Thanks. As a curiosity, plotting the normal around that new strip seems to indicate that it is orientable?
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Would you mind sharing the code for that normal vector?
The orientability depends on the parity of the number of twists.
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That depends on how many times the band is twisted before it is glued back together.
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Depends whether it is an even or an odd number of turns 
, factor 3s corresponds to 6 turns which is even, here is s/2 one turn
lower = [Point3f0(.2cos(s/2),0.0, 0.0) .+ (1 + 0.2sin(s/2))*Point3f0(0, cos(s), sin(s)) for s in t]
upper = [Point3f0(-.2cos(s/2),0.0, 0.0) .+ (1 - 0.2sin(s/2)).*Point3f0(0, cos(s), sin(s)) for s in t]
band(lower, upper, color = [1.0:length(t); length(t):-1:1.0], show_axis=false)
Not orientable. I also do a little trick with the colouring.
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@dpsanders, the code is the same as in the Mobius strip further above (using the partial derivatives and cross product). Just changed M(u,v) consistently with @mschauer’s strip definition:
M(u,v) = (v/2*cos(3u), (r + v/2*sin(3u))*cos(u), (r + v/2*sin(3u))*sin(u)) # other strip by @mschauer
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