Classifying the segmentochora

Discussion of known convex regular-faced polytopes, including the Johnson solids in 3D, and higher dimensions; and the discovery of new ones.

Re: Classifying the segmentochora

Postby wendy » Sun Mar 08, 2015 11:04 am

My guess is that there is a fold in Richard's new lace-tower, unless exactly one of the figures contains the centre of the sphere.
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the dream we dream together is reality.
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Re: Classifying the segmentochora

Postby 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
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Re: Classifying the segmentochora

Postby wendy » Sun Mar 08, 2015 11:18 pm

Yes, i figured that out last night.
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Re: Classifying the segmentochora

Postby Klitzing » Thu Mar 12, 2015 12:44 pm

In an other forum I recently made up for a challenge of naming that recent find of mine, i.e. that xooo5oxo5/2oox&#xt.
Hedrondude there already replied (just for reference thus being mentioned here too):
Hedrondude wrote:Hmm, that one might be a bit tough to name. How about something like stellidodecahedral rectibicupola - short name -
Sidrebcu.
--- rk
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