Workshop on Dynamical Systems and Aperiodic Order
Bielefeld University, Germany
14th - 17th March 2011
All talks take place in Room V3-201 ("Common Room") in the Bielefeld
University main building.
Click here for
a description of the main building.
Toward classification of spherical tilings by congruent
quadrangles
Yudai Sakano
Abstract:
Ueno-Agaoka provided an exhaustive classification of spherical tilings
by congruent triangles, and proved that for spherical tilings by
congruent quadrangles, the proto tile has at least two edges of the
same length. In this talk, we are concerned with classifications of
spherical tilings by congruent quadrangles. For the spherical tilings
by congruent quadrangles that are divided into two congruent
triangles, we completed an exhaustive classification by using the
Ueno-Agaoka's classification. For the spherical tilings by congruent
convex quadrangles that are not divided into two congruent triangles,
we completed classification so long as the number of faces are 6 or 8,
and generalize the classification for the case the number of faces is
even.
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