This paper is concerned with commutation classes of reduced words in Weyl groups. It is divided in three sections. In the first, we give a recursive formula for the number of reduced words in a commutation class. In the second, we give a tableau-like description of all the reduced words adapted to a quiver in the case of simply laced root system. In the last, we consider the case of the longest element w 0 for the symmetric group S 5 and illustrate the fact that the set of commutation classes of reduced words of w 0 have nice symmetries and a topological structure.

Two approaches to the synthesis and structure determination of NaZnPO 4 ‚H 2 O, a new open-framework, chiral, hydrated sodium zincophosphate phase, are reported. The ordered, alternating, vertex-sharing ZnO 4 and PO 4 groups in NaZnPO 4 ‚H 2 O form a new framework topology, which includes novel 4-ring "squares" and edge-sharing helixes of 4-rings. The disordered extra-framework species (Na + , H 2 O) are located in pear-shaped cavities (12-ring diameter), interconnected through 8-rings and 6-rings. Crystal data: NaZnPO 4 ‚H 2 O (I), M r ) 201.36, hexagonal, space group P6 1 22 (No. 178), a ) 10.4797(8) Å, c ) 15.089(2) Å, V ) 1435 Å 3 , Z ) 12, R ) 5.99%, R w ) 5.29% (709 observed reflections with I > 3σ(I). NaZnPO 4 •H 2 O (II), M r ) 201.36, hexagonal, space group P6 5 22 (No. 179), a ) 10.412(2) Å, c ) 15.184(2) Å, V ) 1426 Å 3 , Z ) 12, R ) 6.90%, R w ) 8.10% (687 observed reflections with I > 4σ(I).

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The syntheses, representative crystal structures, and some properties of a new family of microporous zincophosphate/arsenate materials, denoted M3Zn4O(XO4)3·nH2O (M = Li, Na, K, Rb, Cs, ...; X = P, As; n = ∼3.5−6), are reported. All these materials are based on a flexible, anionic Zn4O(XO4)3 network built up from vertex-linked tetrahedral ZnO4 and XO4 units. Four ZnO4 units share a vertex, resulting in novel OZn4 centers. The use of mixed four-coordinate anion types (XO4 3-, O2-) results in a number of interesting structural and stability properties. The M3Zn4O(XO4)3·nH2O network contains only pairs of 3-rings (a spiro-5 unit) and 8-rings, and no 4-rings or 6-rings: it encloses roughly spherical cavities connected by a three-dimensional network of 8-ring channels propagating in the orthogonal [100], [010], and [001] directions (cubic unit-cell axes). Extraframework cations and water molecules occupy these cavities and channels. These phases display typical “zeolitic” dehydration/rehydration and ion-exchange reactions with thermal stabilities up to 600 °C, the highest known for this type of open-framework Zn(P/As)O material. The included guest cation (Na, Rb, K, Li, ...) has a crucial effect on crystal structure, by ordering in and modifying the configuration of the intercavity 8-ring channels. The crystal structures of Rb3Zn4O(PO4)3·3.5H2O, K3Zn4O(AsO4)3·4H2O, and Na3Zn4O(PO4)3·6H2O are presented. Crystal data: Rb3Zn4O(PO4)3·3.5H2O, M r = 881.40, cubic, space group F4̄3c (No. 219), a = 15.3423(9) Å, V = 3611.4(6) Å3, Z = 8, R p = 5.12%, R wp = 6.78%, 27 parameters, 1874 data points (X-ray Rietveld refinement). K3Zn4O(AsO4)3·4H2O, M r = 883.63, cubic, space group F4̄3c (No. 219), a = 15.4638(2) Å, V = 3697.9(2) Å3, Z = 8, R p = 8.69%, R wp = 11.42%, 24 parameters, 2124 data points (X-ray Rietveld refinement). Na3Zn4O(PO4)3·6H2O, M r = 739.49, trigonal, space group R3c (No. 161), a = 10.7489(3) Å, α = 60.114(2)°, V = 880.4(4) Å3, Z = 2, R = 2.49%, R w = 2.61%, 180 parameters, 846 observed reflections with I > 3σ(I) (single-crystal data).

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