In this article we will delve into the geometry of crystals. Platonic solid geometry is most easily seen in the mineral world through crystals.
As Samuel Colman writes, “Of all the inorganic combinations in Nature’s store, the crystal is pre-eminently the example of harmonic form.”
“When a crystalline structure is formed of your physical material the elements present in each molecule are bonded in a regularized fashion with the elements in each other molecule. Thus the structure is regular and, when fully and perfectly crystallized, has certain properties. It will not splinter or break; it is very strong without effort; and it is radiant, traducing light into a beautiful refraction giving pleasure of the eye to many.”1
Professor Amstutz of the Mineralogical Institute at the University of Heidelberg tells us, “Matter’s latticed waves are spaced at intervals corresponding to the frets on a harp or guitar with analogous sequences of overtones arising from each fundamental. The science of musical harmony is in these terms practically identical with the science of symmetry in crystals.”
Here we remind you of the science of Cymatics and how waves (frequencies, wavelengths, and harmonics) automatically create standing waves of geometry for matter to coalesce upon. This happens with ice crystals (snowflakes) and mineral crystals. The difference is in scale, duration and speed of movement.
Universal Geometry and Crystals
The Universe is composed of a fluid-like Aether that is geometrically structured (crystallized) on all scales.
Physical matter becomes a whirlpool that precipitates upon the geometric foundation of the fluid-like Aether, like crystals precipitate upon a string.
Matter is not ‘particles’. Matter is resonance of geometry.
Remember, All is Motion. The Universe = Processes.
“Crystals can be considered frozen music holding the proportions of musical intervals in the relationships of their corners, edges, and faces.”2
Others have said that Crystals are frozen light.
Discovering the geometric source and structure of music and light, we can see that crystals are both frozen light and frozen music.
The structure of light and music is geometric in nature and both are built upon harmonic proportions.
Crystals have fascinated humanity for eons due to their beauty and harmonic proportions.
Jade has been treasured by China and the Far East for thousands of years. Jade is also found in Central America where it was sacred to the Olmecs, Mayans and Toltecs.
The Aztecs treasured gold and precious stones – as did the Spanish conquistadors who destroyed the Aztecs.
The ancient Egyptians valued lapis lazuli, black onyx, and gold, among other precious stones.
The Celtic people set precious stones, such as garnet and amber, in gold.
“The medieval abbess and mystic Hildegard of Bingen, who lived in southern Germany in the twelfth century, was also a writer on medical topics. She advocated the use of many gems, including rubies and topaz, as gem remedies to help with a variety of physical complaints. The gems would be soaked in wine and the liquid taken as medicine.”3
Crystals, Light and Color
“Light split into the colors of the spectrum can have noticeable effects on body and mind. Light is energy. Light projected through crystalline structures can be even more powerful, as used in some lasers, in which rubies or sapphires are used to create highly concentrated beams of light particles. Crystals reflect different colors because of their mineral composition; they attract us because of that color, their shape, and their beauty. In this way, it can be said that the mineral kingdom communicates with us.”4
- Brown: Anchoring, grounding, strengthening, supporting; associated with Earth
- Smoky quartz, petrified wood, brown jasper
Tiger’s Eye, Brown Citrine, Petrified Wood, Desert Rose & Smoky Quartz
- Red: Warming and stimulating effect; can raise blood pressure& increase circulation; associated with blood, physical life and survival
- Garnet, ruby, red tiger’s eye, red jasper, zincite, spinel
Rhodochrosite, Spinel, Ruby, Zincite & Garnet
- Pink: lowers aggression; increases compassion
- rose quartz, kunzite, lepidolite, pink tourmaline, rhodochrosite, pink sapphire
Pink Fluorite, Pink Tourmaline, Pink Rhodochrosite & Rose Quartz
- Orange: Energizing, warming, stimulating, anti-depressant, cheering and enhancing self-confidence
- Orange calcite, aragonite, carnelian, sunstone, copper
Citrine, Vanadinite & Sunstone (Heliolite)
- Yellow: stimulates the rise of the sun; awakens mental awareness, promotes self-confidence, courage and self-expression
- Golden topaz, citrine, amber, yellow tiger’s eye, yellow jasper, sulfur, chrysoberyl, pyrite, gold
Amber, Citrine, Pyrite, Sulfur & Topaz
- Green: soothing effect; calms the breathing; promotes balance; expands awareness; enables expressions of love
- Golden green: peridot, chrome diopside, serpentine
- Pale green: apophyllite, prehnite, green calcite
- Middle green: emerald, aventurine, green fluorite, jade, malachite
- Dark green: moldavite, moss agate, seraphinite
