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 ($n=k_2/k_1$) and the cosine of the angle between them ($cos{theta}$). 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 $k_1$-triangles ($k_1 leq 0.6 ,{rm Mpc^{-1}}$) is negative in most of the unique triangle space. It takes a positive sign for squeezed, stretched and linear $k_1$-triangles, specifically for large $k_1$ values ($k_1 geq 0.6 ,{rm Mpc^{-1}}$). The RSD affects both the sign and magnitude of the bispectra significantly. It changes (increases/decreases) the magnitude of the bispectra by $50-100%$ without changing its sign (mostly) during the entire period of the EoR for small and intermediate $k_1$-triangles. For larger $k_1$-triangles, RSD affects the magnitude by $100-200%$ 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.
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