Though the subdivision of the grid is mutable from house to house - and often from
floor to floor - there appears to be one more restriction imposed by Eisenman. That
is the grid in all of these houses (and on each floor) has a reflective (i.e. bilateral)
symmetry composed along a diagonal axis from one corner of the grid to the opposite
corner. And of course, if you construct a reflective symmetry like this along a diagonal
axis and then subdivide an overlaid grid you are left with what Eisenman often
describes as his main composition element - the 'el' shape. The exceptions are: the
ground floor of House II where the reflective symmetry occurs parallel to the plane of the grid in one-dimension; and House IV which is perfectly symmetrical in that it
possesses reflective, rotational, translative and glide reflective symmetries (Stewart,
1992). House X shows a greater complexity in that the reflective symmetry of the
plan is rotated on the 1st floor by 90˚ in relation to the floors above and below it. In
answering the question we started with, i.e. how are these houses composed, we
have uncovered what we would suggest are some interesting and quite elegant rules.
Square grid composition is constant - subdivision of the grid is mutable. All elements
are in some predetermined angular relationship (usually parallel or perpendicular)
with other elements. Each grid composition possesses at least one reflective symmetry,
usually along a diagonal axis from corner to corner of the grid. However, let us be
clear - this is not an objective or analytical design process. The rules are set but it is
Eisenman making the design decisions. The variation from house to house arises
from the mutable aspects - the grid subdivision, the rotation of the reflective
symmetries along whichever axis, the difference in scale, and the introduction of
‘random objects’ - not from the rules themselves.