The Platonic Solids
There are five key sacred patterns making up all matter in this
universe. Known as the Platonic Solids, these shapes are
tetrahedron, hexahedron, octahedron, icosahedron, and
dodecahedron. The Platonic Solids are called the perfect solids
because, in each of them, every facet has equal side length, equal
facet size, and equal angle. Moreover, all these structures fit
perfectly within a sphere.
The five Platonic Solids are regarded as the building blocks of
the universe. These shapes occur regularly in nature and are
equated with the five classical elements with which everything is
made of fire, earth, air, water, and ether.
So how did the Platonic Solids come to be?
Evidence suggests that the work of the Pythagoreans (a brotherhood
devoted to the study of mathematics and was founded by Pythagoras)
about the solids was influenced by the Egyptians who knew about at
least three of them. It is generally agreed that the ancient
Pythagoreans discovered the tetrahedron, the cube, and the
dodecahedron. Later, Athenian mathematician Theaetetus, a disciple
of Socrates added the octahedron and the icosahedron.
The shapes are called Platonic Solids after the Greek philosopher
Plato who wrote about the five solids in a work called Timaeus. It
was Plato who assigned the solids to the elements generally
believed to make up all matter in the universe. During his time,
the people believed that all things are made up of five different
atoms (earth, fire, water, air, ether). Therefore, they are
considered as the fundamental components of the physical universe
– the archetypical foundation of all forms.
What makes platonic solids special?
Only the 5 platonic solids of all polyhedra meet these conditions:
- Platonic solids are the only polyhedral shapes with exactly
the same faces. Each face is identical to every other face.
For example, all the faces of a cube (hexahedron) are
congruent squares.
- There are the same numbers of faces that meet at each and
every vertex. For example, each vertex of a tetrahedron has 3
adjacent equilateral triangles.
The five Platonic solids
Tetrahedron
The tetrahedron also known as a triangular pyramid, it has four
triangular faces, four vertex corners, and six straight edges. It
is the simplest of the solids and the only one with less than five
faces. A tetrahedron is a 3-simplex. This is because all its
vertices are equidistant from each other unlike the rest of the
platonic shapes.
The tetrahedron is known as the triangular pyramid due to its
triangular base, which could be any of the four faces. It is a
unique pyramid with the faces connecting the base to a common
point. The tetrahedron is termed as self-dual meaning that its
other dual is another tetrahedron, combined they form a stellated
octahedron or Stella Octangula (a compound figure of two dual
regular Tetrahedron).
This perfect solid represents the element of FIRE. As Plato
described it, the heat of the fire is sharp and stabbing, not
unlike the points of the tetrahedron. Regardless of how it is
turned, each side of the tetrahedron sits flat, perfectly
symbolizing balance and stability, both physically and
spiritually. It is also a symbol of courage, self-confidence,
passion, and willpower. The tetrahedron is associated with the
Power of Creation. In the human body, the tetrahedron is like the
solar plexus, a critical part of the nervous system that is
responsible for the smooth functioning of the organs and the
required metabolic changes that allow the body to handle stress by
preparing it for change, by increasing vitality and stimulating
action.
Cube (Hexahedron)
A cube also known as a hexahedron is a three-dimensional object
made up of six square faces, twelve edges, and eight vertices. It
is the only finite perfectly symmetrical solid whose faces are
square instead of triangular. At each vertex, three identical
square faces meet.
The duplication of a cube is among the popular unsolved
mathematical problems (Delian problem). The ancient Greek
mathematicians used a compass and straightedge only, to construct
a cube that should have twice the volume of the given cube. They
found it to be impossible and later it was discovered that it is
because the cube root of 2 is not a constructible number.
The hexahedron represents EARTH, the densest element. Conversely,
each side of the hexahedron (cube) is made up of not one but two
triangles (square). Like the tetrahedron, the hexahedron lies flat
and perfectly balanced no matter how it is turned, and is,
therefore, a natural symbol for security, stability, structure,
safety, grounding, and self-confidence. It brings forth material
consciousness.
Octahedron
Octahedron is a three-dimensional shape with eight faces, twelve
edges, and six vertices. The eight faces are a composition of
equilateral triangles, four meeting at the same vertex creating a
square-bottomed pyramid. When the two shapes are put together base
to base, they create a complete octahedron. It is the dual
polyhedron of a cube and a rectified tetrahedron.
The Octahedron is a simple well-covered polyhedral, meaning it
requires complete removal of the four vertices to disconnect all
the vertices. Note: there are irregular octahedra and the one
under discussion is a regular octahedron - all faces are the same
size and shape - and therefore the only one that qualifies as a
platonic shape.
The octahedron is associated with the AIR element, symbolizing
inspiration, mental power, and new beginnings. It also relates to
the law of cause and effect. The octahedron integrates and
balances the spiritual and material realms. In the human body, the
octahedron is linked to the heart, the center of love, compassion
and one’s spiritual nature. It is from the heart where our healing
and nurturing nature comes from. Compared to spicy foods
associated with the tetrahedron, the octahedron is associated with
foods that are “airy”, rather dry and rough like crackers or
popcorn, which are more difficult to digest.
Dodecahedron
The dodecahedron is any polyhedron with a total of twelve flat
faces (it is where the name comes from - Greek Dodeca - meaning
12). However, the regular dodecahedron is the Platonic solid. It
is made up of twelve pentagonal faces (5-sided), thirty edges and
twenty vertices where at each, three edges meet with an internal
angle of 3240.
Each of the twelve regular pentagons has internal angles of 1080
and each face is the same identical polygon. The dodecahedron has
geometrical relations with the icosahedron as the two shapes are
duals.
The dodecahedron is associated with the fifth element, ETHER
(aether in Latin). This element is also called “quintessence”, or
simply “spirit”. Above the terrestrial sphere, it is what the
universe is made of. It symbolizes wholeness, completion and
divine connection. It relates to spiritual consciousness and
accountability.
While observing and measuring, ether has proven difficult because
of its all-encompassing pervasiveness, it is interesting to note
that all observation thus far indicates that it behaves like a
fluid.
Icosahedron
The Icosahedron is a polyhedron with 20 faces, the name comes from
the Greek word Icosa- meaning 20. It has twenty equilateral
triangular faces, thirty edges, and twelve vertices. At each
vertex, five edges and five faces meet.
As mentioned earlier, the icosahedron is the dual of the
dodecahedron having three regular pentagonal faces around each
vertex.
The icosahedron represents the WATER element, symbolizing dreams,
intuition, and emotions. Compared to the sharpness of the
tetrahedron which is associated with the sharpness of spicy foods,
the icosahedron’s much duller angles make it the closest in shape
to the sphere. Soothing, creamy foods associated with water are
generally gentler, sweeter and more pleasing to the tongue. The
icosahedron also relates to the water elements characteristic
flow, movement, transformation, and change.
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About the Author
David Weitzman
The jewelry artist David Weitzman combines ancient and sacred knowledge into a unique line of jewelry designed to bring people both beauty and inspiration. David's artwork harnesses the power of spiritual symbols and sacred geometry from around the world to bring those wearing this sacred jewelry happiness, vitality, excitement, and love.
