Veatchite: Structural relationships of the three polytypes

Reference:
▪ Grice, J.D. & Pring, A. (2012): Veatchite: Structural relationships of the three polytypes. American Mineralogist, 97, 489-495.

Abstract:
Crystal structures of the three polytypes of veatchite, Sr2B11O16(OH)5·H2O, are determined by X-ray, single-crystal studies. The polytypes are: veatchite-1A, triclinic space group P1-, with a = 6.6378(6), b = 6.7387(6), c = 20.982(2) Å, α = 87.860(1), β = 82.696(12), γ = 60.476(1)°, V = 809.7(2) Å3; veatchite-1M, monoclinic space group P21, with a = 6.7127(4), b = 20.704(1), c = 6.6272(4) Å, β = 119.209(1)°, V = 805.4(2) Å3; and veatchite-2M, monoclinic space group Cc with a = 6.6070(3), b = 11.7125(5), c = 20.6848(9) Å, β = 91.998(1)°, V = 1599.7(2) Å3. The crystal structures have two layer types with similar fundamental building blocks: A layer FBB = 3Δ2□:<Δ2□>-<2Δ □> and B layer FBB = 3Δ2□,1Δ:<Δ2□>-<2Δ □>,Δ (Grice et al. 1999). Unique in this FBB is the lone polyhedron with triangular coordination, which consists of a neutrally charged [B(OH)3] group. Layering has a directional component and depending on layer sequence the symmetry may be centrosymmetric or non-centrosymmetric. Related layered borate structures, biringuccite, nasinite, gowerite, and volkovskite, are compared. Observations indicate that veatchite-1A is the low-temperature and low-pressure polytype, veatchite-1M the high-temperature polytype, and veatchite-2M the moderate temperature and higher pressure polytype.

Are any of these the same as veatchite-A and/or veatchite-P? Since these are all polytypes, does that mean then that only veatchite is a valid mineral?

The valid species is just one (with two additional polytypes). The original find (Switzer, 1938) is now the veatchite-2M and it is the valid species with type locality Lang, Los Angeles County, California.
The ex p-veatchite is now called polytype veatchite-1M; it was found in the Königshall-Hindenburg potash-salt mine, near Reyershausen, Göttingen, Lower Saxony, Germany, as described by Braitsch (1959) [structure works by Gandymov et al. (1968) and Rastsvetaeva et al. (1993)].
The Emet deposit, Kütahya, Turkey (Kumbasar, 1979) occurrence, ex veatchite-A, is now called polytype veatchite-1A.

thank you Marco!