In this paper, various Euler characteristic formulas for simplicial maps ar
e ob tained, which generalize the Izumiya-Marar formula [14], the Banchoff
triple point formula [3] and the formula due to Szucs for maps of surfaces
into 3-space [27]. Moreover, we obtain new results about the Euler characte
ristics of the multiple point sets anti the images of generic smooth maps a
nd the numbers of their singularities.