A

A quanta module

• A and B Quanta Modules
• See also: Quanta modules

Additive twoness

• The Multiplicative and Additive Two

All-space filling

• The Minimum All-Space-Filling Tetrahedon: “MITE”
• Tetrakaidecahedron and Pyritohedron
• A and B Quanta Modules

Area and Volume

• Areas and Volumes in Triangles and Tetrahedra
• Calculating Areas of Regular Polygons
• Pyritohedron Dimensions and Whole-Number Volume
• Polyhedra With Whole Number Volumes

Axes of Symmetry

• The Seven Axes of Symmetry

Axis

• Distribution of Radially Close-Packed Spheres on the 25 Axes and Great Circle Planes of the Vector Equilibrium
• Inter-Sphere Connections via the 25 Great Circles of the VE

B

B quanta module

• A and B Quanta Modules
• Kelvin Truncated Octahedron
• See also: Quanta modules

Basic Disequilibrium LCD Triangle

• Basic Disequilibrium LCD Triangle
• Great Circles: The 31 Great Circles of the Icosahedron
• A and B Quanta Modules
• Icosahedron Phases of the Jitterbug

Basic Equilibrium LCD Triangle

• Basic Equilibrium LCD Triangle
• Great Circles: The 25 Great Circles of the Vector Equilibrium (VE)

Bow Tie

• Great Circle Bow-Ties of the VE
• Great Circle Bow-Ties of the Icosahedron

Bubbles, closest packing

• Tetrakaidecahedron and Pyritohedron
• See: Weaire-Phelan Matrix

C

Cannonballs

• There’s Just One Way to Stack Cannonballs

Center Sphere (see Nucleus)

Central angles and surface angles

• Basic Equilibrium LCD Triangle
• Basic Disequilibrium LCD Triangle
• Operational Geometry

Circles, great

• The 31 Great Circles of the Icosahedron
• The 25 Great Circles of the Vector Equilibrium (VE)
• Icosahedron: Spherical Polyhedra Disclosed by Great Circles
• VE: Spherical Polyhedra Disclosed by Great Circles
• Great Circle Bow-Ties of the Icosahedron
• Great Circle Bow-Ties of the VE

Closest packing of bubbles

• Tetrakaidecahedron and Pyritohedron

Closest packing of icosahedra

• Close Packing of Icosahedra
• Icosahedron Phases of the Jitterbug

Closest packing of spheres

• Close-Packing of Spheres
• Equations for the Close-Packing of Spheres
• Formation and Distribution of Nuclei in Radial Close-Packing of Spheres
• Multiplication and Merger of Spheres in the Jitterbug
• Space-Filling Polyhedra as Close-Packed Spheres

Compression-tension

• Tensegrity
• Tensegrity Equilibrium and Vector Equilibrium

Concave vector equilibrium (space)

• Spheres and Spaces
• Spaces and Spheres (Redux)

Conversion Factors

• General Unit Conversions
• Pi and the Synergetics Constants

Convex-concave

• The Multiplicative and Additive Two
• Anatomy of a Sphere
• Spheres and Spaces
• Spaces and Spheres (Redux)

Coupler

• The Minimum All-Space-Filling Tetrahedon: “MITE”
• Quanta Module Constructions of the Rhombic Dodecahedron

Cube

• The Cube
• Polyhedra With Whole Number Volumes

Cube, in rhombic dodecahedron

• The Rhombic Dodecahedron

Cube, in tetrakaidecahedron and Weaire-Phelan matrix

• Tetrakaidecahedron and Pyritohedron

Cube, synergetics conversion constants

• Pi and the Synergetics Constants
• General Unit Conversions

Cuboctahedron (See: Vector Equilibrium; VE)

D

Dimension

Dodecahedron

• The Rhombic Dodecahedron
• Quanta Module Constructions of the Rhombic Dodecahedron
• Pentagonal Dodecahedron

Dodecahedron, Pentagonal

• The Golden Ratio

Domain of sphere

• The Rhombic Dodecahedron

Domain of nucleus

• The Kelvin Truncated Octahedron
• Tetrakaidecahedron and Pyritohedron
• Formation and Distribution of Nuclei in Radial Close-Packing of Spheres

