  Three-dimensional icosahedral random tilings are studied in the semi-entropic
model. We introduce a global energy measure defined by the variance of the
quasilattice points in orthogonal space. The specific heat shows a pronounced
Schottky type anomaly, but it does not diverge with sample size. The flip
susceptibility as defined by Dotera and Steinhardt [Phys. Rev. Lett. 72, 1670
(1994)] diverges and shifts to lower temperatures, thus indicating a transition
at T=0. Contrary to the Kalugin-Katz conjecture, the self-diffusion shows a
plateau at intermediate temperature ranges which is explained by energy
barriers and a changing number of flipable configurations.
