Let (𝑋,𝑑) be a semimetric space. A permutation φ of the set 𝑋 is a combinatorial self similarity of (𝑋,𝑑) if there is a bijective function 𝑓 : 𝑑(𝑋 × 𝑋) → 𝑑(𝑋 × 𝑋) such that 𝑑(𝑥,𝑦) = 𝑓(𝑑(φ(𝑥),φ(𝑦))) for all 𝑥,𝑦 ∈ 𝑋. We describe the set of all semimetrics ρ on an arbitrary nonempty set 𝑌 for which every permutation of 𝑌 is a combinatorial self similarity of (𝑌,ρ).