In this article we will continue our discussion from the previous article about the geometry of molecules.

This article will be more of a visual journey through the world of molecules of compounds both familiar and unfamiliar.

Throughout all, notice the distinct geometry these molecules use to take shape. Also notice the frequency of the occurrence of hexagonal and pentagonal arrangements, specifically noticing hexagons and pentagons side by side.

Now image billions and trillions of these molecules coming together to form 3D geometric lattices that form the familiar matter we know.

Molecular lattices resemble Islamic tiling patterns.

Just as we see on a quantum and atomic level, without geometry there would be no order. Without the order inherent in geometry these molecules would not be able to group accordingly and their associated properties and functions could not be accessed.

Geometry on all scales is absolutely necessary for life to operate – for elements to form, for molecules to combine and recombine, and for life on all scales to function.

Specific Geometry Found in Chemistry

Triangular:

Triangular molecules have 120º ideal bond angles.

Trigonal bipyramidal molecules also have 120º ideal bond angles.

Tetrahedral:

Tetrahedral molecules have 60° or 109.5° ideal bond angles.

For example:

Water (H₂O)

Methane (CH_{4) –}In manifestation the tetrahedron is the bonding pattern of carbon and hydrogen which we call methane gas. Symbolically, methane marks the transit between “the eater and the eaten.”

Ethane

Ammonia (NH₃)

SiH₄

Quartz – silicon dioxide (SiO2). Every silicon atom is at the center of a tetrahedron with oxygen atoms at its four corners.

Diamonds are structured as a tetrahedral network of only carbon atoms – each is at the center of a tetrahedron having four other carbon atoms at its corners.

Furthermore, most rough diamonds come out of the earth as octahedra.

Diamonds are the hardest naturally occurring substance on Earth.
They are the best conductor of heat.
Diamond cutters cut them along their tetrahedral faces – between the sheets of tetrahedrally arranged carbon atoms.
Diamond tipped tools are used in many industrial purposes for cutting hard objects or minerals that could not be cut otherwise.

Read Tom Zoellner’s non-fiction The Heartless Stone for a fascinating and harrowing journey through the world of the diamond industry.

Cubic:

Tablesalt (NaCl) – sodium chloride

Salt is absolutely essential for human life.

Cubane – A synthetic hydrocarbon molecule that consists of eight carbon atoms arranged at the corners of a cube with one hydrogen atom attached to each carbon atom.

Before cubane was synthesized it was believed that cubic carbon-based molecules would be too unstable to exist. “The cubic shape requires the carbon atoms to adopt an unusually sharp 90° bonding angle, which would be highly strained as compared to the 109.45 angle of a tetrahedral carbon.”1

Pentagonal:

Fullerene molecules (Buckyballs – C₆₀) consist of 60 carbon atoms, five around each corner of a dodecahedron.

“It has a cage-like fused-ring structure (truncated icosahedron) which resembles a soccer ball, made of twenty hexagons and twelve pentagons, with a carbon atom at each vertex of each polygon and a bond along each polygon edge.”2
It is found in small quantities in soot.
Solid and gaseous forms of the molecule have been detected in deep space, inside a vast cloud of particles locked in orbit around the double-star system XX Ophiuchi.
“Astronomers spotted vast quantities of the tiny space balls, enough to create 10,000 Mount Everests, circling a pair of stars 6,500 light-years from Earth.”3
“On Earth, buckyballs can be used in superconductors, medicines, water purifiers and armor, NASA officials explained. They can form naturally as a gas from burning candles and appear in solid form in rock minerals.”4
Mike Werner, NASA’s Spitzer telescope project scientist at the Jet Propulsion Laboratory in Pasadena states, “They may be an important form of carbon, an essential building block for life, throughout the cosmos.”5
These fullerenes are also one of the largest objects to have been shown to exhibit wave-particle duality. This was covered in Article 122.

DNA nucleotides

The building blocks of life (DNA nucleotides) have internal bond angles which approximate the 108 degree internal angle of a pentagon.

