Any convex cone has an accumulation point in the base by the action of its automorphism group. In this paper, we prove the converse of this statement, more precisely, a convex domain $\Omega$ with a face $F$ of codimension 1 is a cone over $F$ if there is an Aut($\Omega$)-orbit accumulating at a point of $F$.
Proc. Japan Acad. Ser. A Math. Sci.
84(10):
175-178
(December 2008).
DOI: 10.3792/pjaa.84.175
