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The BASKET modules

The Synergetics Particle Zoo

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Particle Zoo

Particle in the sense of “Partition”
Partition: divider between Inside and Outside
Container: has an inside where it contains “content”
B, E, A, S, T: partitions in the Synergetics namespace, K added later
Zoo: borrowing from particle physics (“whatsons”)

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Lane, Henry C.: Study of Shelter Logistics for Marine Corps Aviation, A. Portland: synchronofile.com, 2008.

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slide from Graph Theory slide deck

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Edges a - f; A = a²… F = f²

Four corners in Quadray Coordinates

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Figure 913.01

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Figure 916.01

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Plane Net: A

Plane Net: B

A,B = 1/24

A & B Modules

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MITE = (A+)(A-)(B-) = (B+)(A+)(A-)

by Richard Hawkins

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Synergetics vocab:

MITE (AAB or BAA)

RITE (SYTE)

BITE (SYTE)

½ RITE

¼ RITE

SYTE = 2 MITEs

A,B in BEAST

RITE

MITE

BITE

½ RITE

¼ RITE

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Fig 950.12 Three Self-Packing, Allspace-Filling Irregular Tetrahedra

MITE

RITE

BITE

(labels added)

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T & E Modules

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SuperRT: 20 √(9/8) = ~21.21 (CO * S3) ¹

RT: 7.5 (shares vertices with RD 6)

RT(E): 5+ (120 E modules), radius = 1

RT(T): 5 (120 T modules), radius = ~.99948 ²

¹ Super RT: = RT(E) * Φ³

² (2/3)^(1/3) * (Φ / √2) = 0.9994833322623434400464...

RHOMBIC TRIACONTAHEDRA OF VARIOUS SIZES

(in tetravolumes)

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(2/3)^(1/3) * (Φ / √2) = 0.9994833322623434400464...

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120 E RT; Vol. 5.007758; R = 1

120 T RT; Vol. 5; R = 0.9994

Red IVM Ball Pokes Through Marble RT 5’s Faces

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Cube 24

RT 7.5

RD 6

Octa 4

Cube 3

RT5 scaled up by 3/2

by DBK using vZome

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By Casey House, Syn-U

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Sφ³ + Sφ⁶= 1 (unit tetravolume)

Volume-preserving morphing shapes

“page on a slider” slice vs “apex + frustum” slice

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_{B volume = 0.039283710065919306911}

_{E volume = 0.039344662916631616068}

_{A volume = 0.039283710065919306911}

_{S volume = 0.042506519122975187196}

_{T volume = 0.039283710065919306911}

_{B volume = 0.041666666666666666667}

_{E volume = 0.041731316927773654299}

_{A volume = 0.041666666666666666667}

_{S volume = 0.045084971874737120511}

_{T volume = 0.041666666666666666667}

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E

B

A

S

T

XYZ

IVM

Syn3

1/Syn3

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(2.5 CUBOCTA)(E2S)² = (~2.92 ICOSA)

OCTA: 4

ICOSA: ~2.917960675

CUBOCTA: 2.5

sfactor = E2S = ~1.08036302695

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From Synergetics

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sfactor = E2S = ~1.08036302695

1/sfactor = S2E = ~0.92561479391

CUBOCTA (S2E) = ICOSA

CUBOCTA: 20

ICOSA: ~18.512295868

OCTA: 4

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Frame

1. Marble IVM ball

2. Marble IVM ball + Red Octa (4)

3. Red Octa (4) + Cyan IW (60S + 20s3)

4. Red Octa (4) + Purple RT (60S + 60s3) + Brown PD (48S + 24s3)

5. Red Octa (4) faces filled in, above shapes poking through

6. Purple RT (60S + 60s3) + Blue RD (48S + 48s3), shared vertices

7. Blue RD (48S + 48s3) + Brown PD (48S + 24s3) + Green Cube (24S + 24s3)

8. Marble IVM ball + Red Octa (4) + Purple RT (7.5) + Blue RD (6)

9. Marble IVM ball + Purple RT (7.5) + Blue RD (6), shared vertices

... and repeat

All volumes in tetravolumes (unit edge = Red Octa edge)

S from BEAST:

S = 1/(2 * PHI * PHI * PHI * PHI * PHI)

s3 = S * (1/(PHI * PHI * PHI)) i.e. "S phi down"

Notes:

Given any Icosa, an RT follows with Icosa as long face diagonals, dual PD (pentagonal dodeca) as short face diagonals.

Icosa Within (IW), faces flush to Octa (4), defines a corresponding RT (60S + 60s3) and PD (48S + 24s3)

The corresponding RT defines an RD with shared vertices with volume ratio RT/RD = 5/4

The RD (6) with edges scaled down by 2 / (PHI * PHI) is the RD (48S + 48s3) meshed with the RT (60S + 60s3)

Green Cube (24S + 24s3) + 24S = Brown PD (48S + 24s3) i.e. each "tent" on a cube face is 4S

Cyan IW (60S + 20s3) + 24S = Red Octa (4) i.e. same difference of 24S

Source code: test17

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Frames:

1. Marble IVM ball + Red Octa (4)

2. SuperRT (15*rt2(2)) + Marble IVM ball + Red Octa (4)

3. RT_E (120 Emods) + Marble IVM ball + Red Octa (4)

4. RT_T (5) + Marble IVM ball + Red Octa (4)

5. RT (60S + 60s3) + IW + Marble IVM ball + Red Octa (4)

6. RT_K (7.5) + Blue RD (6) + Red Octa (4)

7. SuperRT (15*sqrt(2)) + Marble IVM ball + Icosa(20*1/sfactor) + PD (3 * rt2(2) * (PHI**2 + 1))

... and repeat

Key:

sfactor = S/E where S, E in BASKET

RTs in order of appearance:

Frames:

2. SuperRT (21.21..) = cage for Icosa (18.51...) + dual PD (15.35..)

3. RT_E = RT of 120 E mods (volume 5.0077..), faces tangent to IVM ball

4. RT_T = RT of 120 T mods (volume 5) -- virtually indistinguishable from RT_E

5. RT (60S + 60s3) cage for IcosaWithin (IW) with faces flush to Octa (4)

6. RT_K = RT of 120 K mods (volume 7.5) shares verts with RD (6)

7. SuperRT (15*rt2(2)) same as in 2.

CO (20) --> Icosa (20 * 1/sfactor) is the first step in the Jitterbug Transformation

CH: Concentric Hierarchy

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Synergetics:

where BASKET

meets STEAM

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Tractatus

Thank you to friends and collaborators