Such a uniform shrinking of simplices is known to be necessary in order for piecewise flat manifolds to approach their continuum counterparts . On the 44-lattice, with the -measure and , they determined for decreasing . For small , the choice of seems to have only little influence, but towards the transition point , simultaneously decreases. Next they investigated a variety of measures of the form (see also ). For , only a mild -dependence of is observed as . However, for , there are significant differences for the entire range of , and some evidence that the geometry degenerates.
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