Dymaxion Vector Constant

• Pi and the Synergetics Constants

E

E quanta module

• T and E Quanta Modules
• See also: Quanta modules

Edges of polyhedra

• Topological Abundance Formulas
• See also: Vectors

Equations

• Calculating Volumes of Regular Polyhedra
• Calculating Areas of Regular Polygons
• Equations for the Close-Packing of Spheres
• Topological Abundance Formulas
• Areas and Volumes in Triangles and Tetrahedra

Equilibrium

• Vector Equilibrium and the “VE”
• Tensegrity Equilibrium and Vector Equilibrium
• Jessen Orthogonal Icosahedron and Tensor Equilibrium

Euler

• Topological Abundance Formulas

Expansion-contraction (see: Jitterbug)

F

Faces of polyhedra

• Topological Abundance Formulas

Folding, Foldability

• Polyhedra From Polygonal Strips
• Great Circle Bow-Ties of the Icosahedron
• Great Circle Bow-Ties of the VE
• Tetrahelix
• See also: quanta modules

G

Gears

• Inter-Geared Mobilities of the De-Nucleated Vector Equilibrium

Geodesic Polyhedra

• Geodesics

Gibb’s phase rule

• Topological Abundance Formulas

Goldberg Polyhedra

• Geodesics
• Tensegrity

Golden Ratio

• The Golden Ratio
• Icosahedron
• Icosahedron Phases of the Jitterbug
• Jessen Orthogonal Icosahedron and Tensor Equilibrium
• Pentagonal Dodecahedron
• Rhombic Triacontahedron
• T and E Quanta Modules

Great circles

• The 31 Great Circles of the Icosahedron
• The 25 Great Circles of the Vector Equilibrium (VE)
• Icosahedron: Spherical Polyhedra Disclosed by Great Circles
• VE: Spherical Polyhedra Disclosed by Great Circles
• 25 Great Circles of the VE (new illustrations)
• Distribution of Radially Close-Packed Spheres on the 25 Axes and Great Circle Planes of the Vector Equilibrium
• Inter-Sphere Connections via the 25 Great Circles of the VE
• Distribution of Radially Close-Packed Spheres on the 25 Axes and Great Circle Planes of the Vector Equilibrium
• Inter-Sphere Connections via the 25 Great Circles of the VE

Great circles, foldability

• Great Circle Bow-Ties of the Icosahedron
• Great Circle Bow-Ties of the VE

Growth

• Concentric Sphere Shell Growth Rates

H

Helix

• Tetrahelix
• A Curious Helical Structure

I

Icosidodecahedron

• Rhombic Triacontahedron

Icosahedron

• The Icosahedron
• The 31 Great Circles of the Icosahedron
• Icosahedron Inside Octahedron
• Icosahedron: Spherical Polyhedra Disclosed by Great Circles
• Great Circle Bow-Ties of the Icosahedron
• Icosahedron Phases of the Jitterbug
• Jessen Orthogonal Icosahedron and Tensor Equilibrium
• Close Packing of Icosahedra
• The Diagonal of the Icosahedron
• The Golden Ratio
• Pentagonal Dodecahedron
• Rhombic Triacontahedron
• Tensegrity Equilibrium and Vector Equilibrium

Icosahedron, Space-Filling Complement to

• Close Packing of Icosahedra
• Icosahedron Phases of the Jitterbug
• The Golden Ratio

Inscribed Polyhedra

• Equivalence of Tetrahedron Edge Length and Structural Quanta per Volume of its Inscribed Polyhedra
• Icosahedron Inside Octahedron

Insideness, Outsideness

• Anatomy of a Sphere
• The Dual Nature of the Tetrahedron
• The Multiplicative and Additive Two
• Spheres and Spaces
• Unique Properties of the Tetrahedron

Interstices

• Isotropic Vector Matrix
• Spheres and Spaces
• Spaces and Spheres (Redux)

