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 Amy C. Edmondson A Fuller Explanation

Appendix E: Glossary

Includes specific terminology coined and/or used in an unusual way by Buckminster Fuller (in italics) as well as terms from conventional mathematics and geometry that may be unfamiliar.

A-module: Asymmetrical tetrahedron, which encompasses one twenty-fourth of the regular tetrahedron.

acute angle: Angle less than 90 degrees.

angle: Formed by two lines (or vectors) diverging from a common crossing. An angle is necessarily independent of size.

angular topology: Fuller's term, intended to describe a principal function of synergetics, that is, description of all structure and pattern by variation of only two variables: angle and frequency. (See "frequency."

arc: A segment of a curve.

B-module: Asymmetrical tetrahedron, which is the result of subtracting an A module from one forty-eighth of the regular octahedron.

complementarity, or inherent complementarity of Universe: Necessary coexistence, inseparable pairs. Fuller emphasizes that Universe consists of complementary teams, such as concave-convex, tension-compression, positive-negative, and male-female, and concludes that "unity is inherently plural."

concave: Curved toward the observer, such as the surface of a sphere, or other enclosure, as seen from the inside.

convex: Curved away from the observer, such as the surface of a sphere as seen from the outside.

coupler: Semisymmetrical octahedron, which consists of sixteen "A-Modules" and eight "B-Modules," or eight "Mites."

degrees of freedom: This term is used by Fuller to mean the number of independent forces necessary to completely restrain a body in space, and by Loeb in reference to the overall stability of systems.

design: Deliberate ordering of components.

design science: See Chapter 16

dimension: See Chapter 6. Used by Fuller to include spatial extent, orders of complexity, and distinct facets of symmetry.

dimpling: Yielding inwardly to produce local indent in structural system, caving-in.

Dymaxion: Fuller's trademark word, created by Marshall Fields Department Store in the late 1920s, for use in promotion of exhibit featuring Fuller's revolutionary house design. Also used by Fuller to mean "doing more with less."

edge: Geometry term: connection between points (or vertices) and boundary between two faces, line. Fuller prefers to substitute "vector" or else refer to the specific material of construction, such as toothpick or straw.

energy event: Fuller's substitute for geometric term "point." Also descriptive term for natural phenomena, discrete constituents of Universe. Replaces obsolete" vocabulary such as "solid," "point," "thing," etc.

ephemeralization: Doing more with less, via design science and technological invention.

face: Geometric term: polyhedral window, polygon, area.

finite accounting system: Describes concept of physical reality consisting, on some level, of discrete indivisible particles, as opposed to continuous surfaces or masses. See Chapter 2

frequency: Used by Fuller to specify length and size in general. The intention is to employ a more precisely descriptive term for both geometric systems and events in nature, than provided by specific units of measurement. Fuller points out that frequency never relates to the quantity "one," for it necessarily involves a plurality of experiences.

high-frequency energy event: Describes most tangible structures, which might be popularly thought of as "solids." A good example to illustrate the concept of "high-frequency energy event" through a visible image is found in the white foam of breaking ocean waves. Upon closer inspection, the apparent continuum of whiteness is a result of an enormous number of tiny clear bubbles, which appear continuous because of their close proximity. This punctuated consistency is analogous to all matter, although most examples are not visible to the naked eye.

frequency of modular subdivision: Number of subdivisions per edge, in a polyhedron, or number of discrete subdivisions per module in any system.

generalized principle: Rule that holds true without exception. Eternal law of nature. See Chapter 1

great circle: A circle on the surface of a sphere, which lies in a plane intersecting the center of that sphere. Equatorial ring.

great-circle arc: Segment of great circle.

Greater Intellectual Integrity of Universe: Sum total of all "generalized principles," complex "unknowable" totality of Universe. Divine intellect. Perfection of eternally regenerative pattern integrities of Universe.

in, out: Seen by Fuller as appropriate replacements for up, down, to describe the directions toward the earth's center and away from the earth's surface, respectively.

inherent complementarity of Universe: See "complementarity."

interior angle of polygon: Angle between two edges measured through the inside.

interprecessing: See precession

intertransformability: Phenomenon of significant relationships between systems, allowing transformations from one to another. Applies to both polyhedra and natural structures. Examples include shared symmetry among polyhedra and common constituents arranged differently to produce different substances.

isotropic vector matrix, IVM: Space-filling array of unit-length vectors, in which all vectors are identically situated. The "omnisymmetrical" matrix consists of an indefinite expanse of alternating tetrahedra and octahedra, with 60-degree angles between adjacent vectors. This conceptual IVM framework can be actualized with building materials to create an Octet Truss, which is an extremely efficient and lightweight architectural space frame.

jitterbug transformation: Transformation of a cuboctahedron model, in which flexible joints allow the unstable polyhedron to contract in a radially symmetrical manner, and thereby take on the shape of various other polyhedral systems.

