3D Geometries

Mirrored geometric solid cameo on new whodunit

Friday, 30 December 2022 by Bruce Rawles

Spoiler Alert: This post will reveal the Platonic Solid that stole the show (at least for me) on the latest flick by director Rian Johnson. If this isn’t an issue, read on! May I have the envelope, please…

I don’t often watch murder mysteries unless there’s a generous amount of tongue-in-cheek involved, such as my favorite classic of this genre, “Murder by Death” which I recommend if you haven’t seen it. The “22 Twain” punny address of the mansion at the beginning of that film had me hooked at the get-go.

Based on Johnson’s prior whodunit, we thought we’d give his new one a go, and enjoyed it, also. So… for silly fun, we recently watched (streamed at home) “Glass Onion: A Knives Out Mystery” which featured – in addition to the expected absurd assemblage of characters with a preposterous plot, and a fun puzzle box invitation featuring a “whirling squares” (Fibonacci) spiral, other familiar geometries plus assorted over-the-top glass sculptures in a billionaire island mansion with an infinity pool – a few witty pop-culture-for-nerds cameos like a Boston Dynamics “dog robot” porter and momentary dialogue about Google alerts – which I find helpful every week for feeding me news about sacred geometry and other metaphysical topics.

Regular readers will recall that this isn’t the first time I’ve featured the lovely geometric artwork of artist Anthony James … The (virtual envelope) contents of that award-winning geometric art (from my perspective) is … cue the drum roll … James’ Mirrored Icosahedron with the illuminated interior edges presenting the viewer with an exotic labyrinthine landscape of triangular tunnels. That’s it! At the focal point heart of the bulbish-shaped centerpiece glass onion sphere-like feature of the larger mansion sits a mirrored icosahedron which sure looks a lot like James’ handiwork! (If anyone knows any different, please let me know.)

The screen snap of a frame from the trailer doesn’t do it justice… Here’s a frame close-up from a video giving the “star” more exposure:

Speaking of mirrored and/or virtual polyhedra, see also: Sara Frucht’s Kaliedoscapes!

Alternate ending: If you were hoping for a dodecahedron, you might want to read this post on my other niche blog; the original model that appeared in the Lawrence Livermore Lab bulletin my Dad brought home early in the development of laser fusion showed a translucent plexiglass dodecahedron with 12 plexiglass cones centered on each pentagonal face all converging at a hydrogen pellet target.

Happy New Year all!

In memoriam: William Goldstein

Friday, 14 October 2022 by Bruce Rawles

I recently learned of the passing of William Goldstein (a.k.a. Will Gold), who left us on August 11, 2022. William was a fellow geometer, researcher, historian, mystic, and much more. It was only fairly recently (September 2021) that I discovered his work, our many common interests, and favorite books while exploring his extensive fascinating writings which are a great complement to my more mathematical leanings. I began a brief stint as his webmaster and I was hoping to be able to share many recorded conversations between William and myself with my GeometryCode readership, but that was not to be.

Rather than have this important body of work disappear, I offered his family the opportunity to keep the site going so that others might benefit from his insights, and helpful resources including an extensive library of unique and interesting books, most of which are still available. The newly relocated website (formerly Chartres-sacred-geometry.com) is now live at Chartres.GeometryCode.com. It is my hope that my readers will avail themselves of his thoughtful and insightful writing and excellent book (and other media) recommendations of particular value for geometry enthusiasts, particularly the in-depth cultural and historical underpinnings behind so many important discoveries and real human progress.

Here is the prior article I wrote about William’s site which I would recommend reading as well.

Thank you, William, and to your family as well!

2023 Martineau Solar System Calendars available now

Friday, 23 September 2022 by Bruce Rawles

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 2023!

Martineau Solar System Calendars

These 12 images are highly accurate geometric models of our solar system; details 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 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. A newly revised calendar (which is updated every year) with images from the Martineau Solar System is again available for 2022.

Are Physics, Geometry and Science pointing to (Non-Dual) Metaphysics?

Tuesday, 28 June 2022 by Bruce Rawles

I just finished listening to an extended (almost 3 and half hour) fascinating podcast interview of cognitive scientist and author Donald Hoffman by Lex Fridman speaking on “Reality is an Illusion – How Evolution Hid the Truth” – (Here is a YouTube clip, evidently excerpted from the longer podcast.) If nerdy math and physics is over your head (as much of this was for me) you might want to skip to the last half hour or so where Hoffman delves into a more philosophical discussion with Fridman where more arcane subjects like Amplituhedron, Permutation matrices, Birkhoff polytopes and cosmological polytopes (new or minimally explored concepts to me) give way to a conversation that seems to lead one toward non-dual metaphysics (with which I’m much more familiar.) Here’s a related TEDtalk by Hoffman: Do we see reality as it is? I don’t pretend to understand much of the in-depth new math and physics that Hoffman talks about but I particularly appreciate his willingness to consider the idea that matter derives from consciousness and not necessarily the other way around! Here’s a quote that hopefully, I haven’t taken out of context: “The notion of self can be an artifact of projection…” (at about 2:16:39 into the podcast).

While doing some very preliminary perusals of some of the links above, I found a few interesting geometric links, including:

A 3D Printed Model of the Substructure of the Universe (the photo shows obvious icosahedral and dodecahedral symmetries)
The Golden Ratio and Us … and … Why is 1.61803399 considered a golden ratio?
… both the links above found from the Quantum Gravity Research site (which has a lovely polyhedra animation on the home page) and links to this nicely done video visually sharing the idea that the “20-group encodes 4-dimensional space” (from which the featured image for this post was derived.)
… and more in-depth physics here (The Einstein-Podolsky-Rosen Argument in Quantum Theory)

TurboSquid 3D geometric models

Tuesday, 31 May 2022 by Bruce Rawles

Fellow geometer, 3D animator, techno-nerd, mystic, and life-long friend, Dave Van Dyke alerted me to some examples of very cool 3-dimensional models using TurboSquid (3D Models for Professionals) a couple of days ago. The links below connect with a small set of the many examples of 3-d geometric models – some free, others inexpensive – all gems, especially considering the “labor of love” efforts put into these detailed models! Going beyond geometric constraints, you have orders of magnitude more to explore! They can be downloaded and adapted wherever your imagination might lead! Here are some samples to pique your interest!