Isotropic Vector Matrix

• Close-Packing of Spheres
• Distribution of Radially Close-Packed Spheres on the 25 Axes and Great Circle Planes of the Vector Equilibrium
• Isotropic Vector Matrix
• The Isotropic Vector Matrix as Transverse Waves

J

Jitterbug

• The Jitterbug
• Icosahedron Phases of the Jitterbug
• The Multiplication and Merger of Spheres in the Jitterbug
• Jitterbug Animations with Spheres

Jessen Orthogonal Icosahedron

• Icosahedron Phases of the Jitterbug
• Jessen Orthogonal Icosahedron and Tensor Equilibrium
• Tensegrity
• Tensegrity Equilibrium and Vector Equilibrium
• The Jessen Orthogonal Icosahedron in the Isotropic Vector Matrix

K

Kelvin truncated octahedron

• The Kelvin Truncated Octahedron
• Formation and Distribution of Nuclei in Radial Close-Packing of Spheres
• Rhombic Triacontahedron
• Tetrakaidecahedron and Pyritohedron

Kissing point

• Close-Packing of Spheres
• Inter-Sphere Connections via the 25 Great Circles of the VE
• Tensegrity

L

Lattices

• Close Packing of Icosahedra

Layers

• Close-Packing of Spheres
• Concentric Sphere Shell Growth Rates
• Formation and Distribution of Nuclei in Radial Close-Packing of Spheres
• See also: Shells

Line, linear

• Powers and Dimensions
• See also: Edges; Vectors

M

Matrix

• Isotropic Vector Matrix
• The Isotropic Vector Matrix as Transverse Waves
• See: Weaire-Phelan Matrix

Minimum

• The Minimum All-Space-Filling Tetrahedon: “MITE”

Mite (minimum tetrahedron)

• The Minimum All-Space-Filling Tetrahedon: “MITE”

Modules, quanta

• A and B Quanta Modules
• T and E Quanta Modules
• Quanta Module Constructions of the Rhombic Dodecahedron
• The Minimum All-Space-Filling Tetrahedon: “MITE”

Multiplicative twoness

• The Multiplicative and Additive Two

N

Negative-Positive

Neutrality

Nuclear Void

• Categories of Spheres in the Isotropic Vector Matrix: Nuclei, F1 Shells, and “Nuclear Voids”

Nucleus

• Categories of Spheres in the Isotropic Vector Matrix: Nuclei, F1 Shells, and “Nuclear Voids”
• Formation and Distribution of Nuclei in Radial Close-Packing of Spheres
• Inter-Geared Mobilities of the De-Nucleated Vector Equilibrium
• The Kelvin Truncated Octahedron
• Tetrakaidecahedron and Pyritohedron

O

Octahedron

• A and B Quanta Modules
• Polyhedra With Whole Number Volumes
• The Octahedron

Octet truss

• Isotropic Vector Matrix

Operational Geometry

• Operational Geometry
• Great Circle Bow-Ties of the Icosahedron
• Great Circle Bow-Ties of the VE
• Polyhedra From Polygonal Strips

Oscillation (See: Jitterbug)

P

Pairings

• Concentric Sphere Shell Growth Rates

Pentagonal Dodecahedron

• Pentagonal Dodecahedron
• Rhombic Triacontahedron

Pi

• Pi and the Synergetics Constants

Planck’s Constant

• Pi and the Synergetics Constants

Points (See: Vertices)

Polarity

Polygons

• Calculating Areas of Regular Polygons
• Polyhedra From Polygonal Strips

Polyhedra

• Calculating Volumes of Regular Polyhedra
• Icosahedron: Spherical Polyhedra Disclosed by Great Circles
• VE: Spherical Polyhedra Disclosed by Great Circles
• Polyhedra With Whole Number Volumes
• Polyhedra From Polygonal Strips

Polyhedra, Regular

• Icosahedron
• Kelvin Truncated Octahedron
• Tetrahedron
• Octahedron
• Pentagonal Dodecahedron
• Rhombic Dodecahedron

