  Three-dimensional icosahedral random tilings with rhombohedral cells are
studied in the semi-entropic model. We introduce a global energy measure
defined by the variance of the quasilattice points in the orthogonal space. The
internal energy, the specific heat, the configuration entropy and the sheet
magnetization (as defined by Dotera and Steinhardt [Phys.Rev.Lett. 72 (1994)
1670]) have been calculated. The specific heat shows a Schottky anomaly which
might indicate a phase transition from an ordered quasicrystal to a random
tiling. But the divergence with the sample size as well as the divergence of
the susceptibility are too small to pinpoint the phase transition conclusively.
The self-diffusion coefficients closely follow an Arrhenius law, but show
plateaus at intermediate temperature ranges which are explained by energy
barriers between different tiling configurations due to the harmonic energy
measure. There exists a correlation between the temperature behavior of the
self-diffusion coefficient and the frequency of vertices which are able to flip
(simpletons). Furthermore we demonstrate that the radial distribution function
and the radial structure factor only depend slightly on the random tiling
configuration. Hence, radially symmetric pair potentials lead to an energetical
equidistribution of all configurations of a canonical random tiling ensemble
and do not enforce matching rules.
