986.560 Surprise Nestability of Minimod T into Maximod T

986.561 The 6+10+15 = 31 great circles of icosahedral symmetries (Fig. 901.03) produce the spherical-surface right triangle AC"B; CAB is sub-divisible into four spherical right triangles CDA, CDE, DFE, and EFB. Since there are 120 CAB triangles, there are 480 subdivision-right-surface triangles. Among these subdivision-right triangles there are two back-to-back 90-degree surface angles at DCDA and CDEand two back-to-back 90-degree surface angles at FCFE and EFB. The surface chord DE of the central angle DOE is identical in magnitude to the surface chord EB of the central angle EOB, both being 13.28 degrees of circular azimuth. Surface chord FB of central angle FOB and surface chord AD of central angle AOD are identical in magnitude, both being 10.8 degrees azimuth. In the same manner we find that surface chord EF of central angle EOF constitutes the mutual edge of the two surface right triangles CFE and BFE, the central-angle magnitude of EOF being 7.77 degrees azimuth. Likewise, the central angles COA and COF of the surface chords CA and CF are of the same magnitude, 20.9 degrees. All the above data suggest a surprising possibility: that the small corner triangle ACB itself can be folded on its three internal chord lines CD, CE, and EF, while joining its two edges AC and CF, which are of equal magnitude, having central angles of 20.9 degrees. This folding and joining of F to A and ofB to D cancels out the congruent-letter identities F and D to produce the tetrahedron ABEC. (See Fig. 986.561.)

986.562 We find to our surprise that this little flange-foldable tetrahedron is an identically angled miniature of the T Quanta Module OABC‘ and that it can fit elegantly into the identically angled space terminating at O within the inner reaches of vacant OABC, with the miniature tetrahedron’s comer C becoming congruent with the system’s center O. The volume of the Minimod T is approximately Vis that of the Maximod T Quanta Module or of the A or B Modules.