First of all, these values of student91 would reflect the required angles of the trips attached to the 4 polar triangles. The other ones would ask for the third dihedral angle, not mentioned in his post.

The required value of about 73 degrees at a square can be matched easily by several small attaching cells. But the required value of 58 cannot be matched by any cell!

This is simply because the "sharpest" segmentochoron with one trip base and without a retrograde top base clearly is the trippy = pt || trip. And that one already has dihedral angles of

• at {4} between squippy and trip: arccos(sqrt[1/6]) = 65.905157°

At least for straight segmentochora. If you look at sheered segmentochora (thus asking for a dimensional degenerate top base!) you might be more lucky.

But the case of a point for top base already is done by trippy. The case of a line segment there is done either by bidrap or by tepe (depending on relative orientation). And the case of a triangle for opposing base is done by triddip resp. traf = K-4.6 (depending on relative gyration). - Therin only bidrap implements some shift of the degenerate base. But none of these would bow to the above requirements.

This then concludes the proof that a snadow prism cannot be augmented.

--- rk