A&B QUANTA MODULE HYPERTOONS

A & B QUANTA MODULE HYPERTOONS**



 


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A MODULE

The A module is derived by first subdividing the tetrahedron into quarter tetra from the center of volume to each of its' four triangular faces, then further subdividing these quarter tetra into six irregular tetra (3 left handed ,3 right handed; 3 A+ & 3 A-)


TETRA

24 (12 A+, 12 A-) mods


B MODULE

The B module is derived by first subtracting the A module composed quarter tetra from each octant of the octahedron leaving concave octants to be further subdivided into six irregular tetra (3 left handed, 3 right handed; 3 B+ & 3 B-). So the B module is derived from the OCTA which is comprised of both A and B modules.


OCTA

96 (24 A+, 24 A-,24 B+ ,24 B-) mods


MITE

MITE


-MITE( B-, A-, A+) + MITE ( B+, A+ A- )



The MITE is the MInimum TEtrahedral allspace filler. Each MITE is comprised of one B module and two A modules. MITES are positive or negative according to the B module's sign (+ or -). Positive and negative MITES are outwardly identical in shape and interchangeable in allspace packing. MITES form into COUPLERS as they pack into allspace.


MITE LATTICE


SYTE

+ MITE ( B+, A+, A-) - MITE( B-, A-, A+)


OCTET


The hexahedral octet is 3 sytes, more specifically 3 bites. It is one eighth octahedron (above the equator) and one quarter tetrahedon (below the equator) face bonded. Four OCTETS form a CUBE:

3 +MITES ( B+, A+, A-)3 -MITES( B-, A-, A+)


COUPLER= 8 +and/or- MITES

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

3 orientations

COUPLERS are comprised of eight + and/or - MITES. The COUPLER is the universal MITE aggregate in allspace. 8 MITES can pack one each into the 8 octant domains of the COUPLER; or they can pack crossoctant, each MITE resting in two of the COUPLER'S octant domains; or a combination of the two forms of packing, the hybrid.

OCTANT-PACKED___ CROSSOCTANT-PACKED___ HYBRID_____

24 (8 A+, 8 A-, and a total of 8 B+ and/or B-) mods


HOMOGENOUS COUPLERS
PATTERN RECOGNITION IN ALLSPACE MITEPACKING

RHOMBIC DODECA 1&2

MOVIES

144 (48 A+, 48 A-,24 B+ ,24 B-) mods

in rhombic dodeca

COUPLER LATTICE

COUPLERS pack into Rhombic Dodeca in allspace. One COUPLER can integrate either as whole or half into six possible different Rhombic Dodecahedral domains. There are only four different rhombic dodeca lattices in allspace since rhombic dodeca on either side of the 2 rhombic equators in the COUPLER are part of the same lattice. In the image above,the two yellow RD are in one lattice, the two green RD in another, and the blue and red RD are members of the other two lattices.


ISOSCELES DODECA

The Isosceles Dodeca is sort of a hybrid between the tetra and the cube. Like the tetra (or duotet cube), there are two ways it can nest inside the cube. In the face-matched packing of MITES in allspace , the A modules aggregate into Isosceles Dodeca.

MOVIE

48 (24 A+, 24 A-) mods


RHOMBIC DODECA 3

MOVIE

This Rhombic Dodeca is constructed from the COUPLER which is all negative MITES

( B-, A-, A+).

144 (48 A+, 48 A-, 48 B-) mods

The modules in this construction do not face match as they pack into allspace.


STELLATED RHOMBIC DODECA

MOVIE

The STELLATED RD is 12 COUPLERS or 96 MITES. It is a self-packing allspace filler


A & B MOD DOMAINS IN ALLSPACE

MOVIES

The Isosceles Dodeca and OCTA B-mods are equal volume entities which define the A and B mod domains in allspace packing of the Rhombic Dodecas 1 & 2 above. The Isoceles Dodeca is comprised of 48 A-mods and there are 48 B-mods in the OCTA form at the core of the RD . In RD3, the "48 A-mod" aggregates are not Isosceles Dodeca and show one of the many other aggregate forms that are possible as MITE orientations and signs are varied in the COUPLERS which pack into RD.


CUBE

MOVIE

72 (24 A+, 24 A-,12 B+ ,12 B-) mods


VECTOR EQUILIBRIUM

(CUBOCTAHEDRON)

MOVIE

480 (168 A+, 168 A-,72 B+ ,72 B-) mods


* The term and concept of HYPERTOONS was created by Kirby Urner and relates to the idea of linking from one animated scene to another within and among websites, assimilating information mosaically rather than linearly. See his page On the Concept of Hypertoons for more information.


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*copyright 2002, richard hawkins@gmail.com-this website may be downloaded and reproduced without limitation for private and educational purposes but replication for commercial purposes in whole or in part is prohibited without express permission.

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