We study continuum percolation of three-dimensional randomly oriented soft-core polyhedra (prisms). The prisms are biaxial or triaxial and range in aspect ratio over 6 orders of magnitude. Results for prisms are compared with studies for ellipsoids, rods, ellipses, and polygons and differences are explained using the concept of the average excluded volume, $\left\langle v_{ex} \right\rangle$. For large shape anisotropies we find close agreement between prisms and most of the above mentioned shapes for the critical total average excluded volume, $n_c\left\langle v_{ex} \right\rangle$, where $n_c$ is the critical number density of objects at the percolation threshold. In the extreme oblate and prolate limits simulations yield $n_c\left\langle v_{ex} \right\rangle \approx 2.3$ and $n_c\left\langle v_{ex} \right\rangle \approx 1.3$, respectively. Cubes exhibit the lowest shape anisotropy of prisms minimizing the importance of randomness in orientation. As a result, the maximum prism value, $n_c\left\langle v_{ex} \right\rangle \approx 2.79$, is reached for cubes, a value close to $n_c\left\langle v_{ex} \right\rangle = 2.8$ for the most equant shape, a sphere. Similarly, cubes yield a maximum critical object volume fraction of $\phi_c = 0.22$. $\phi_c$ decreases for more prolate and oblate prisms and reaches a linear relationship with respect to aspect ratio for aspect ratios greater than about 50. Curves of $\phi_c$ as a function of aspect ratio for prisms and ellipsoids are offset at low shape anisotropies but converge in the extreme oblate and prolate limits. The offset appears to be a function of the ratio of the normalized average excluded volume for ellipsoids over that for prisms, $R = \left\langle \overline{v_{ex}} \right\rangle_e / \left\langle \overline{v_{ex}} \right\rangle_p$. This ratio is at its minimum of $R = 0.758$ for spheres and cubes, where $\phi_{c(sphere)}=0.2896$ may be related to $\phi_{c(cube)}=0.22$ by $\phi_{c(cube)} = 1 - [1 - \phi_{c(sphere)}]^R = 0.23$. With respect to biaxial prisms, triaxial prisms show increased normalized average excluded volumes, $\left\langle \overline{v_{ex}} \right\rangle$, due to increased shape anisotropies, resulting in reduced values of $\phi_c$. We confirm that $B_c = n_c\left\langle v_{ex} \right\rangle = 2C_c$ applies to prisms, where $B_c$ and $C_c$ are the average number of bonds per object and average number of connections per object, respectively.

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