Positive-Negative

Powers and Dimensions

• Pi and the Synergetics Constants

Precession

• See: Jitterbug

Prime numbers

Prime volumes

• Polyhedra With Whole Number Volumes

Pulsation (See: Jitterbug)

Push-pull

Pyritohedron

• Tetrakaidecahedron and Pyritohedron
• Pyritohedron Dimensions and Whole-Number Volume
• Construction Method for the Pyritohedron and Tetrakaidecahedron of the Weaire-Phelan Matrix

Q

Quanta modules

• A and B Quanta Modules
• S Quanta Module
• T and E Quanta Modules
• Quanta Module Constructions of the Rhombic Dodecahedron

Quantum loss

Quantum jump

Quantum model

Quark

• The Minimum All-Space-Filling Tetrahedron: “MITE”

R

Radial-Circumferential

Radiation-Gravitation

Radius, Radii, Radial

• Areas and Volumes in Triangles and Tetrahedra

Rational whole numbers

• Polyhedra With Whole Number Volumes

Rectilinear grid

Reflection, mirror-image

Regenerative

Relationships

Rhombic dodecahedron

• The Rhombic Dodecahedron
• Quanta Module Constructions of the Rhombic Dodecahedron
• Formation and Distribution of Nuclei in Radial Close-Packing of Spheres

Rhombic Triacontahedron

• Basic Disequilibrium LCD Triangle
• The Golden Ratio
• Polyhedra With Whole Number Volumes
• T and E Quanta Modules
• Rhombic Triacontahedron

Right triangle

• Basic Disequilibrium LCD Triangle
• Basic Equilibrium LCD Triangle

Rotational symmetry

S

S Quanta Module

• S Quanta Module

Scheherazade numbers

Scribing tools

• Operational Geometry

Seven axes of symmetry

• The Seven Axes of Symmetry

Shape

Shells and lattices

• Close Packing of Icosahedra

Shell growth rate

• Concentric Sphere Shell Growth Rates

Sixness

• Concentric Sphere Shell Growth Rates

Spaces

• Spheres and Spaces
• Quanta Module Constructions of the Rhombic Dodecahedron

Space-Filling

• A and B Quanta Modules
• Isotropic Vector Matrix
• Kelvin Truncated Octahedron
• Minimum All-Space-Filling Tetrahedron: “MITE”
• Rhombic Triacontahedron
• Space-Filling Polyhedra as Close-Packed Spheres
• Tetrakaidecahedron and Pyritohedron

Spheres

• Anatomy of a Sphere
• Categories of Spheres in the Isotropic Vector Matrix: Nuclei, F1 Shells, and “Nuclear Voids”
• Close-Packing of Spheres
• Distribution of Radially Close-Packed Spheres on the 25 Axes and Great Circle Planes of the Vector Equilibrium
• Equations for the Close-Packing of Spheres
• Formation and Distribution of Nuclei in Radial Close-Packing of Spheres
• Inter-Sphere Connections via the 25 Great Circles of the VE
• The Multiplication and Merger of Spheres in the Jitterbug
• Spaces and Spheres (Redux)
• Spheres and Spaces

Spherical domain

• The Rhombic Dodecahedron
• Pentagonal Dodecahedron

Spherical polyhedra

• Icosahedron: Spherical Polyhedra Disclosed by Great Circles
• VE: Spherical Polyhedra Disclosed by Great Circles
• 25 Great Circles of the VE (new illustrations)
• Geodesics

Spherical Trigonometry

• Operational Geometry

Spin

Spiral (See: Helix)

Structure

• Tensegrity

Structural Quanta

• Equivalence of Tetrahedron Edge Length and Structural Quanta per Volume of its Inscribed Polyhedra

Star tetrahedron

Struts

• Tensegrity

Symmetry

• The Seven Axes of Symmetry

Synergetics hierarchy

Synergetics power constants

• Pi and the Synergetics Constants

System

Syte (symmetrical tetrahedron)

T

T quanta module

• T and E Quanta Modules

Tensegrity

• Tensegrity
• Tensegrity Equilibrium and Vector Equilibrium
• Tensegrity Sphere Equations

