  The spectrum of the Dirichlet Laplacian on any quasi-conical open set
coincides with the non-negative semi-axis. We show that there is a connected
quasi-conical open set such that the respective Dirichlet Laplacian has a
positive (embedded) eigenvalue. This open set is constructed as the tower of
cubes of growing size connected by windows of vanishing size. Moreover, we show
that the sizes of the windows in this construction can be chosen so that the
absolutely continuous spectrum of the Dirichlet Laplacian is empty.
