A simplex is always defined in an 
-dimensional (Cartesian) space.
From both a conceptual and implementation view, it is advantageous to
treat the dependent variables of a field like additional spatial
coordinates. This means, e.g., that a scalar value that is defined
on a two-dimensional triangular grid (this corresponds to a scalar
function which depends on two variables 
) is
represented by a set of 2-simplexes (triangles) in
three-dimensional space where the
third coordinate 
is assigned the scalar value of the dependent
variable (
).
The obtained quasi-three-dimensional surface object is of course nothing
essentially new. The really important aspect, however, is that no
semantics besides the purely geometrical meaning
is any longer associated with the additional coordinates.
This idea of generalized coordinates has a significant impact on the utility and generality of the operations and increases the resulting architectural flexibility of the system. For example, it is impossible for a given module to distinguish between a simplex in ``real four-dimensional space'' and a simplex in three-dimensional space on which one scalar value is defined. And from a rigorous point of view, there should be no restriction or preference as to whether a given operation (like cutting, slicing, or projection) can be applied to spatial or non-spatial coordinates.
From an implementation point of view, the more specialized operations (like the flowline module) have to make certain additional assumptions about the semantics of the generalized coordinates. Some other implemented modules are restricted (by the lack of implementation rigorousity) to certain allowed subsets of general simplex data. This is, however, strictly an implementation insufficiency and not an architectural limitation.
This generalization of coordinates leads to higher-dimensional coordinate tuples. For all practical purposes within VISTA, the maximum point dimension is six, which is sufficient to represent a three-dimensional vector field in three-dimensional space.