Patterns in the inorganic world

Introduction

Greek scientists tried to understand the world through observations.

After the Greeks discovered mathematical patterns in music, they began to express music in numbers (see Harmonia). They could now used numbers to model the world. But the Greek scientists went further.

The 'Platonic figures' were chosen as the smallest building blocks of life: all matter on Earth was composed of tetrahedrons (pyramids), cubes, octahedrons, and icosahedrons. The heavens, which the Greeks believed to be unchanging, consisted of dodecahedrons. Timaeus (360 BC) describes this as '... and God formed them by form and number...'.

The five Platonic solids were later expanded by Archimedes to include the 13 Archimedean solids.

The 5 Platonic solids: tetrahedron (pyramid), cube, octahedron, dodecahedron and icosahedron.

Problem statement

But how did the Greek arrive at this theory? Did nature inspire them to model the smallest particles of matter as Platonic figures? And if so, where do Platonic shapes appear in nature?

The mutual arrangement of atoms has only recently become observable with X-rays. Crystals are reflections of patterns at the atomic level. The invisible, internal atomic world becomes visible to the naked eye when atomic structures grow proportionally into crystals.

Timaeus seems to allude to this with: 'We must imagine that all these particles are so small that we cannot see a single particle of any of the four kinds because of their smallness; but when many of them are collected, we see their aggregates. And the proportions of their numbers, motions, and other properties, God has everywhere, as far as necessity permitted or allowed, accurately perfected and harmonized in their proper proportions.'

The internal cubic atomic structure of these pyrite crystals is revealed by the proportional crystal growth.

Several of the Platonic and Archimedean figures find their counterparts in the inorganic crystal world.

However, I haven't yet found conclusive proof that this was indeed the ancient world of thought. So, for now, only meager references, but I've certainly acquired a taste for the mineral world.

To be clear: the crystals below are all naturally formed; no machinery was used. And all these crystals are available as part of the educational presentation.

Laurium

In the mines of Laurium, the Greeks (meaning slaves in their service) mined for lead ore. Silver was extracted from this lead ore, and silver was used to make silver coins, among other things. Galena, which contains lead, is found in these mines, as is fluorite. Both galena and fluorite develop crystals in the shape of a cube or octahedron, so the Greeks must have been familiar with these crystal forms.

The below galena and fluorite crystals come from the mines of Laurium.

The ancient miners were very thorough, and that is why such large galena crystals from Laurium are rare. I was fortunate enough to acquire this find from the private collection of an old collector, who in turn had acquired this crystal from another collector long ago.

The mines in Laurium still exist, but searching for crystals has now become dangerous due to the ignorance of some amateur diggers and climate change.

Cube (6 planes)

• Halite is derived from the ancient Greek word for salt: ἅλς (háls).
• Flourite is derived from the Latin word 'fluor', meaning 'to flow away'.
• Galene (PbS) contains lead and sulfur.
• Because pyrite (FeS2) contains sulfur, it was used as flint.

Octahedron (8 planes)

Dodecahedron (12 planes)

Icosahedron (20 planes)

(left) A rock crystal prism cut in the shape of an icosahedron from the second half of the 1st century AD, found in Pompeii (Museo Archeologico Nazionale di Napoli, Italy), (right) a reproduction of a rock crystal icosahedron.

Truncated

Cutting off the corners of the Platonic figures results in the truncated shapes.

Hexagonal (6 angles)

• Sapphire & ruby: both sapphire and ruby belong to the corundum family and have a high hardness. Sapphire turns blue due to traces of iron, whilst ruby turns red due to traces of chromium.
• Aragonite: consists of multiple crystals combined. This crystal is pseudo-hexagonal and reddish due to inclusions of iron-containing clay. The hexagonal appearance is due to cyclic twinning.
• Rock crystal: According to Pliny the Elder (Naturalis Historia), rock crystal is formed by freezing water so hard that it can no longer change its state anymore (which is incorrect).

Rhombic