Abstract:
The closed non-self-intersecting geodesics on the surface of
a three-dimensional simplex are studied. It is proved that
every geodesic on an arbitrary simplex can be realized on a regular
simplex. This enables us to obtain a complete classification of all
geodesics and describe their structure. Conditions for the existence
of geodesics are obtained for an arbitrary simplex. It is proved that
a simplex has infinitely many essentially different geodesics if and
only if it is isohedral. Estimates for the number of geodesics are
obtained for other simplexes.
Bibliography: 13 titles.
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