This was tricky! The key is to use very carefully placed construction lines. I also tried to get maximum quads, but did end up with one triangle per arm.
The image was an accident. I had Arctic viewport mode and then did a reflection E-map. Cool effect!
Hey @schultzeworks , If you use RadiateFind on a SubDTorus with eight faces around the torus, you will get the radial symmetry without having to do the angle math 
Personally I only use RadiateFind starting with a SubD torus or cylinder.
The final step to get the center filled would be to RemoveSymmetry > Delete the interior face loops and use Fill on the holes…
I tried the radiate find and got a mangled mess. I will DEFINITELY try again with your most excellent suggestion. Thanks!
The torus was genius. Keep the hole open for simplicity, then close it when done. Amazing.
My mangling was very likely due to geometry at the center. That seems to cause the issues I am seeing.
I see what you did there. Very nice!
However, by eliminating the triangle, you increased the complexity of the arms. Note that my arms are 1 x 1 quads so that I can purposely keep them clean and siimple. Four faces per section.
Your arms are 2 x 1, with an extra edge as a center line. Six faces per section.
I think ther might be a way to do both.
Brian’s Topology layout is exactly how I’d lay this out.
Your result is good, but I’d always challenge every user to play the game of “how many edges can I delete before the model falls apart”
then simply add the last one you deleted back in.
this process will keep you honest and avoid having more edges than you absolutely need, which keeps your parts smooth and easily editable.
I want symmetry on a single arm.
you can reflect a single arm then radiate that reflected arm… now this is a single part not a true octopus, but you could get it close then simply bridge or stitch the parts when you are happy with the individual shape.
Ok, how about one more octopus? I’m going for simplicity and quads.
We may have achieved the elusive Octopi singularity.
@theoutside @BrianJ @martinsiegrist
More pics. I did a little extra work to make the character complete and rendered.
Hello Dave
I don’t know if it exists in Rhino but I made a tool to change the radial symmetry. So I can work on one part and apply to the whole and change the number if needed.
these are great Dave!
Looks like you are having fun- (Don’t tell anyone)
Yes. Yes I am. 
