It must be a Sunday; else why would I be using Geomags to duplicate this drawing in 3D?
Still, the process may have had its rewards. I did notice, for example, something -- which may or may not have been known to BlueJayWay (but who did NOT draw lines to connect the appropriate dots) -- is that the 3 and 15 connect to mid-points in the blue and red tetrahedrons in the following manner:
3 + 7 + 17 = 27
3 + 11 + 13 = 27
and
15 + 11 + 1 = 27
15 + 7 + 5 = 27
(Each mid point is actually combined twice, with 1 + 17, 5 + 13 being combined with 9 to, of course, yield 27.)
As already pointed out: 3 + 8 + 16 = 27; 15 + 2 + 10 = 27; and 3 + 15 + 9 = 27...
Therefore... not counting the links between the green and blue/red tetrahedrons, both 3 and 15 connect in three "directions" via the common midpoints (just like the vertices in the blue and red tetrahedrons) to yield 27, and can therefore also be viewed as a part of their respective ("extra-dimensional") green tetrahedrons. Meanwhile, both the "green tetrahedrons" are intermingled with the red and blue tetrahedrons.
Accordingly, it might appear that this yields 4 tetrahedrons with possibly 9 as a focal point.
Admittedly, one could also add 8 (BV) + 6 (RV) + 13 (MP) to yield 27... as well as 12 (BV) + 16 (RV) + 5 (MP) to yield 27... but then again there are roughly eight combinations for any given number (nine if zero is included).
BTW, there are four (and only four) "doubles": 10 + 17, 11 + 15, 12 + 15, and 13 + 14... all of which add to 27. But with only four "sides", they are insufficient for a fifth tetrahedron (even including "0" in the mixes). On the other hand, BlueJayWay's suggested additional imaginary number might be 18, that would combine with 9 for the fifth side of a fifth tetrahedron.
Obviously, my college minor in addition is paying off. Now if I just figure out what it
means!
