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5 nature’s geometry of crystals/ minerals, quartz, rocks



Nature’s Geometry of Crystals / minerals, quartz, rock 183

ROCKS, MINERALS, CRYSTALS AND QUARTZ

Minerals – Tere are some two thousand known minerals on

earth, each with its own distinctive structure and chemical

makeup. Teir character is dened by hardness and weight, crys-

tal structure and cleavage (how they break). Minerals are made

o one or more chemical elements. Elements are pure substances

made rom only one kind o atom. In a mineral, the atoms are ar-

ranged in repeating patterns that orm crystals. Tere are seven

main crystal orms. Tey are the cubic (pyrite, diamond), the

hexagonal (ice crystals, snow akes), the monoclinic (gypsum),

the tetragonal (zircon), the orthorhombic (olivine, topaz), and

the tri-clinic (plagioclase eldspars). All crystals have a precise

internal geometric structure. Teir shape, size, and color can

vary greatly. Most crystals are ound underground. Rocks are

made either o one mineral or, more oen, a mixture o min-

erals. Minerals are made o elements. Elements are simple sub-

stances that cannot be broken down into any other substance.

Some minerals, such as gold, are made o only one element. But

most minerals are made o two or more elements. For example,

salt is made o sodium and chlorine, and can be written as the

ormula NaCl. Minerals grow into special recognizable shapes

that are used to identiy them. Tey grow into unique shapes

having at suraces. I a mineral is ound with at suraces it’s

likely to be a crystal. All crystals are symmetrical.



184 The Geometry of Nature

THE SEVEN CRYSTAL SYSTEM

Te diagram on the ollowing page with the seven-pointed star

is pointing at the seven crystal system that has been created by

modiying the shape o the cube into seven new and unique geo-

metric orms. o create these new orms, the shape o the cube

has been extended, compressed, twisted, and assembled. All these

new crystal orms are symmetrical and made up o straight lines.

Teir angles are made up o whole numbers that make them ac-

ceptable to more crystal design variations or creating thirty-two

more new crystal designs, which are called the 32 crystal groups.

Tese seven crystal shapes shown on the chart are used to create

the 32 crystals shown below. Te crystals are more complex in

detail and have more renement in their construction. Tis detail

makes each crystal distinguishable rom the others. From these

32 classes o crystals there are hundreds more that are generated.As more crystals are created, they become even more complex in

their geometric orms and aceted conguration. Color and tex-

ture play a major role in distinguishing their character. At times

these crystals have to be taken to a laboratory and X-rayed to

nd out how their internal structure is constructed, that is, their

crystallo-graphic axes, unit cell, type o symmetry, etc.

External symmetry o Crystals and theMagic Number 32: Te external symme-try o crystals can be characterized by reection planes and rotation axes, simi-lar to the symmetry o polyhedra, as thecrystal shapes are indeed the shapes o polyhedra. Tere are 32 possible crystalshapes. Tey are called the 32 CrystalGroups. Tey are shown by examples o actual minerals (For one o the 32, nomineral has yet been ound.)




CRYSTAL SYSTEMS AND CRYSTAL FORMS

Te Greek word crystal is derived rom the word krystallos or

kryos, meaning ice cold. Most minerals are crystalline. Tey

develop crystal orms, geometric bodies which are specic to

and typical o that mineral. All crystal orms can be assigned to

seven crystal systems (cubic, tetragonal, hexagonal, trigonal, or-

thorhombic, monoclinic, or triclinic). Tese systems are dier-

entiated according to the axes o the crystal, the angle at which

the axes intersect, and the symmetry. Te crystal systems are

shown with one example crystal orm. Crystals are ormed when

cooling gas or vapor atoms slow down, get closer together, grasp

each other with strongly attractive orce, and become locked in

a regimented order. Every snowall illustrates this beautiully.

When the air, heavy with water vapor cools sufciently, atomic

groups composing the water vapor slow down and nally lock

each other into the beautiul hexagon patterning o snow crys-

tals. Tese crystals are made up o dierent kinds o polygons

that are tted together to create these orms. Tis is similar to

the polyhedrons. Te dierence is that the crystals are not lim-

ited to just six types o polygons which are used to go into their

construction. Te polygons seen on some crystals are somewhat

distorted. Crystals can be large or small, slender or thick, straight

or crooked. Te ideal orm (ideal crystal), as it is always pictured

in a textbook or identication manual is almost never attained

in nature. Te ull grown crystal is usually rather deormed, that

is to say, distorted. But despite the dierence in appearance, the

crystal still retains regular eatures, which are clearly discern-

able. Te angles are ound always to be the same in each kind

o crystal. Tere are thirty-two classes o crystals that all have a

given system o symmetry in common. Each system is recogniz-

able by a set o unique symmetry axes assigned to it by which

its symmetry amily can be easily described. Another thing that

makes crystals o dierent classes conusing is that crystals have

a way o growing together, which is called twins. In other words,

crystals cross one another at varying angles. Sometimes the term

is interpenetration. win and cruciorm twin are used as syno-

nyms. Tis is also called individuals multiple twins. Crystals are

the owers in the mineral amily.




THE GEOMETRY OF CRYSTALS

1. Tis hexagonal crystal is shown with the at acet-

ed sides acing down and the other one up. Te length

o the crystal is created by one h reerence point at

the top and bottom o the main square.

2. Tis tetragonal crystal is shown with the square

centered on the center point. Te diagonal o the

small square in the corner o the main square has cre-

ated the size o this center square.

3. Tis dipyramid crystal is shown with the square

centered on the center point. Te diagonal o the

main square intersects the horizontal center line andhas created a reerence point.

4. Tis rhombohedron crystal is shown with the

main square divided into thirds by the two coordi-

nate lines that run diagonal through the main square

top to bottom.

5. Tis clinopinacoid crystal is shown with the main

square divided into thirds by two coordinate linesthat run diagonally through the main square, top to

bottom. Te acet around side is created by points as

shown.

6. Tis spinacoids crystal is a rectangular orm with

½" or its width.




CUBES THAT HAVE BEEN MODIFIED

Te cube is a solid orm with six equal sides and is illustrat-

ed here in another example o a basic cube being used with

modication. Parts o the corners and edges have been cut

away to create a new and unique orm. Tis new orm is usedas a basic solid orm or dierent kinds o crystal material,

as the sample names shown imply. One sample shown has

another cube the same size inserted through it to create a

double crystal conguration. Tis is quite common in the

crystal world. Te other dierence is that the same new de-

sign crystal can come in dierent sizes, colors, and textures.

Te internal structure is also unique in each crystal design.

Tis is called cleavages pattern. You can oen identiy min-

erals by a combination o their crystal shape and cleavagepattern. You can oen identiy minerals by a combination o

their crystal shape and cleavage pattern.

Fluorite Crystal

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