I also found some more members of the prismatic honeycombs' regiments. The ones I found involve blending the honeycombs with polygon-apeirogon duoprisms, but I suspect some prismatic honeycombs have many other regiment members yet to be discovered.
First, prismatic honeycombs made from tilings containing n-gons can be blended with n-gonal apeirogonal duoprisms. However, no more than one of them can blend around each lateral edge of a prism (corresponding to a vertex in the original tiling). To find blendings that are uniform honeycombs, we need to find ways to color one type of face of a uniform tiling so that
exactly one face around each vertex is colored and
the tiling is still vertex transitive under the coloring.
I know of several ways to do this:
Blend 1/4 of the squares in squat (already listed as quabassiph)
Blend 1/4 of the squares in squat, but shifted on alternate layers (a new member of the chon regiment!):
Blend 1/6 of the triangles in trat (e.g. the blue triangles in this picture of s3s3s3*a:
https://commons.wikimedia.org/wiki/File ... 121314.png):
Blend 1/3 of the hexagons in hexat
Blend half the triangles in that
Blend the squares in tosquat
Blend half the octagons in tosquat
Blend the squares in quitsquat
Blend half the octagons in quitsquat
Blend the triangles in toxat
Blend the triangles in quothat
Blend the triangles in rothat
Blend the hexagons in rothat
Blend the triangles in shothat
Blend the hexagons in shothat
Blend the triangles in ghothat
Blend the hexagons in ghothat
Blend the triangles in qrothat
Blend the hexagons in qrothat
Blend the squares in sossa
Note: This and the next one are wild honeycombs because the pseudo-apeirogons in the middle of squats in the sossa pseudoprismatic honeycomb are intercepted by the ridge between two vertical azips.
Also, if we try to blend the apeirogons in any of these tilings' pseudoprismatic honeycombs, we end up with subdivisions with vertical rows of apeirogons instead of squats, so they would go in Category B (subdivisions) , not here.
Blend the squares in gossa
Blend the hexagons in shaha
Blend the hexagons in ghaha
Blend the squares in grothat
Blend the hexagons in grothat
Blend the dodecagons in grothat
Blend the octagons in satsa
Blend the octagrams in satsa
(If we blend the apeirogons it will just lead to a subdivided version of the satsa prismatic honeycomb, which will go into category B as before)
Blend the dodecagons in hatha
Blend the dodecagrams in hatha
Blend the octagons in qrasquit
Blend the octagrams in qrasquit
Blend the squares in qrasquit
Blend the dodecagons in thotithit
Blend the dodecagrams in thotithit
Blend the hexagons in thotithit
Blend the squares in quitothit
Blend the hexagons in quitothit
Blend the dodecagrams in quitothit
Blend half the squares in snasquat
Blend half the squares in rasisquat
Blend half the squares in snassa
Blend the non-snub triangles in snathat
Blend the hexagons in snathat
There may well be other blendings with snubs that I haven't investigated yet.
Each of these 43 selections of polygons from tilings corresponds to two honeycombs: one where the n-gonal apeirogonal duoprisms blend with the tiling's prismatic honeycomb, and another where the duoprisms are blended with tiling prisms which take up half the layers. Thus we have a total of 86 new uniform honeycombs.
Climbing method and elemental naming scheme are good.