987.211 In Symmetry #1 and Cleavage #1 three great circlesthe lines in Figs. 987.210Athrough F are successively and cleavingly spun by using the midpoints of each of the tetrahedron’s six edges as the six poles of three intersymmetrical axes of spinning to fractionate the primitive tetrahedron, first into the 12 equi-vector-edged octa, eight Eighth-octa (each of 16-tetra-volume), and four regular tetra (each of 1-tetravolume).
Figure 35: Fig. 987.132F Net Diagram of Angles and Edges for Basic Disequilibrium 120 LCD Triangle: This is a detail of the basic spherical triangle shown shaded in Fig.Figure 35: Fig. 987.132F Net Diagram of Angles and Edges for Basic Disequilibrium 120 LCD Triangle: This is a detail of the basic spherical triangle shown shaded in Fig.
987.132E and at Fig. 901.03. It is the key to the trigonometric tables for the spherical central angles, the spherical face angles, the planar edge lengths, and the planar face angles presented at Table 987.132G.
987.212A simple example of Symmetry #1 appears at Fig. 835.11. Cleavage #1 is illustrated at Fig. 987.210E.
987.213 Figs. 987.210A-E demonstrate Cleavage #1 in the following sequences: (1) The red great circling cleaves the tetrahedron in to two asymmetric but identically formed and identically volumed “chef’s hat” halves of the initial primitive tetrahedron (Fig. 987.210A).(2) The blue gr eat circling cleavage of each of the two “chef’s hat” halves divides them into four identically formed and identically volumed “iceberg” asymmetrical quarterings of the initial primitive tetrahedron (Fig. 987.210B).(3) The yellow gr eat circling cleavage of the four “icebergs” into two conformal types of equi-volumed one-Eighthings of the initial primitive tetrahedronfour of these one-Eighthings being regular tetra of half the vector-edge-length of the origi nal tetra and four of these one-Eighthings being asymmetrical tetrahedra quarter octa with five of their six edges having a length of the unit vector = 1 and the sixth edge having a length of V2=1.414214. (Fig. 987.210C.)
image Fig. *987.137B Composite of Primary and Secondary Vector Equilibrium Great Circle Sets:*This is a black-and-white version of color plate 16. The Basic Equilibrium 48LCDtriangle as presented at Fig. 453.01 appears here shaded in the spherical grid. In this composite vector equilibrium spherical matrix all the 25 primary gr eat circles appear together with the four sets of secondary great circles. (The f our sets of secondary vector equilibrium great circles are shown successively at color plates 12–15.) Fig. 987.137C Net Diagram of Angles and Edges for Basic E q uilibrium 48LCDTriangle in Vector Equilibrium Grid: This is a coded detail of t he basic spherical triangle shown shaded in Fig. 987.137B and at Fig. 453.01. It is the key to the trigonometry tables for the spherical central angles, the spher ical face angles, the planar edge lengths, and the planar face angles presented a t Table 987.137D. (The drawing shows the spherical phase: angle and edge ratios are given for both spherical and planar phases.) imageimageimageimageimageimageF.