Behold, the holmium-magnesium-zinc quasicrystal. Is it a representative of the mystical powers of prime numbers that defy predictability incarnated into the physical world?
Holmium–magnesium–zinc quasicrystal - Wikipedia.
☞ https://en.wikipedia.org/wiki/Holmium%E2%80%93magnesium%E2%80%93zinc_quasicrystal
Holmium, magnesium, and zinc form an alloy in this quasicrystal that results in a dodecahedron formed by nature—for some strange reason—which is one of the five platonic solids.
Dodecahedron - Wikipedia.
☞ https://en.wikipedia.org/wiki/Dodecahedron
Platonic solid - Wikipedia.
☞ https://en.wikipedia.org/wiki/Platonic_solid
• holmium—(Ho) atomic number 67, average atomic weight 165
• magnesium—(Mg) atomic number 12, average atomic weight 24
• zinc—(Zn) atomic number 30, average atomic weight 65
‣ 67*—the 19th prime number (19† is itself the 8th prime number), which meets several other intriguing classifications: it is an irregular prime, a lucky prime, a Pillai prime, palindromic in base 5 (232₅) and base 6 (151₆), and is equivalent to the sum of five consecutive primes (7 + 11 + 13 + 17 + 19). Does the fact that 67 has relations with 5 in this manner have anything to do with the pentagonal (5–sided regular polygon) faces of the dodecahedron in the quasicrystal? Its digital root (6+7) is 13‡, which is the sixth prime and the smallest emirp (prime that is still prime upon reversal of its digits), a Fibonacci number, and a member of the Pythagorean triple 5² + 12² = 13². However, the base 10 digital root may be a distraction, as the base of the numeral system supplies perspective but little of unique value. So if one formulates the question as “Is 67 related to a 5–sided polygon under any perspective?”, one might put 67 under the lens of 232₅, because that is one way of aligning the perspective to match 5. If it is recalled that every simple polygon can be decomposed into a number of triangles§ (the simplest, simple polygons), then if a number is representative of a polygon, then the base, foundational numbers which compose it can be considered representative of triangles. In a straightforward triangulation of a polygon, the number of triangles = the number of vertices - 2.‖ So 5 - 2 = 3, which is also the number of digits in 232₅. So is a pentagon composed of 2 similar triangles on opposing sides and 1 unique triangle in between when divided in this way? Yes, they are all isosceles triangles—36°–36°–108° × 2 and 36°–72°–72° × 1 respectively.¶ 2₅ + 3₅ + 2₅ = 12₅ (7₁₀—the 4th prime number) and 1₅ + 2₅ = 3₅—the 2nd prime number.
‣ 12—coincidentally? the number of faces on a dodecahedron
‣ 30—coincidentally? the number of edges on a dodecahedron
* 67 (number) - Wikipedia.
☞ https://en.wikipedia.org/wiki/67_(number)
† 19 (number) - Wikipedia.
☞ https://en.wikipedia.org/wiki/19_(number)
‡ 13 (number) - Wikipedia.
☞ https://en.wikipedia.org/wiki/13_(number)
§ Polygon Triangulation
☞ https://people.csail.mit.edu/indyk/6.838-old/handouts/lec4.pdf
‖ Triangles of a Polygon - Math Open Reference.
☞ https://www.mathopenref.com/polygontriangles.html
¶ Euclid's Elements, Book IV, Proposition 11.
☞ https://mathcs.clarku.edu/~djoyce/elements/bookIV/propIV11.html
Thus, the holmium-magnesium-zinc quasicrystal is correspondent to the principle of higher level order arising from lower level chaos and of “magic” from the realm of abstract forms made concrete in nature.