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Table 1:

Statistical characteristics of coefficients ai of the dominant (ith order) term in the radial and orthogonal components of the residual acceleration $\ddot{r}$ in perfectly regular well-proportioned spaces, for approximately isotropic displacements $\vec{r}$a.
space $\mbox{term}^{b}$ $\parallel/\perp^{c}$ $\left<a_i\right>$ $\sigma_{\left<a_i\right>}^{d}$ $\sigma_i^{e}$ $\gamma_i^{f}$
3-torus (r/La)3 $\parallel$ 0.00 0.00 6.11 0.58
3-torus (r/La)3 $\perp$ 6.39 0.00 6.82 -0.42
octahedral $(r/R_{{\rm C}})^3$ $\parallel$ 0.01 0.01 3.18 -0.58
octahedral $(r/R_{{\rm C}})^3$ $\perp$ 3.33 0.00 1.26 -0.42
${\rm tr. cube}$ $(r/R_{{\rm C}})^3$ $\parallel$ -0.05 0.05 14.24 0.58
${\rm tr. cube}$ $(r/R_{{\rm C}})^3$ $\perp$ 14.94 0.02 5.63 -0.42
${\rm dodec/num}^{g}$ $(r/R_{{\rm C}})^5$ $\parallel$ -0.30 0.53 288.29 0.75
${\rm dodec/alg}^{h}$ $(r/R_{{\rm C}})^5$ $\parallel$ 0.00 0.01 288.26 0.74
${\rm dodec/num}^{g}$ $(r/R_{{\rm C}})^5$ $\perp$ 286.33 0.22 121.65 -0.37
a Coefficients ai as defined in Eqs. (14), (19), and (20); these are approximately constant with respect to r; the constant factor of Gm/La2 for the T3 model or  $Gm/R_{{\rm C}}^2$ for the other models has been ignored here; all values shown are dimensionless.
b Dominant ith power of displacement, as derived in this paper.
c Radial $\parallel$ or orthogonal $\perp$ component.
d Standard error in the mean $\sigma_{\left<a_i\right>} = \sigma_i/\sqrt{N-1}$ for $N \gg 1 $ test particles.
e Sample standard deviation.
f Sample skewness $\gamma_i = \left<[(a_i- \left<a_i\right>)/\sigma_i]^3 \right>$.
g From 70-bit significand numerical calculations using Eq. (9).
h Using the algebraic expression in Eq. (21).

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