## 1 Introduction and Scope  
Stereographic projection methods have been widely extended to slope analysis in jointed rocks and the possible failure modes [1] since the first studies by [PERSON] in 1972 [2] and [PERSON] in 1968, 1972 [3, 4]. Although 40 years have passed since these works were published and powerful computer tools have been developed, stereographic projection in block kinematic analysis is still current. Stereographic projection allows a quick view of the possible failure modes of the slope, such as planar, wedge, and toppling, and reduces the analyzed elements to one dimension: planes to curves, straight lines to points, etc. This research focuses on an analysis of the three-dimensional geometry of slopes with several faces, which has not been much studied in the literature [1].  
Most kinematic analyses of rock slopes only consider the fact that the slope face has a constant strike (single-faced SPS) [5]. In 2002, [PERSON] et al. [5] introduced the concept of and kinematic criterion for multifaceted (also known as multi-faced) slope MFS failure in an intuitive and highly effective way by focusing on the analysis of planes and vectors, not on the pole criterion, which is the most common method [1].  
_\"In stereographic projection, the sliding envelope of a multi faced slope (MFS) is the union of single-face envelopes formed on the surface of the slope\"_ ([PERSON] et al. [5]). [PERSON] et al. [1] proposed to combine the methodology for multi-faced slopes [5] with the most usual approach for the kinematic assessment of single-faced slope daylight envelope and pole analysis [6, 7].  
The aim of this research is to show a real case of a failed slope for which the stability assessment can only be explained using a methodology that unifies the traditional criteria for rock-slope analysis based on poles [6, 7, 8, 9] with the conclusions of the work of [PERSON] et al. [5] for MFS, where the criteria for instability were defined using the representation of the polesof the plane approach. The unstable sector in stereographic projection is defined using poles and daylight envelopes [1] instead of planes [5]. The conventional kinematic analysis using constant-strike slopes cannot explain or assess this case. The suggested methodology for the back analysis is effective in explaining the mechanism of planar failure of real slopes, for example, the slate rocks on the Manta coast of Ecuador, and can be extrapolated to other slopes on the Spondylus coast, many of which are typical situations of multi-faced slopes (MFS). The coast of Ecuador, like other coasts with outcrops of marked stratification (Flysch de Zumaia in Spain), presents inlets and outlets, the analysis of which can be approached with the MFS methodology that we propose in this work. There are few studies on the kinematic stability of rocky slopes in Ecuador [10; 11; 12]. This work reinforces the database and the methodology proposed by [PERSON] et al. [5] for the Andean zone.  
The stability of rock slopes in superficial situations in relatively competent rock masses is usually controlled by the equilibrium of the blocks that form them. This equilibrium is normally studied using kinematic assessment methods that only consider the friction of the most relevant joints and their orientation with respect to the slope. The main contribution and objective of this study is to apply the aforementioned approach to a real slope and verify its effectiveness. It is important to note that this is the first application of this methodology in the Andes, a mountain range with complex slope stability problems, many of which are difficult to model. This study demonstrates that this methodology can be an effective stability methodology.