Tension-compression

Tensor

• Tensegrity
• Tensegrity Equilibrium and Vector Equilibrium
• Jessen Orthogonal Icosahedron and Tensor Equilibrium
• Tensegrity Sphere Equations
• Model Making

Tetrahedron

• A and B Quanta Modules
• Areas and Volumes in Triangles and Tetrahedra
• The Dual Nature of the Tetrahedron
• Polyhedra With Whole Number Volumes
• Spheres and Spaces
• The Tetrahedron
• Unique Properties of the Tetrahedron

Tetrahelix

• Tetrahelix

Tetrakaidecahedra

• The Kelvin Truncated Octahedron
• Tetrakaidecahedron and Pyritohedron
• Pyritohedron Dimensions and Whole-Number Volume
• Tetrakaidecahedron Dimensions and Whole Number Volume
• Construction Method for the Pyritohedron and Tetrakaidecahedron of the Weaire-Phelan Matrix

Topology

• Topological Abundance Formulas

Transformation (See: Jitterbug)

Triacontahedron

• See: Rhombic Triacontahedron

Triangle

• Basic Disequilibrium LCD Triangle
• Basic Equilibrium LCD Triangle

Triangle in cube

• The Jitterbug

Triangular number

• Concentric Sphere Shell Growth Rates

Tricontahedron, Rhombic

• Polyhedra With Whole Number Volumes
• The Golden Ratio
• T and E Quanta Modules
• Basic Disequilibrium LCD Triangle

Trigonometry

• Operational Geometry

Truncated cube

• Vector Equilibrium and the “VE”
• Cube

Truncated icosahedron

• Pentagonal Dodecahedron
• Tetrakaidecahedron and Pyritohedron

Truncated octahedron

• Vector Equilibrium and the “VE”
• Kelvin Truncated Octahedron

Truncated tetrahedron

• Octahedron
• Seven Axes of Symmetry

Twelve degrees of freedom

• Tetrahelix

Twinkle angle

• A and B Quanta Modules
• Basic Disequilibrium LCD Triangle
• The Minimum All-Space-Filling Tetrahedron: “MITE”

Twoness

• The Multiplicative and Additive Two

U

Unit radius

• Close-Packing of Spheres

Unit vector

• Isotropic Vector Matrix

Units, Conversion from 90° to 60° accounting

• General Unit Conversions
• Pi and the Synergetics Constants

Unity is plural

• Dual Nature of the Tetrahedron
• Twoness: The Multiplicative and Additive Two
• Anatomy of a Sphere

Universe

Unzipping angle

• Tetrahelix

V

Vectors

• Isotropic Vector Matrix
• Vector Equilibrium and the “VE”

Vector equilibrium, VE

• The 25 Great Circles of the VE (new illustrations)
• Close-Packing of Spheres
• Distribution of Radially Close-Packed Spheres on the 25 Axes and Great Circle Planes of the Vector Equilibrium
• Great Circles: The 25 Great Circles of the Vector Equilibrium (VE)
• Inter-Geared Mobilities of the De-Nucleated Vector Equilibrium
• Tensegrity Equilibrium and Vector Equilibrium
• Vector Equilibrium and the “VE”

Vertices

• Topological Abundance Formulas

Volume

• Areas and Volumes in Triangles and Tetrahedra
• Calculating Volumes of Regular Polyhedra
• Polyhedra With Whole Number Volumes
• Pyritohedron Dimensions and Whole-Number Volume

W

Weaire-Phelan Matrix

• Tetrakaidecahedron and Pyritohedron
• Formation and Distribution of Nuclei in Radial Close-Packing of Spheres

Wave

• Polyhedra From Polygonal Strips
• The Isotropic Vector Matrix as Transverse Waves

Whole numbers

• Polyhedra With Whole Number Volumes
• Pyritohedron Dimensions and Whole-Number Volume
• Tetrakaidecahedron Dimensions and Whole Number Volume

XYZ

XYZ coordinate system

Zero nineness

Zero tetrahedron

Zerophase

Zerowave