A Response to “Sacred Geometry”

It is unlikely that anyone knows how many types of superstitious nonsense exist, for counting them would be an enormous task, with no compelling reason to do it, and only a slim hope of actually finding them all. However, a given person will be more likely than other people to know about a particular type — if it is related to things the first person finds of interest. For example, a physician will be more likely to be aware of homeopathy, and the faulty ideas upon which it is based, than would a randomly-selected college-educated adult.

It won’t take long, reading this blog, for anyone to figure out that I have a strong interest in geometry. Were it not for this, I likely would be unaware of another type of superstitious nonsense: “Sacred Geometry,” which I cannot bring myself to type without quotation marks. If you google that term, you’ll quickly find an amazing number of websites devoted to that topic, with many extraordinary claims about certain polygons and polyhedra, but you won’t find more than miniscule amounts of logical reasoning on any of these sites, mixed in with large portions of utter nonsense.

Geometry is inherently interesting, and many geometrical shapes and patterns are aesthetically pleasing. However, to search for their mystical or spiritual qualities is to do nothing more, nor less, than to waste one’s time.


I did not create, nor discover, the figure above, but found this picture at http://earthweareone.com/a-new-form-has-been-discovered-in-sacred-geometry-meet-the-chestahedron/. It is described there as a polyhedron with seven faces (well, they call them “sides,” but they clearly mean faces) of equal area — three faces with four sides each, and four faces with three sides each. Knowing that, I tried to figure out exactly what the back side of the figure would look like, but the text at that website isn’t particularly helpful in that regard, being filled with claims, allegedly related to this shape, regarding the human heart as an “organ of flow,” not a pump (What’s the difference?);  “the earth in its foundational form [as] not a sphere but rather [with] its basis [being] a ‘kind of tetrahedron'” (What?); and a (claimed) special relationship between this polyhedron, and the oh-so-profoundly-mystical Platonic Solids. If none of that makes sense to you, you are not alone. It doesn’t make sense.

I often use software called Stella 4d (which you may try at http://www.software3d.com/Stella.php) to investigate the geometric properties of polyhedra. Based upon comments about this polyhedron written by Stella 4d‘s author, Robert Webb,  I was able to create the rotating virtual model below, with Stella, to help me understand what all the faces of the green polyhedron above look like, included those on the back side, as the figure is shown in the picture above. This polyhedron is similar to an octahedron, with a single face augmented by a tetrahedron, and with three pairs of coplanar equilateral triangles then fused into rhombi. Here is that figure:

Augmented Octa

This isn’t the exact polyhedron in the first picture, but is isomorphic to it. Vertices and edges are moved a bit, changing the size and shapes of the four-sided faces, as well as the dihedral angles between the triangular faces, until all faces are equal in area. This process turns the three rhombic faces into kites.

On the above-linked “Earth We Are One” website, where the “sacred geometry” of this polyhedron is “explained” (and where I found the non-moving first picture here), this is called a “Chestahedron.” While Stella can help someone understand the geometrical properties of the Chestahedron, it offers no information whatsoever about the spiritual or mystical properties of this polyhedron, nor any other. There’s a good reason for this, though: the complete lack of evidence that any such properties exist, for the Chestahedron, or, indeed, for any geometrical figure.

As for the people, whom I’m calling the “Sacred Geometricians,” who are pouring so much time and effort into investigations of these alleged non-mathematical properties of hexagons, pentagons, enneagons, many polyhedra, and other geometrical figures, I have three things to say to them:

  1. This isn’t ancient Greece, and you aren’t in the Pythagorean Society.
  2. That part of the work of the Pythagoreans had no basis in reality in the first place, anyway. Geometry, together with religion and/or mysticism, as it turns out, can be mixed — the Pythagoreans were correct, on this one point — but such mixtures are invariably incoherent and illogical, revealing the efforts to create them as activities which are both pointless, and useless. Just because two things can be blended does not imply that they should be blended.
  3. Please stop. You give me a headache.

Thirteen Images, Each, of Jynx, the Black Kitten, on Two Hendecagonal Prisms

11- Prism

The above hendecagonal prism shows what Jynx is like when he’s in “kyperkitten” mode. (If you have a kitten, you know what that means.) It’s also rotating rapidly in an effort to make those who fear black cats, and/or the number thirteen, feel even more jumpy, in the hope that Jynx and I can, by working together, startle them into rationality.

On the other hand, Jynx does sometimes like to just lounge around, and watch the world go by — so I’ll show him in “tiredcat” mode as well.

11- Prism

Software credit:  I used Stella 4d: Polyhedron Navigator to make these images, a program which is available at this website.

Ten Easy Ways to Oppose Secular Superstitious Nonsense


It is a common mistake for skeptics, such as myself, to focus too much attention on religion. Do I understand why so many people lack religious belief, due to a lack of evidence to support it, and/or bad experiences with religious fanatics? Yes, I do. However, I also understand that the First Amendment, which protects my right to live my life without religious belief, equally protects the right of believers to practice the religion of their choice — and I recognize that it is unreasonable to expect one of those protections to exist, without the other, for both are important. If no one tries to force their religious beliefs on me (and very few people do), what harm do those beliefs do to me? Also, I know many people who find comfort in religious belief, especially in difficult times. I have no wish to deny others that particular form of comfort, even though I am incapable of experiencing it myself. To do so, after all, would be cruel. The world has plenty of cruelty already, and it certainly doesn’t need more.

When referring to myself, I prefer the term “skeptic,” over “atheist,” even though both labels are accurate. The reason is simple:  “skeptic” covers more ground. It’s a broader term, and using it reminds me that the world is (still) filled with superstitious nonsense which has nothing whatsoever to do with religion. What’s more, non-skeptics are generally far less tied, emotionally, to the beliefs they hold which are non-religious in nature. If skeptics wish to persuade others to abandon beliefs they do not share, therefore, increased attention to non-religious beliefs offers a greater chance of success, combined with a much lower risk of alienating and/or offending people.

With these things in mind, then, I offer this list of ten easy ways to oppose, by example, some of the many secular superstitions which have not — yet — been abandoned.

  1. When a mirror is accidentally broken, by yourself or others, remain calm, and simply clean up the mess, so no one gets cut by broken glass.
  2. Deliberately open umbrellas indoors, after checking to make certain no one is close enough to get struck by the umbrella in the process.
  3. When you see a ladder leaning against a building, and it is safe to do so, casually walk under it, without comment.
  4. Ask people in tall buildings to help you find the thirteenth floor, after checking for the (usually missing) “13” button in the elevator. (If the building actually has a floor numbered “13,” though, just wait for another tall building.)
  5. Adopt a black cat. (The cat, itself, will take care of the “crossing your path” part of the superstition.)
  6. If you are ever offered homeopathic “medicine,” ask for at least twenty doses, to take all at once. (Twenty or more, times zero, is still zero, and homeopathic products are nothing more than harmless-but-expensive placebos.) 
  7. Stare directly into a mirror, with witnesses present, and say “redrum,” or “bloody Mary,” repeatedly.
  8. Each time you are asked for your astrological sign, refuse to give any answer, other than “skeptic.”
  9. Don’t throw salt over either shoulder, ever. Why waste perfectly good salt?
  10. Have your children vaccinated.

I saved the most important one for last.