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I consider the $\mathbb{Z}_\lambda,$ $\lambda$ prime free-bosonic permutationorbifolds as interacting physical string systems at $\hat{c} = 26\lambda $. Asa first step, I introduce twisted tree diagrams which confirm at theinteracting level that the physical spectrum of each twisted sector isequivalent to that of an ordinary $c=26$ closed string. The untwisted sectorsare surprisingly more difficult to understand, and there are subtleties in thesewing of the loops, but I am able to propose provisional forms for the fullmodular-invariant cosmological constants and one-loop diagrams with insertions.

The Orbifolds of Permutation-Type as Physical String Systems at Multiples of $\mathbf{c=26}$ V. Cyclic Permutation Orbifolds