wondering how octagons fit just so:
i'll make a template octagon object
as i've already done with a hexagon
and i could start from scratch, but
i want to maintain some continuity
so, i'll just import that object
and make an octagon out of that


 
overhead, rendered wireframe composite
of the hexagonal object group i made...
full, selected red outline (below right)
...and a tight zoom of the far left corner
(below, far left) showing individual objects






so, in making an octagon from my hexagon:
using the same objects i have, already...
using the same textures, so they'll match
(and i can always change the color later)



my hexagon object group
measures 41 x 35.64 units
...discounting the thickess
of the sides and corners...
which are each 1 unit thick
(twice one half, each side)
point to point, it measures
40 x 34.64 = 2 (20 x 17.32)





i have it further grouped by sides and corners
to change those categorically, anytime (above)
but i'll just ungroup this whole thing (below)
...keeping only the top side and its 2 corners
...deleting the rest (they'll only confuse me)




so... just keeping the
2 corners and one side
from the hex object...



group those together, duplicate... and
put the new one negative Z from center
i now have 2 identical sides (as groups)
opposite center, positive and negative Z
each with 2 rounded corners (cylinders)...
and when grouped, together that's centered





what remains, grouped together or not
...their mutual Z coordinate is 17.32
 ...that is: up, or north, from center
(as: the top side of a hex centered)







now, duplicate that group and rotate it 90°
group both of those, duplicate n rotate 45°
so, now i have eight sides, all centered...
 and with twice as many corners as i need...
i'll delete the extras later, when i'm done






here's my octagon sides... but too long...
first, ungroup all of this... just once...
not to first level, of 8 individual groups
...or zero level, of individual objects...
...i want 4 pairs of sides, at 90° and 45°
 select just one group and reduce its width
(below) until dots match top line of 17.32



the side's width remains one unit
only its length is being adjusted
 ...and it's still proportional...
with the dots being squashed here
what i'm aiming for is the center





and then there's this:
little freaky thing...
i almost didn't notice
 ...see, it started at 21
...and i just reduced it
a couple units at a time
 ...it landed right on it
...at an exact even unit
so that got my attention
 cuz i started with a hex
20 proportioned >> 17.32
 the line groups measure:
...15 units wide x 35.64
 and the dot's new coords
...close: (7.20, 17.30)
but my target is: 17.32






so that's interesting
...stumbled upon some
...basic, fundamental
...geometry, there...
 proportional to the hex sides of: 20 x 1
but, with an additional 1 unit (2 halfs)
(for the radii, of the cylinder corners)
the actual side, point to point is 14.29





...and... just noticing: it's
close enough at an even 15...
 which, in half, is 7.5
over 10 is 0.75 or 3/4
 but that's the whole group...
see, the program is computing
the proportions automatically
 ...notice the polygon's
sides are still true...
16 sided, right edge on



...the dot is squashed to 0.71
which, i can only assume to be
rounded up from .707 sine wave
or anyways, close enough again





so, back to the group, up from 15
stretching the group out to 15.07
puts the dot right on the line...
so, that would probably be 0.0707




