Journal for Geometry and Graphics 21 (2017), No. 2, 141--152
Copyright Heldermann Verlag 2017
Simplicial Surfaces Controlled by One Triangle
Karl-Heinz Brakhage
Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany
brakhage@igpm.rwth-aachen.de
Alice C. Niemeyer
Lehrstuhl B für Mathematik, RWTH Aachen, Pontdriesch 10--16, 52062 Aachen, Germany
alice.niemeyer@mathb.rwth-aachen.de
Wilhelm Plesken
Lehrstuhl B für Mathematik, RWTH Aachen, Pontdriesch 10--16, 52062 Aachen, Germany
wilhelm.plesken@mathb.rwth-aachen.de
Ansgar Strzelczyk
Lehrstuhl B für Mathematik, RWTH Aachen, Pontdriesch 10--16, 52062 Aachen, Germany
ansgar.strzelczyk@mathb.rwth-aachen.de
Embeddings of combinatorial closed simplicial surfaces in Euclidean 3-space with all triangles congruent to one control triangle are investigated, where the control triangle may vary. Definitions and general methods for construction and classification are outlined. For one infinite family of combinatorial surfaces its dihedral symmetry is used to construct all embeddings and to characterize the possible congruence classes of the control triangle. The investigation is motivated by problems in rigid origami.
Keywords: Simplicial surfaces, polytopes, moduli spaces, origami, tesselations, symmetry.
MSC: 52B10; 51M20, 52B15
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