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We study the influence of the shape of compact dimensions to the Casimirenergy and Casimir force of a scalar field. We examine both the massive and themassless scalar field. The total spacetime topology is $M^D\timesT^2_{\theta}$, where $M^D$ is the $D$ dimensional Minkowski spacetime and$T^2_{\theta}$ the twisted torus described by $R_1$, $R_2$ and $\theta$. Forthe case $R_1=R_2$ we found that the massive bulk scalar field Casimir energyis singular for $D$=even and this singularity is $R$-dependent and remains evenwhen the force is calculated. Also the massless Casimir energy and force isregular only for D=4 (!). This is very interesting phenomenologically. Weexamine the energy and force as a function of $\theta$. Also we address thestabilization problem of the compact space. We also briefly discuss somephenomenological implications.

The Shape of Compact Toroidal Dimensions $T^d_{\theta}$ and the Casimir Effect on $M^D\times T^d_{\theta}$ spacetime