Hans
Walser, [20130821]

Tribar Spirals

# 1
The Tribar

Figure
1 shows the usual tribar.

Fig. 1:
The Tribar

The
tribar is an impossible structure, it cannot be realized in the three
dimensional world.

# 2
Spirals

Now we
try to extend the tribar into spirals.

## 2.1
Archimedean Tribar Spiral

Figure
2 shows the Archimedean tribar spiral.

Fig. 2:
Archimedean Tribar Spiral

We
have a real end in the center. All branches of the spiral have he same width. This
figure shows a *not *an impossible
structure.

We
explain this in a smaller version (Fig. 3). (The indicated numbers give the
total lengths of the edges, if the structure is built from unit cubes. The edge
lengths are multiples of three. )

Fig. 3:
Smaller Version

In
Figure 4 we have another view of the same structure. Clearly we see that this
is possible in the three dimensional world.

Fig. 4:
Other View

## 2.2
Logarithmic Tribar Spiral

In
Figure 5 we have a logarithmic tribar spiral. We have a point at infinity in
the center.

Fig. 5:
Logarithmic Tribar Spiral

Can
you imagine that this Spiral is constructible in the three dimensional world?

Figure
6 gives another version. It goes down and down.

Fig. 6:
Another Logarithmic Tribar Spiral

But
the perspective in Figure 6 is not correct.

Figure
7 gives a better, but still not correct version.

Fig. 7:
Staircase to Hell