16 Mar
2018
16 Mar
'18
12:17 p.m.
Hi Rich: I'm not SUre that I understand your dimensions and trees. "All directions": is this in 3-space or 4-space? Is there any relation to the 24 Hurwitz quaternions? At 04:47 PM 3/15/2018, rcs@xmission.com wrote:
It's a different covering structure, but the products of 2+-i, 2+-j, 2+-k generate a dense covering of all directions. (Divide the generators by sqrt5 to get units.) Except for the cancellations of conjugates, like (2+i)(2-i) = 5, every product is different. You can view the pre-space as a tree with node degree 5, except the root is degree 6. The post-space is points on the unit quaternion sphere. I assume the covering is near uniform, but haven't seen the confirming theorem.