Apatite, Green Fluorite, Forsterite (Olivine), Malachite, Peridot & Emerald
- Blue-Green: bridge communication and love – heart and throat – intuition and rational thinking
- Turquoise, labradorite, apatite, amazonite, chrysocolla
- Pale blue-green: aquamarine, chrysoprase
Labradorite & Bismuth
- Blue: Increases relaxation responses; simulates night falling; facilitates communication and self-expression; encourages higher levels of awareness
- Pale blue: blue lace agate, blue moonstone, chalcedony, kyanite, celestite
- Sapphire blue: lapis lazuli, sodalite, blue sapphire, azurite
- Dark blue: iolite, blue tiger’s eye
Azurite, Afghanite, Agate, Sodalite & Lapis Lazuli
- Purple: supports spiritual evolution and enlightened creativity
- Dark purple: amethyst, sugilite
- Light purple: charoite, purple fluorite
- Lilac: spirit quartz, lavender quartz
Purple Fluorite, Amethyst & Purpurit
- Silver: cleansing, dissolves old emotional patterns; represents starlight
- Silver, hematite
Hematite & Gallium
- Black: balances personal inner power; helps overcome fear
- Black obsidian, black tourmaline, jet, black onyx
Black Obsidian
- White: encourages transformation and the ability to recognize the truth of unity
- White moonstone, selenite, diamond, danburite, azezatulite, phenacite, clear quartz
Boracite, Quartz, Diamond, Moonstone & Selenite (Gypsum)
We will now take a look at crystallography and mineral crystal systems. Much of the following information is taken from Introduction to Crystallography and Mineral Crystal Systems5 by Mike and Darcy Howard.
First Molecular Crystal Structure Theory
The first molecular crystal structure theory came from Abbe Rene Just Hauy (1743-1822), a French mineralogist often called ‘Father of Modern Crystallography’.
Rene Just Hauy
A crystal was defined as having “a regularly ordered, repeating 3D pattern”.
Crystals are a regular ordered array of atoms and molecules.
Abbe Hauy found that blocks of the same shape can be arranged together to make a crystal.
Blocks may be rotated in different positions.
A single unit cell is repeated indefinitely along three principal directions, not necessarily perpendicular.
In the 1830’s Hauy’s molecular crystal structure models was combined with the chemical atomic theory to produce a view of the chemical molecule as the arrangement of atoms in space.
Crystallography
“Crystallography is the interdisciplinary science that studies condensed matter of any origin from the structural point of view.”6
Spinel Octahedron
Crystallography is divided into three sections:
- Geometrical
- Physical
- Chemical
Crystal Shapes
Crystals normally form during the change of matter from liquid or gas to the solid state.
Liquids and gases take on the shape of their container.
Solids take on one of several regular geometric forms.
It is as if solids take on the shape of their “container” as well, since solids are nothing more than captured light. The “container” would be the geometric standing wave fields of the Aether on all scales.
In nature perfect crystals are rare.
The faces that develop on a crystal depend on the space available for the crystals to grow.
If they are growing in a restricted environment, it is possible that no well-formed crystal faces will be developed.
Distorted crystals are common and result from less-than-ideal growth conditions or breakage and recrystallization.
Factors such as pressure, temperature and rate of cooling influence the shape crystals take.
Rough Diamonds
Wikipedia states, “Crystal growth differs from growth of a liquid droplet in that during growth the molecules or ions must fall into the correct lattice positions in order for a well-ordered crystal to grow. The schematic below shows a very simple example of a crystal with a simple cubic lattice growing by the addition of one additional molecule.”
Interestingly, crystal dissolution (the opposite of growth) has interesting pulsating wave properties. “When German researchers examined time-lapse images of dissolving crystals at the nanoscale, they found a surprise: Dissolution happened in pulses, marked by waves that spread just like ripples on a pond.
“What we see are waves or rings,” said lead investigator Cornelius Fischer, who conducted this research at the University of Bremen in the group of Prof. Andreas Lüttge. “We have a pit in the middle, and then around these pits are rings of mass removal.”
The research has been published in the Proceedings of the National Academy of Sciences. Fischer and Lüttge specialize in studying minerals-fluid interactions, and have collaborated for more than 15 years in the US and Germany.”7
Crystal Habits (38)
The term used to describe general shape of a crystal is its habit.
Some habits very closely resemble Platonic solid geometry and others not so much. However, they are all geometric in nature and come from parts of Platonic solid geometry (for example two arms coming together instead of the whole structure) or they are from Platonic solid geometry that has been compressed, stretched, combined, stellated, or truncated.
