by **
E. Hertel**

**Preprint series:**
00-09, Reports on Algebra and Geometry

**The paper is published:**
Jenaer Schriften zur Mathematik und Informatik, Math/Inf/00/22, Universität Jena, 2000

**MSC:**- 52B45 Dissections and valuations (Hilbert's third problem, etc.)
- 51N10 Affine analytic geometry

**Abstract:** A convex $n$-gon $\CP$ is called $k$-self-affine if $\CP$

can be dissected into $k \ge 2$ $n$-gons, each affine

equivalent to $\CP$.

Each triangle is trivially $k$-self-affine for all

$k \ge 2$. It is proved that for self-affine convex

$n$-gons holds $n \le 5$ and conjectured $n < 5$. For the

(only interesting) quadrangles first results for $k=2,3$

are given.

**Keywords:** *polygons, selfaffinity*

**Upload:** 2000-08-18

**Update:** 2000-08-21

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