OCTOPLEX

Interconnected pairs
Interconnected pairs

Here we have several pairs of chps displaying strong ties to each other via simple products, although, in a highly nontrivial fashion. In each case we observe that a pair of chps interact with each other through their verses and ords (I and U arrows) (see Glossary). It's rather interesting that the chps in these pairs are so tightly coupled, despite the fact that individually, they seem so far apart.

In the first product we have chps 24 and 61 which are cross related to their mutual verses 64 and 14 respectively (V-arrows) via the product 1464! The coupling between chps in this pair is further strengthened once we realize that 24 is also the number of polytupes which contain 61 chps! In the second product we notice that 52 is the verses of chp 14 and that 56 is of ord 28 which itself is of ord 14.

In the third product we have only two chps that are tightly connected to each other only through their mutual verses. Chps 24 and 28 have 64 and 88 verses respectively correlated via the product 2464! Additional links can be established by the fact that 88 is of ord 59 which itself has 24 verses. Furthermore, 24th ord is 52, which provides a link with the previous product. Since, 38 is the only other chp with 88 verses, it's interesting to note that 3 × 8 = 24 and 8 × 8 = 64!!!

Finally, the last product illustrates the relationship between 32 and 59 as is nicely illustrated in their product 1888. As mentioned previously, 59 relates to 88, and 32 is of ord 18. As is often the case, this simple link between the two chps serves as a hint which points to a deeper relationship between them. There are 13 EV's from 32 to 59 where the chps and their verses add up to 1416 = 59 × 24!!! and 24 is of ord 13! Moreover, from 32 to 114 there are 44 EV's spanning 1584 = 18 × 88 verses!!! and 44 has 59 verses! The number of EV's in turn points back to the pair 32 and 59 symmetrically, in that from 59 to 114 there are 32 EV's!