Buckminster Fuller’s Vector Equilibrium:
The Most Balanced Shape In The Universe!
The most balanced shape in the Universe is the entity known as the Cuboctahedron or Vector Equilibrium (VE) whose geometrical signature is 3-4-3-4 because at each of its 12 vertices, are met a Triangle-Square-Triangle-Square, suggesting that it is a 4th dimensional geometry, since it is also composed of 6 interacting hexagons at 60 degree angles.
Aka, The 12 Around the One, and revered by Buckminster Fuller, this shape surpasses the functionality of the 3-dim cube, that has a signature of 4-4-4 because at each of its 8 corners or vertices is a square-square-square configuration. Bucky measured all volumes with the Tetrahedron, thus the Cube has a Tetra Volume (TV) of 3, and the Cuboctahedron has a TV of 20. This chalkboard lesson is thus a tribute to Buckminster Fuller, showing the superiority of the Cuboctahedron over the Cube. Bucky often showed that a Cube, made out of dowel edges and rubber joins, under compression flattens to a hexagon, whereas the Tetrahedron remains unchanged, strong and stable.
Also, this shape under Compression, known as The Jitterbug, forms the Icosahedron which means the Golden Ratio is hidden inside, it is the shift from the Hexagon or 6-ness, to the Pentagon or 5-ness, which are the numbers and shapes of our DNA.
This is a chalkboard tribute to Buckminster Fuller, showing the superiority of the Cuboctahedron over the Cube.
More Notes on the Superiority of the VE versus the Cube Numbers:
“0” – Zerophase, Omni-Directional. Unified field. The Heart of the construct that connects all that surrounds it.
“1” – The Central Point or Sphere of the 12 Around The One.
“2” – The 6 Pairs of Diametric Opposite Vertices. Each of the 6 squared-based pyramids, whose apexes meet at the centre, have a TV or Tetra Volume of 2 units.
“3” – 3 is for Triangle. There are 8 Triangles on the surface or 8 Tetrahedra touching at the centre. The Cube has a TV or Tetra Volume of 3 units.
“4” – 4 is for Square. There are 4 edges at each vertex of VE. This is suggested in the signature code name of 3-4-3-4 meaning at each vertex or corner there is a Triangle-Square- Triangle-Square configuration. These 4 planes meeting at a point suggest a subtle 4th-dimensional quality about this VE.
“5” – The Icosahedron forms from the VE Under Compression “UC”. This requires a half compression, whereas a full compression squashes this VE to an Octahedron. The formation of this Icosahedron tells us that VE contains the Golden Ratio suggestive of the Pentagon Mathematics containing Phi. This is the shift from Hexagon to Pentagon aka Penta-Hexa phenomenon.
“6” – There are 6 Cubes on the surface or 6 Square-Based Pyramid touching at the centre. Also, Under Compression the VE forms a Double Tetrahedron which has 6 Triangular Faces. There are also 6 Pairs of Diametric Opposite Vertices.
“7” – The 6 Around The One is the symbol for Nano-Technology called Carbon 7. This is symbolic of the biblical 6 days of Creation and God rested on the 7th.
“8” – There are 8 Triangles on the surface or 8 Tetrahedra touching at the centre. 8 is also for the Octahedron that has 8 Triangles UC.
“12” – There are 12 internal Radials aka Vectors. The Icosahedron having 12 Vertices forms from the VE Under Compression “UC”. This requires a half compression, whereas a full compression squashes this VE to an Octahedron. The formation of this Icosahedron tells us that VE contains the Golden Ratio suggestive of the Pentagon Mathematics containing Phi. This is the shift from Hexagon to Pentagon aka Penta-Hexa phenomenon.
Also, the Cuboctahedron has a Dual, (joining internally the 14 Face-Centres of 6 Squares and 8 Triangles) known as the Rhombic Dodecahedron which essentially has 12 diamond faces based on Root 2 (1.414…). In the natural crystal world this shape belongs to Garnet Crystal.
The Cube has 12 edges.
“13” – The 12 Spheres Around the Central 13th. This is called the sacred Code 13. Cuboctahedron is formed by joining the centre of the 12 spheres. When the 13th is removed and they compress further towards a centre, this forms the Icosahedron of 12 vertices.
“14” – The 14 Faces, includes the 6 squares and the 8 triangles.
“20” – Tetra Volume of 20. Bucky measured all volumes with the Tetrahedron as the basic shape of unit volume, thus the Cube has a Tetra Volume (TV) of 3 units, and the Cuboctahedron has a TV of 20 units. This would mean that the 6 square-based pyramids must have a TV of 12 units and that each square-based Pyramid has a TV of 2 units.
“24” – There are 24 edges, 12. There are also 24 triangular vectors that meet at the centre. 24 is the Stargate Number, sacred to revealing the mysteries of the Fibonacci Sequence and the Prime Numbers.
Bucky further divided the single unit Tetrahedron, in his creation of the TV or Tetra Volume, into 24 equal-sized prisms or partitions or volumes that he called “Quanta”, a finer way for measuring volumes. See Number 480
“42” – If we continue the spherical packing of balls around the 12 Around The 1, we get a second shell or layer that totals 42 spheres that includes both layers. The 3rd layer would have a total of 92 spheres. Of interest, if you continue this onion-like layers of shells of sphere packing, all the totals have a number that ends in the number 2: Here is the Sequence of Cuboctahedral Shells: 12, 42, 92, 162, 252, etc but the actual sequence of Full Cuboctahedral Shells that includes the sum of all spheres within is: 1, 13, 55, 147, 309, 561…
“60” – The dominant angle with the VE are is the 60 degree angle, which is harmonious, like the transition of liquid water to solid ice as in the snowflake is 60 degrees. That is why VE is the most balanced shape in the Universe. That is why VE is composed of 6 hexagonal planes at 60 degree angles, suggesting a 4th-dimensional array.
“90” – The Cubes corner and face angles are all 90 degrees or a quadrant of the circle.
“92” – Refer to Number 42 above. The 3rd cuboctahedral shell is composed of 92 spheres or balls.
“120” – 2 x 60 degrees is 120 being the distance between alternate hexagon vertices.
“125.26” – The dihedral angle is the angle between 2 intersecting planes, is 125.26 degrees.
“444” – The Cube, at each of its 8 corners, has a square-square-square or 4-4-4 configuration. 444 here is only a symbolic number reference to this.
“480” – Each TV has 24 Quanta, thus the VE that is comprised of 20 TV must have 24 x 20 = 480 Quanta.
“3,600” – Sum of all the surface angles of VE is based on the sum of 6 Squares and 8 Triangles = (6 x 360) + (8 x 180) degrees = 2,160 + 1,440 = 3,600 degrees. This value of 3,600 can be reduced to Harmonic 360 which is VE’s connection to the Harmonics of the Circle.