986.410 T Quanta Module |
Fig. 986.411A Fig. 986.411B Fig. 986.411C |
986.411 The respective 12 and 30 pentahedra OABAB of the rhombic dodecahedron and the triacontahedron may be symmetrically subdivided into four right-angled tetrahedra ABCO, the point C being surrounded by three right angles ABC, BCO, and ACO. Right- angle ACB is on the surface of the rhombic-hedra system and forms the face of the tetrahedron ABCO, while right angles BCO and ACO are internal to the rhombic-hedra system and from two of the three internal sides of the tetrahedron ABCO. The rhombic dodecahedron consists of 48 identical tetrahedral modules designated ABCO^{d}. The triacontahedron consists of 120 (60 positive and 60 negative) identical tetrahedral modules designated ABCO^{t}, for which tetrahedron ABCO^{t} we also introduce the name T Quanta Module. |
Fig. 986.413 |
986.413
The rhombic dodecahedron has a tetravolume of 6, wherefore
each of its 48
identical, internal, asymmetric, component tetrahedra
ABCO^{d} has a regular tetravolume of
6/48 = 1/8 The regular tetrahedron consists of 24 quanta
modules (be they A, B, C, D,^{5} *
or T Quanta Modules; therefore ABCO^{d}, having l/8-tetravolume,
also equals three quanta
modules. (See Fig.
986.413.)
(Footnote 5: C Quanta Modules and D Quanta Modules are added to the A and B Quanta Modules to compose the regular tetrahedron as shown in drawing B of Fig. 923.10.) |
986.416 1 A Module = 1 B Module = 1 C Module = 1 D Module = 1 T Module = any one of the unit quanta modules of which all the hierarchy of concentric, symmetrical polyhedra of the VE family are rationally comprised. (See Sec. 910). |
Fig. 986.419 |
986.419 The 120 T Quanta Modules of the rhombic triacontahedron can be grouped in two different ways to produce two different sets of 60 tetrahedra each: the 60 BAAO tetrahedra and the 60 BBAO tetrahedra. But rhombic triacontahedra are not allspace-filling polyhedra. (See Fig. 986.419.) |
Next Section: 986.420 |