Oxolene

Dodecahedrane

Fibonacci numbers:

seen in uranium oxide compounds U₂O₅, U₃O₈, U₅O₁₃, U₈O₂₁, U₁₃O₃₄
Uranium (atomic number 92) is a silvery-white metal that is weakly radioactive.
“It occurs naturally in low concentrations of a few parts per million in soil, rock and water, and is commercially extracted from uranium-bearing minerals such as uraninite.”6

Golden Ratio:

“Interestingly the golden ratio also appears in aqueous chemistry as the ratio between atomic and ionic diameters. Thus the diameter of an anion (A-) is twice its atomic diameter divided by φ and the diameter of a cation (A+) is twice its atomic diameter divided by φ2; with the diameter of A- being the golden ratio times the diameter of A+, and simple functions of φ also relating ion-water distances to covalent radii. The golden ratio has also been associated with the genetic code.”7

Credit: Dr. Mark White

We will explore all the ways the golden ratio appears in DNA over the next for articles.

Hexagonal:

Graphite – grows in hexagonal sheets of carbon that slide off the pencil as we write

Uranium hexafluoride (UF₆) – nuclear fuel

Vitamin D2

Aspirin

Oxytetraceycline – antibiotic

Cortisol, testosterone

Cholesterol

Caffeine

Protein

Kevlar

Ice crystals – (Snowflakes: frozen water in hexagonal arrangement)

Credit: Samuel Colman

Soap bubbles eventually settle into 6-around-1 arrangements.

The molecules strive to balance forces with minimum surface tension.

Benzene ring (C6H6)

This is the basic structure of organic chemistry.
It was discovered by German chemist Friedrich August Kekule (1829-1896) after he dreamed of the ouroborus. See Article 16.

Octahedral:

SF₆– Sulfur Hexaflouride

PCl^–₆– Phosphorus hexacholoride anion

CaB₆

Credit: ChemTube3D

Stereoisomers

Stereoisomers are each of two or more compounds differing only in the spatial arrangement of their atoms.

Enantiomers are two stereoismoers that are related to each other by a reflection: they are mirror images of each other that are non-superimposable.

For example:

Lemon and Orange

Sweet and Bitter

Spearmint and Caraway

These molecules are identical except in their chirality. Chirality refers to the way the molecule spirals – either left-handed or right-handed.

The Geometry of Photosynthesis

Hydrogen, nitrogen and magnesium of the chlorophyll molecule are arranged in a complex twelve-fold symmetrical pattern, similar to a daisy.

Credit: Robert Lawlor

Any other arrangement cannot transform the radiant energy of light into life substance, known as the process of photosynthesis.

“In mythological thought, twelve most often occurs as the number of the universal mother of life, and so this twelve-fold symbol is precise even to the molecular level.”8

“Here we find twelve-fold symmetry as the life-giver or womb which transforms light into the basic spectrum of organic substance. This is recalled symbolically in the stained-glass window, which transforms light into the color spectrum.”9

Furthermore, there is a strong resemblance of the structure of hemoglobin to chlorophyll.

Hemoglobin in the blood carries oxygen from the respiratory organs (lungs or gills) to the rest of the body.

Chlorophyll is essential in photosynthesis, allowing plants to absorb energy from light.

Further Molecular Structures – Compound Interest

The following images are from www.compoundchem.com created by Andy Brunning, chemistry teacher in Cambridge, UK. These images are for educational purposes only. Andy creates these graphics in his spare time and I encourage everyone to take a look at his website. He has hundreds of images explaining the chemistry of various compounds, familiar and unfamiliar.

We will take a look at a select few here at Cosmic Core.

The key is to notice the geometry involved.

Without geometry, molecules could not combine in the way they do and they would be rendered useless. Without this geometric arrangement of order in molecular structure we would not have access to all the properties of various foods and substances. This includes the tastes, smells, industrial properties, visual organization, healing or destructive properties, and biological properties…to name a few.

Geometry is the key to understanding how life works and how reality is organized on all scales.