The bispectrum can quantify the non-Gussianity present in the redshifted 21-cm signal produced by the neutral hydrogen (⁠HI⁠) during the Epoch of Reionization (EoR). Motivated by this, we perform a comprehensive study of the EoR 21-cm bispectrum using simulated signals. Given a model of reionization, we demonstrate the behaviour of the bispectrum for all unique triangles in k space. For ease of identification of the unique triangles we parametrize the k-triangle space with two parameters, namely the ratio of the two arms of the triangle (n = k₂/k₁) and the cosine of the angle between them (cos θ). Furthermore, for the first time we quantify the impact of the redshift space distortions (RSD) on the spherically averaged EoR 21-cm bispectrum in the entire unique triangle space. We find that the real space signal bispectra for small and intermediate k₁-triangles (⁠k1≤0.6Mpc−1⁠) is negative in most of the unique triangle space. It takes a positive sign for squeezed, stretched, and linear k₁-triangles, specifically for large k₁ values (⁠k1≥0.6Mpc−1⁠). The RSD affects both the sign and magnitude of the bispectra significantly. It changes (increases/decreases) the magnitude of the bispectra by 50−100 per cent without changing its sign (mostly) during the entire period of the EoR for small and intermediate k₁-triangles. For larger k₁-triangles, RSD affects the magnitude by 100−200 per cent and also flips the sign from negative to positive. We conclude that it is important to take into account the impact of RSD for a correct interpretation of the EoR 21-cm bispectra.