Samuel Colman tells us, “Indeed, few other angles than those of 30°, 45°, 60° and 90° will be found controlling their important spaces, and we see the equilateral triangle, the square, and the hexagon repeatedly laid out a with ruler and compass.”
Some of the geometry is very simple. Other is very complex and fractal-like.
- Acicular
- long, slender crystals
- natrolite
- rutile
Powellite & Apophyllite
- Amigdyloidal
- contains almond-shaped vesicles (amygdules)
- Amygdules form when gas bubbles or vesicles in volcanic lava (or other extrusive igneous rocks) are infilled with a secondary mineral such as calcite, quartz, chlorite or one of the zeolites.
- Heulandite
- subhedral zircon
Amigdyloidal vesicles in basaltic lava
- Bladed
- like a wedge or knife blade
- actinolite
- kyanite (pictured below)
- Botryoidal
- smooth bulbous or globular shapes
- hematite (pictured below)
- pyrite
- malachite
- smithsonite
- hemimorphite
- adamite
- variscite
- Columnar
- similar to fibrous: long, slender prisms often with parallel growth
- calcite
- gypsum/selenite
Lepidolite on Quartz
- Coxcomb
- aggregated flaky or tabular crystals closely spaced
- barite
- marcasite
Barite on Fluorite. Credit: James St. John
- Cubic
- cube shapes
- Sodium Chloride (NaCl) pack tightly into cube shaped crystals
- Halite forms cubes
- Pyrite forms cubes (pictured below)
- Dendritic
- tree-like growths
- romanechite
- magnesite
- native copper
Pyrolusite
- Dodecahedral
- rhombic dodecahedron, 12-sided
- Garnet (pictured below)
- galena
- Druzy
- small crystals that cover a surface
- uvarovite (pictured below)
- malachite
- azurite
- Enantiomorphic
- mirror-image habit; right and left handed crystals
- quartz
- plagioclase
- staurolite
- Equant
- length, width and breadth roughly equal
- olivine
- garnet
Boracite – cuboctahedron
- Fibrous
- elongated clusters of extremely slender prism fibers
- serpentine group
- tremolite (asbestos)
Scolecite on Quartz
- Filiform
- hair-like or thread-like
- zeolites
Millerite on Quartz
- Foliated or micaceous or lamallar (layered)
- layered structure, parting into thin sheets
- Mica (pictured below)
- Muscovite
- Biotite
- Granular
- aggregates of anhedral crystals in matrix
- bornite (pictured below)
- scheelite
- Hemimorphic
- doubly terminated crystal with two differently shaped ends
- hemimorphite
- elbaite
- Hexagonal
- hexagon shape, 6-sided
- quartz – hexagonal (pictured below)
- hanksite
- Hopper Crystals
- like cubic, but outer portions of cubes grow faster than inner portions creating a concavity
- halite
- calcite
- synthetic Bismuth (pictured below)
- Mammillary
- breast-like, surface formed by intersecting partial spherical shapes, larger version of botryoidal, also concentric layers of aggregates
- malachite (pictured below)
- hematite
- Massive or Compact
- shapeless, no distinctive external crystal shape
- limonite
- turquoise
- cinnabar (pictured below)
- realgar
- Nodular or tuberose
- deposit of roughly spherical form with irregular protuberances
- chalcedony
- various geodes
Agate
- Octahedral
- octahedron, 8-sided
- Fluorite Crystals form cubes and octahedrons (pictured below)
- diamond
- magnetite
- Platy
- flat, tablet-shaped
- wulfenite
Desert Rose
- Plumose
- fine, feather-like scales
- aurichalcite
- boulangerite
- mottramite
- Prismatic
- elongate, prism-like, crystal faces parallel to c-axis well-developed
- tourmaline
- beryl
Fluorite, Quartz & Tourmaline
- Pseudo-hexagonal
- hexagonal appearance due to cyclic twinning
- aragonite
- chrysoberyl (pictured below)
- Radiating or Divergent
- radiating outward from a central point
- wavellite (pictured below)
- pyrite suns
- Reniform or colloform
- similar to botryoidal/mammillary: intersection kidney-shaped masses
- hematite
- pyrolusite
- greenockite
- Reticulated
- lattice-like or net-like groups of slender crystals
- cerussite (pictured below)
Credit: Crystal Classics
- Rosette
- platy, radiating rose-like aggregate
- gypsum
- barite (desert rose – pictured below)
- Sphenoid
- wedge-shaped
- sphene
Titanite
- Stalactitic
- forming as stalactites or stalagmites; cylindrical or cone-shaped
- calcite
- goethite (pictured below)
- Stellated
- radiating individuals that form a star-like shape
- pyrophyllite
- aragonite
Strengite
- Striated
- not a habit – a condition of lines that can grow on certain crystal faces on certain minerals
- tourmaline (pictured below)
- pyrite
- quartz
- feldspar
- sphalerite
- Tabular
- blocky rectangular shapes
- feldspar
- topaz
Dolomite
- Tetrahedral
- tetrahedron shaped
- tetrahedrite (pictured below)
- spinel
- magnetite
- Wheat Sheaf
- aggregates resembling hand-reaped wheat sheaves
- stilbite (pictured below)
Crystal Family Systems (6)
Crystal family is determined by lattices and point groups.
