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five frequency tetrahedron

We associate frequency with rhythm, with phenomena periodic, such as orbitals and rates of vibration. Frequencies define octaves, and as they subdivide, intervals of time, which, paired with the speed of light, defines distance (in light years for example).

How many revolutions around the sun would have happened, before a radioed message to a star system got there? That’s a question in terms of years, given the period of Earth’s circuit of the sun, measured with shadows and such.

We’re all pretty used to a mental picture that looks like a wavy line, an oscilloscope kind of rendering.

However an advancing wave front has a curved surface aspect, such that picturing the frequency in terms of applied grids, suggests the scale of the surface topography.

Are we looking at mountains, or the rugged surface of some single celled organism? The trapezoidal cells of latitude and longitude might have been replaced with hexagons and twelve pentagons. Frequency remains a variable either way and relates to the density of topological features, relative to the shape as a whole.

Using frequency as an input to simple algorithms, we get our power laws, expressing 2D and 3D rates of growth in terms of a governing F for Frequency. The sequence 1, 12, 42, 92, 162… is especially relevant: with the variable frequency cuboctahedron, we get a shape with all edges the same length and with the same number of subdivisions along all 48 of those edges (24 circumferential and 12 pairs of radials, starting with a mental picture of 8 hinge-bonded tetrahedrons with a common apex at the center).

Frequency is an obvious property, in other words, as distinct from angle or shape, likewise obvious.

We have arrived in our CCP-ville, the sphere packing neighborhood from which others may be derived (HCP, BCC, SCP — for those of you who went to college). The CCP’s frequency tells us about the cuboctahedron’s degree of subdivisioning.

XYZ plays all these same games, with analogous cubes and right angles. We become familiar with XYZ scaffolding through our formal schooling.

If these reveries seem disconnected, I suggest finding some connected hypertoons.


Allow me to explain…

Imagine filming as you walk around in a building, with enough doors and choices to keep us guessing as to which route you’ll take next. You’re like a “playhead” through a “spaghetti ball” of like “Google Street views” (but of your own inner building, if that makes any sense).

Yes, I’m talking Memory Palace, but with the added benefit of letting the playback device randomly choose what to play next from a list with smooth segues.

The viewer need not sense any break in the action. A good hypertoon seems seamless.

A classic scenario might be the Jitterbugging of said cuboctahedron, now in stick figure, to an icosahedron, where it pauses to then unfold.

Or perhaps it grows its own dual (dodecahedron) and morphs into a rhombic triacontahedron.

Or it shrinks, to fit inside an octahedron of edges D, what were a second ago the length of its own edges. Between said internal icosahedron of shared face area, and the D-edged octahedron, develop the 24 modules we name S in a namespace ideal for hypertoon sharing (Synergetics).

The playhead wanders from keyframe switchpoint to keyframe switchpoint, but by a variety of “routes” where each “route” is some scenario animation able to join its two endpoints with in-between frames of some action (transformation).

LCDs mounted throughout the coffee shop, airport, shopping mall, waiting room, would give a mind some repose, assuming the theme is gently geometric, not too jarring. Think of a Japanese garden.

The concept of Frequency is highly amenable to the hypertoon treatment.

Lots online.

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