- We already have a high-level thread about CRFs (convex regular faced polytopes - mostly polychora only).
- So I wonder whether it might be desirable to consider the concave counterpart as well (CvRF, concave regular faced polytopes)?
- At least those special concave ones, which still are non-self-intersecting (nsiCvRF), i.e. which are kind of potato-shaped, might be of higher interest.

And only if those would have appeared as failing to pass the CRF test, and thus elsewise would no-where be mentioned any more, even so already having stumbled upon.

Two such nsiCvRF examples we already have come accross the last week.

One is pautpen (the penta-augmented truncated pentachoron). There the augmenting external blends are octatuts (ox3xx3oo&#x). The full shape is describable as xo3xx3oo3oA&#zx, where A evaluates as A:x=3:2. The total cell count here is: 5 oct + 20 trip + 20 tricu + 5 tet. It already occured here (even so, at that time, erroniously assuming that it would be convex). It has just a single concave dihedral angle type. That one is at the hexagons between the 2 incident tricues. That one measures 360 deg.-arccos(-11/16) = 226.567 deg. (All other ones are convex.)

The other one is spysp (small pyramidic swirlprism). That one was found already in 2000 by George Olshevsky, but recently, meanwhile having forgotten about it, I stumbled upon it again, cf. here and then esp. here. That one is special in that it has just a single vertex type and just a single cell type. Thus it qualifies as noble polychoron. It has 240 peppies for cells. It has just a single concave dihedral angle type. That one is at the pentagons between the pair of incident pyramids. That one happens to be 216 deg. exactly. (The single other one at the triangles is convex.)

Any additions here?

--- rk