
TL;DR
This paper characterizes cyclic quadrilaterals that are reptiles, proving they must be trapezoids, and concludes that all convex reptiles are either triangles or trapezoids, advancing understanding of polygon decomposition.
Contribution
It proves that cyclic quadrilaterals that are reptiles are trapezoids and classifies all convex reptiles as triangles or trapezoids, extending prior results.
Findings
Cyclic reptile quadrilaterals are trapezoids.
All convex reptiles are triangles or trapezoids.
Provides a classification of convex reptile polygons.
Abstract
A polygon is called a reptile, if it can be decomposed into nonoverlapping and congruent polygons similar to . We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of U. Betke and I. Osburg we find that every convex reptile is a triangle or a trapezoid.
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Taxonomy
TopicsAdvanced Materials and Mechanics · Geometric and Algebraic Topology · Point processes and geometric inequalities
