For architectural purposes we are not interested
in a thin mathematical surface, but we want a building structure
with some volume, so we need to consider prismatic structures
of substantial thickness with some built-in twist.
For our initial analysis, we thus give the band a rectangular
cross section and we look for single right-angled shapes
that conserve the essence of a Moebius strip.
Thus if we follow along a face of that prismatic ring,
we expect to have to make more than one loop around the ring
before we came back to the starting point, and in that process
we expect to visit "other" faces of the prismatic structure.
Such a structure can be built for a four-sided prismatic structure
with a suitable assembly of only 10 unit cubes, as shown below.
Three cubes in sequence form either a straight row or a small symmetrical L-shape. Four cubes in sequence can also form an asymmetrical L-shape with one leg twice as long as the other, or a planar "Z"/"S" jog structure, as well as a twisted Z-structure which may appear as a right-handed or as a left-handed version. It is the appearance of this twist element that basically carries a path on the surface of the prismatic structure from "one face" to "another". In the simplest case shown above, there is really only a single connected prism face. Since there is a single occurrence of the twisted Z, our path makes a twist of 90 degrees on every loop around the structure. It thus takes four loops to come back to the starting point, and during this traversal we will have visited all the exposed cube faces on the whole structure. Thus, a building in this particular shape could basically qualify to be a Moebius band if the client is willing to accept such a broad interpretation.
But let's assume that the client wants a "normal" Moebius band,
in which we return to the starting point after only two revolutions.
In this case, we have to introduce two twist elements into the loop,
so that the total prismatic twist around the loop becomes 180 degrees.
There are several basic configurations;
the twist elements could be in adjacent or in opposite corners of a square loop,
with the ribbon returning to the ground plane after each twist element,
so that the two 90-degrees twist add rather than subtract.
Alternatively, we could use an upwards path section as well as a downward section to form a twist element, but then we need to continue the horixontal path in the opposite direction from the original one. The path needs then be closed with either an S-shape through the middle of the vertical loop, as shown below, or with a spiral section around the outside of one of the vertical pillars.
Below are some of the sketches I did in trying to understand the essence
of a Moebius band for building design and the architectural possibilities
to demonstrate such a shape clearly, while still maintaining a shape
that is usable in a traditional way.
To give the building more of a "belt shape" where the "surface" faces are clearly distinguishable from the "edge" faces in our prismatic structure, we will make the cross section of the prism rectangular with a substantial aspec ratio, say at least 3:1. To further enhance the visual distinction between the two types of surfaces, one could make them of different materials, for instance, the wider surface could be made from a combination of steel and glass, and the narrower prism faces could be formed in concrete. The figure below shows a possible basic structure using such a 3:1 prism. In this figure we have put the two twist corners next to one another to minimize the length of the portion where the belt rectangle lies horizontal and where the steel/glass surfaces would have to cover the top and bottom of the building section. Alternatively, if the two types of surface treatments are about equally suited for the treatment of vertical and for horizontal surfaces, the two twist corners could again be placed at diagonally opposite positions, which would result in roughly equal portions of the building with a horizontal and with a vertical cross section.
To make a single, "more visible" edge that one can follow with the eye and convince oneself that there is indeed just one such edge and not two, we can enhance the small side of rectangle with some structure to yield a visibly prominent edge. Perhaps a wedge added to that face would do it. The wedge could be treated somewhat differently depending in what orientation it appears. As a first solution we might try to keep indeed a sharp edge at the apex of this wedge all around the building loop. Where the wedge runs at the side of the building, we might want to still have some windows in it; but for consistency we might then also want windows where the wedge forms an actual roof. Perhaps some differences in window treatment is permissible, and we might then have some mansardes on the roof portions and some different type of small bay windows sticking out from vertical wedge facades.
Alternatively we might want to split the wedge, and represent the single edge as a large "crease" or gap. When it is on top, the wedge would take the form of a gabeled roof, split into two halves with a space in between for air-handling units and other equipment that one typically finds on the roofs of large office buildings or in special louvered "penthouses". When the wedge runs on a vertical face, the gap could be used to place some recessed windows in it; these windows might be sufficient for staircases or for the ends of corridors.
I then started to look at the internal structure of the building and at the generic floor layouts. The ribbon forming the loop of the building has the thickness of two office lengths (15'+15') plus one corridor width (6'). The width of the ribbon is chosen to accommodate about 5-6 offices on a side and to yield an aspect ratio for the ribbon of at least 2:1. The elevators run on the inside edges of the pillars so that they can reach all the way to the top of the loop. The fire stairs will be placed at the outer edges in the loop. I found it rather difficult to fit stairs into the wedge-shape edge of the building, since I needed large enough landings at the end of the central corridors on each floor.
It also occurred to me that the fire marshall may insist on having
at least two stairs serving every floor portion in the pillars.
This would lead to some inefficiency of floor utilization
which might make it difficult to accommodate the 60% utilization rate
specified by the client.
Another problem is that the large bridge forming the upper part of the loop may lead to rather high construction costs.
I tried some variations on the concept to determine the range
of the size of the building and various ways to implement
the vertical loop and the horizontal spiral:
And here is the chosen shape analyzed with the slicer tool.
This time I tried to stay with a simple rectangular cross section
for the ribbon, to keep the loops as narrow as possible
and to avoid the potentially hard-to-use space at the "edges"
of the ribbon.
Here are some conceptual floor layouts:
The problem with this design is that it has too much of its massing
in the base which cannot be made much smaller.
To try to overcome this and to make the vertical structure more dramatic
in a 3-dimensional sense, I tried to put the two pillars at right angles
and to make the top curve follow a cone shape
(roughly pointing at the path of the sun).
This also reduces the size of the base.
This obviously presents some construction problems
for the floors in the cone section.
Also it is difficult to accommodate elevators
that go all the way to the top floor.
Thus here is a more angular variant:
In the vertical loop, the narrow side of the ribbon, will either hide elevators or fire stairs and on the top turn into a "roof" over the air-handling units. On the lobby floors closing the ribbon along the ground, the narrow edges are the main window fronts, and the wide glass walls of the vertical loop transition into the roof of this section. Picking materials that are distinct enough to make the form of the Moebius band clearly visible yet serve the different functions in the different parts of the building will be quite a challenge.
We read in the room specifications into the BDB and then regroup the given functions to make clusters of 5 faculty offices, a visitor office and a couple of administrative support offices. These we try to allocate to the top floors with the FSM. Next we formed some student office clusters and accommodate them in the pillar sections of the building. In some of the pillar sections we will also place the research labs close to the respective student office clusters. One pillar may have most of these labs stacked vertically on the back side towards Evans, while the other pillar will be mostly offices, accommodating the theory and software groups. In the latter floor sections we may place instead some discussion lounges or seminar rooms. On the two lobby floors, we accommodate all the instructional and administrative functions.