a screen-sharing Zoom call) as we thought of prompts together that might provide interesting results; thanks, Dave! Note that Dall-E 3 still doesn’t quite know exactly how to make a precise (regular polyhedron) dodecahedron and other artistic liberties are taken, but still the results seem far more impressive than my more primitive results a few months ago. Here are some of the text prompts used to generate 4 sets of images at a time, some with “more strict” and some with “more creative” parameters selected:

make an image of (a) sea of mirrored geodesic spheres
or
make an image of (a) sea of mirrored dodecahedra

make an image of a translucent dodecahedron filled with multi-colored toroidal rings

make an image of a translucent toroidal ring filled with multi-colored platonic solids

make an image of a large translucent dodecahedron filled with multi-colored jellyfish

make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds (evidently the reference to the prior image wasn’t used and instead the image was drawn from ideas more akin to mythical/fantasy/religious iconography/ideas)

Affiliates and Archives Galore!

Tuesday, 31 October 2023 by Bruce Rawles

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 animation that shows a plane intersecting a torus to reveal a Vesica Piscis cross-section; neat! (I also added the animation to the original post.)

Here’s another post from a while ago:

Dodecahedra Origami Luminaria – a timely holiday project, too!

I just updated our Affiliates page since it’s been quite a while; thanks for many years of support! When you use the links on this page, it helps fund our “labor of love” efforts keeping this site going and this is greatly appreciated!

Spirals, Ferns, and Universal Unfolding Motifs

Thursday, 1 December 2022 by Bruce Rawles

While I try not to obsess about geometric forms, I do observe when certain motifs appear more frequently in various locales. When we visited San Miguel de Allende, Mexico earlier this year, I noticed an abundance of small stellated dodecahedra (and similar shapes) particularly evident in metal lamps, yet also in other art forms as well; each pentagonal pyramidal stellation arm encodes the golden ratio. …

Having just returned from a second visit to New Zealand, it seemed that one of the most ubiquitous geometric shapes we saw on this trip was the spiral, which appears in Maori jewelry, carving, tattoos, art, and culture, connecting the natural world with the art of the indigenous people of Aotearoa. Below I made a mirrored tiling pattern from an image of an unfurling silver fern frond which exhibits an excellent example of fractal geometry.

Wikipedia says “The koru is a spiral shape based on the appearance of a new unfurling silver fern frond. It is an integral symbol in Māori art, carving, and tattooing, where it symbolizes new life, growth, strength, and peace.”

Reflecting intuitively on our spiral “journey” through life like the homeward trajectory Dorothy embarks upon in the Wizard of Oz when she follows the yellow brick road, we find context in the cyclical, yet ever-evolving, ever-unfolding awareness with each revolution of the spiral. In three dimensions, we have the double helix of the DNA molecule in everything we typically call life in this world, embodying the golden ratio in each pentagonal molecule appendaged to the helix and also in the (Fibonacci proportion) 34/21 Angstrom ratio of each complete turn of the helix. Every year, each season has familiar patterns and signs, yet there is a much larger progression we discover when we “zoom out” a bit from our myopic, provincial perspectives. The Chambered Nautilus shell has a pleasing uniformity as one spins the shell around, since each accretion uses the same angular template as the preceding one, and builds upon the strength of sameness throughout.

Here are a few more spirals from our most recent NZ trip; enjoy!