All six systems are derived from the cube:
-
Triclinic
Triclinic is the least symmetrical.
The three axes are all unequal in length and intersect at three different angles (any angle but 90°).
-
Monoclinic
In Monoclinic, three axes, all unequal in length, intersect at three different angles (any angle but 90°).
The third axis is perpendicular to the other two.
-
Orthorhombic
In orthorhombic the three axes are all at right angles, and all of different lengths.
-
Tetragonal
In tetragonal the three axes are all at right angles, two of which are equal in length and one which is different in length (shorter or longer).
-
Hexagonal & Trigonal
In hexagonal (trigonal) there are four axes. Three of which fall in the same plane and intersect at the axial cross at 120° between the positive ends.
These axes are all of the same length.
The fourth axis may be longer or shorter than the others. It passes through the intersection of the other axes set at right angles to the plane formed by the set.
Quartz and beryl crystals form hexagonal structures.
-
Cubic (Isometric)
In cubic (isometric) the three axes are all equal in length and intersect at right angles to each other.
Elements of Symmetry
Planes of Symmetry
Any plane of symmetry divides the crystal form into two mirror images.
Axes of Symmetry
This refers to any line through the center of the crystal around which the crystal may be rotated so that after a definite angular revolution the crystal form appears the same as before.
There are four types possible:
- Hexagonal
Rotation repeats form every 60 degrees – Hexagon.
- Tetragonal
Rotation repeats form every 90 degrees – Square.
- Trigonal
Rotation repeats form every 120 degrees – Equilateral triangle.
- Binary
Rotation repeats form every 180 degrees – Oval.
Samuel Colman prepares a geometric analysis of four different crystals in his book Nature’s Harmonic Unity. These include harmotone, cuprus uranite, dolomite and iolite.
The symmetry and geometry can clearly be seen.
He notes, “It will be understood that in each of the permanent crystals illustrated, the drawing is made in perspective, looking from the top or apex of the pyramid, so that in the case in point the center of the diagram represents the highest portion or apex, the sides sloping up the inclined facets, shown by the converging lines, to their common meeting-place at the center in the pyramidal species.”
Center of Symmetry
Most crystals have a center of symmetry even though they may not possess either planes of symmetry or axes of symmetry.
If you can pass an imaginary line from the surface of a crystal face through the center of crystal (the axial cross) and it intersects a similar point on a face equidistance from the center, then the crystal has a center of symmetry.
Crystal Classification
There are 32 point groups.
20 of the 32 are piezoelectric. This means they can generate an electric charge in response to applied mechanical stress.
All piezoelectric classes lack a center of symmetry.
Below we have a table of isometric (having equal dimensions) crystal forms and non-isometric (different lengths and angles) crystal forms.
Note the Platonic solids, Archimedean solids and variations of each.
Conclusion
In this article we have taken a visual journey through crystal color and structure, noting how the Platonic solids (and variations of) show up in mineral and crystal formation.
In the next article we will continue our discussion of crystals, moving into the realm of quasi-crystals. We will then move into an eight-part series on the geometry of plants, microorganisms, sea creatures, insects and animals.
- Elkins, Rueckert, McCarty, The Law of One, Session 47.7, http://www.lawofone.info/results.php?s=47
- Schneider, Michael, A Beginner’s Guide to Constructing the Universe, HarperPerennial, 1995
- Harding, Jennie, Crystals, Ivy Press Limited, 2007
- ibid.
- http://www.rockhounds.com/rockshop/xtal/index.shtml#index
- Schmahl, Wolfgang & Steurer, Walter, Laue Centennial, Acta Crystollographica, 2012
- Study: Pulsating dissolution found in crystals. Hemholtz Association of German Research Centres, 17 January 2018, https://phys.org/news/2018-01-pulsating-dissolution-crystals.html#jCp
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