by Klitzing » Sun Mar 08, 2015 12:10 pm
Hi Wendy,
its definitely a straight tower, not a fold. I've already checked that.
The circumradius of sissid is sqrt((5-sqrt(5))/8) = 0.587785.
The circumradius of did is 1.
The circumradius of gad is sqrt((5+sqrt(5))/8) = 0.951057.
Given the lacing edge as being 1, one calculates the 4D circumradius of either segmentochoron sissid||did resp. gad||did as sqrt((8+2sqrt(5))/11) = 1.064815.
The respective heights likewise become calculated as well:
The height of sissid||did is sqrt((5sqrt(5)-9)/8) = 0.522056.
The height of gad||did is sqrt((3sqrt(5)-1)/8) = 0.844704.
Now take a circle with radius being the 4D circumradius and look for the angle above or below the equator where the paralel (lattitude) of these given 3D circumradii can be placed.
Thus for sissid we derive possible angles of +/-56.495211 degrees, corresponding to heights above/below the equator of +/-0.887885.
For did we get the angles of +/-20.093994 degrees, corresponding to heights above/below of +/-0.365829.
And for gad we derive likewise the values +/-26.726125 degrees, resp. heights +/-0.478875.
Putting that together with the former segmentochoral heights, we see that
sissid has to be, say, at level +0.887885, then
did at level +0.365829, and finally
gad at level -0.478875.
--- rk