In this paper we study 3-dimensional visibility representations of complete graphs. The vertices are represented by equal
regular polygons lying in planes parallel to the
xy-plane. Two vertices are adjacent if and only if the two corresponding polygons see each other - i.e. it is possible to construct
an abscissa perpendicular to the
xy-plane connecting the two polygons and avoiding all the others.
We give the bounds for the maximal size f(k) of a clique represented by regular
k-gons:
$
\left\lfloor {\tfrac{{k + 1}}
{2}} \right\rfloor + 2 \leqslant f(k) \leqslant 2^{2^k }
$
\left\lfloor {\tfrac{{k + 1}}
{2}} \right\rfloor + 2 \leqslant f(k) \leqslant 2^{2^k }
and we present a particular result for triangles:
f(3) ≥ 14.
Research supported by grant GAUK 159/99.