Odd twists

It occurred to me about a week and a half ago that if you unpaste a Moebius strip and twist it a second time before repasting the ends together, the strip again has two separate surfaces. And, if you [unpaste and] twist it a third time [then repaste it], it has but one again.

I wonder, Did God
command that the number of twists
be odd?

Why is there the quirk
that the Moebius band won't,
even, work?

I'd like for there to be some profound metaphysical significance in this, maybe even something bearing on Howard Nemerov's "Myth of Creation on a Moebius Band." Surely there is...or at least maybe I can make up something, cobble it together using my imagination and powers of reasoning? For isn't significance essentially a matter of a person's exercising curiosity and creativity to bring it into being? Everyone has the potential to be a philosopher or a poet.
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Odd twist:one surface; even twist:two surfaces:

1:1, 2:2, 3:1, 4:2, 5:1, 6:2, 7:1, 8:2, 9:1, 10:2...

Sequence of ratios:

1, 1, 3, 2, 5, 3, 7, 4, 9, 5...

Sequence of sums:

2, 4, 4, 6, 6, 8, 8, 10, 10, 12...

Sequence of differences:

0, 0, 2, 2, 4, 4, 6, 6, 8, 8...

Sequence of products:

1, 4, 3, 8, 5, 12, 7, 16, 9, 20...