## 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

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.
The dream you dream alone is only a dream
the dream we dream together is reality.

wendy
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### Re: Classifying the segmentochora

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.

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

--- rk
Klitzing
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### Re: Classifying the segmentochora

Yes, i figured that out last night.
The dream you dream alone is only a dream
the dream we dream together is reality.

wendy
Pentonian

Posts: 1814
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia

### Re: Classifying the segmentochora

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
Klitzing
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