In the title compound, C(19)H(20)N(2)O(6), the pyrone and pyran rings adopt envelope conformations with the same common C atom as the flap, the dihedral angle between the planes of the remaining ring atoms being 68.27 (4)°. The planar atoms of the pyran ring and the diaza-cyclic ring are almost coplanar, the dihedral angle between their mean planes being 3.29 (7)°. Moreover, the planar atoms of...

The title compound, C16H12N2O8, exhibits two near-planar aromatic ester groups with ar-yl-ester dihedral angles of 2.1 (2) and 4.2 (3)°. The dihedral angle between the aromatic rings is 58.0 (1)°. The two nitro groups are tilted slightly from the plane of the aromatic rings, making dihedral angles of 14.1 (1) and 8.2 (2)°. In the crystal, mol-ecules are connected by weak C-H⋯O inter-actions, fo...

In the title compound, C16H10Cl2N4O4, the pyrazine rings make dihedral angles of 67.82 (9) and 75.91 (9)° with the benzene ring, while the dihedral angle between the pyrazine rings is 44.69 (10)°. The meth-oxy-carbonyl group makes a dihedral angle of 16.82 (8)° with the benzene ring to which it is attached. In the crystal, C-H⋯O hydrogen bonds link the mol-ecules, forming chains running along t...

In the title compound, C(21)H(30)N(2)O(5)S, the plane of the dimeth-yl-thio-carbamic group makes a dihedral angle of 78.41 (7)° with the central benzene ring. One of the carbonyl groups in the α,β-unsaturated malonate side chain makes a dihedral angle of 8.73 (10)° with the central benzene ring, while the other carbonyl group makes a dihedral angle of 81.52 (8)°.

In the title compound, C(23)H(18)O(3), the dihedral angle between the two naphthalene ring systems is 78.02 (3)°. The bridging carbonyl C-C(=O)-C plane makes a dihedral angle of 70.56 (5)° with the naphthalene ring system in the 2,7-dimeth-oxy-naphthalene moiety and a dihedral angle of 11.53 (5)° with the naphthalene ring system in the naphthoyl group. In the crystal, adjacent mol-ecules are li...

In this paper, we investigate $q$-Varchenko matrices for some hyperplane arrangements with symmetry in two and three dimensions, prove that they have a Smith normal form over $\mathbb Z[q]$. particular, examine the arrangement regular $n$-gon plane dihedral model space Platonic polyhedra. each case, matrix associated has Z[q]$ realize their congruent transformation as well.

The title compound, C(10)H(12)N(4)O(2), was prepared as an inter-mediate for the synthesis of metamitron. The benzene ring plane forms dihedral angles of 66.0 (1) and 3.5 (5)° with the hydrazine plane and the acetyl-imino plane, respectively. The crystal structure involves inter-molecular N-H⋯O hydrogen bonds.

In the title compound, C(20)H(12)ClFO(2)S, the O atom and the phenyl ring of the phenyl-sulfinyl substituent lie on opposite sides of the plane of the benzofuran fragment; the phenyl ring is almost perpendicular to this plane [82.44 (5)°]. The 4-fluoro-phenyl ring is rotated out of the benzofuran plane, making a dihedral angle of 20.83 (6)°.

In the title compound, C20H18O7, the dioxolane ring adopts an envelope conformation with the dimethyl-substituted C atom as the flap, and its mean plane makes a dihedral angle of 73.25 (2)° with the pyran ring mean plane. The furan ring makes dihedral angles of 67.43 (12) and 6.20 (11)° with the mean plane of the dioxolane and pyran rings, respectively. The O atom attached to the pyran ring dev...