Mite: Two mirror-image "A-modules" and one "B-module" combined to create an asymmetrical tetrahedron, in which three right angles surround one vertex. Trirectangular tetrahedron.

nature's coordinate system: The mathematically expressible system that governs the coordination of both physical and metaphysical phenomena. Set of generalizations about the way systems are structured and able to cohere over time. Interplay of the principles describing spatial complexity with the requirements of mihimum energy in the organization of natural structures.

nest: Valley, or local indentation, between adjacent closepacked spheres.

net: Planar array of adjacent polygons which can be folded along shared edges and closed together to create a specific polyhedron.

obtuse angle: Angle greater than 90 degrees.

omni-accommodative: Able to accommodate all spatial directions, or model all transformations; omnidirectional.

omni-interaccommodative: Describes cooperative relationship between noncontradictory principles or evidence, which are thus more significant considered together than separately.

omnisymmetrical: Symmetry in all spatial directions.

pattern integrity: Reliable or consistent arrangement of "energy events" (or constituent parts) in dynamically regenerative system. A pattern with structural integrity, that is, a pattern that coheres for some period of time.

precession: Two or more systems in motion with respect to each other involving 90-degree turn. In addition to its meaning in physics describing a complex motion of a rotating body in response to an applied torque- Fuller employs this word (as well as his own "interprecessing") to refer to two geometrical systems which, oriented perpendicularly to each other, reveal a new system or geometric relationship.

quanta: Used by Fuller to mean indivisible discrete units, limit-case particles, isolated energy events. See finite accounting system

regular polyhedron: Polyhedron composed exclusively of one type of polygonal face meeting at identical vertices.

right isosceles triangle: Triangle which includes two equal edges (or arc lengths) with a right-angle between them. Planar version has angles of 45° -45° -90°; one particular spherical version has angles of 60° -60° -90°.

similar: Geometrical term: having the same shape, but not necessarily the same size.

size: Dimension, extent. Relates to actual constructs, or "special-case" systems.

Spaceship Earth: Coined by Fuller to convey a sense of a finite, whole system planet, in which the lives of all human beings (or passengers) are interrelated. The idea is to encourage thinking of Earth as a single system with a common interest in successful survival.

special-case: Relates to specific example rather than generalized system. Used especially to refer to specific manifestation of generalized concept.

spheric: Rhombic dodecahedron. Fuller's term, derived from the fact that the rhombic dodecahedron is the domain of each sphere in closest packing.

spherical triangle: A curved area bounded by three connected great-circle arcs. The result of interconnecting three points on the surface of a spherical system.

structural system: Triangulated system.

supplementary angles: Angles that add up to 180 degrees.

synergy: Behavior of whole systems not predictable from the behavior of separate parts.

system: Four or more interrelated "events."

tune-in-ability: Possibility of isolating or focusing on specific phenomena as independent systems despite interrelatedness of such phenomena to many other systems. (See Chapter 3.) Boundaries can be constantly redefined, according to the particular goal of an investigation. Also refers to limits of resolution in defining systems.

Universe: Paraphrasing Fuller, Universe is the aggregate of all experience. (See Chapter 1.) The role of the observers, or humanity, is an essential component of the definition, for awareness is a prerequisite to defining and understanding. Experience consists of dynamic, regenerative patterns of energy-perhaps "omnidynamic" would be an appropriate term.

-valent Number of connections or elements, such as number of edges meeting at a vertex, or number of sides of a polygonal face; e.g., "four-valent" vertex of an octahedron, and "three-valent" face (triangle) of the same, or three-valent vertex (and face) of a tetrahedron.

valving: Deliberate channeling of energy and resources in preferred ways.

vector: Represents energy event, consists of magnitude and direction, represented on paper by an arrow with specific length (or frequency) and angular orientation, and used by Fuller instead of "edges" in polyhedra. Vectors also represent relationships between energy events.

vector equilibrium: Fuller's term for the cuboctahedron, in recognition of its equal radial and edge lengths.

vertex: Geometrical term: crossing, convergence of lines or edges, joint, point, polyhedral corner.

wealth: Organized capacity of society to apply generalized principles toward present and future life support.

whole number: In mathematics, positive integer, without fractional part.

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