Triangulation of salt systems with barium borate

Quaternary Reciprocal Systems with the Inner Diagonals: Variants of Polyhedration

“…And at last the simplexes list is formed. The system K,Ca,Na||NO 3 ,Cl has two binary D 1 =KCl⋅CaCl 2 , D 2 =KNO 3 ⋅2Ca(NO 3 ) 2 and a ternary D 3 =KNO 3 ⋅2Ca(NO 3 ) 2 ⋅KCl [6] compounds (Fig. 1).…”

“…Algorithm can not divide the polyhedron with inner points [2,6,7] and with competition of inner diagonals and planes. For instance, two variants of polyhedration in the quaternary reciprocal system with a binary compound x 7 in the ternary system x 4 x 5 x 6 (Fig.…”

“…As an original trigonal prism of a quaternary reciprocal system has V 0 =6 vertexes, J E =9 edges and five faces (two triangles and three squares), then its edges are divided by V E points to J E =9+V E segments (simple binary systems). Numbers of diagonals (J F ) and simplexes (S F ) on faces, inner 2D planes-simplexes (S I ) and 3D tetrahedronssimplexes (T) are expressed [6,7] as):…”

Search for internal diagonals in polyhedration of reciprocal systems by the algorithm for topological correction of lists of simplexes of different dimensions

“…The end result of polyhe dration should satisfy the formulas relating the num bers of graph vertices and links between them with the numbers of 1D (internal diagonals), 2D (secant planes), and 3D (tetrahedra) simplexes. For a quater nary reciprocal system, these quantities are related by the expressions [6] S I = 2 + V E + V F -2V I + 2L I , (1) T = 3 + V E + V F -V I + L I , where V E , V F , and V I are the numbers of binary, ter nary, and quaternary compounds, respectively, which are represented by points on edges and faces of the polyhedron and inside it, respectively; L E , L F , and L I are the numbers of edges (or their fragments-binary systems without compounds), diagonals on faces, and internal diagonals, respectively; S F and S I are the numbers of 2D simplexes (triangles) on faces and inside the prism, respectively; and T is the number of 3D simplexes (tetrahedra).…”