Faces are critical in establishing the agency of social robots; however, building expressive mechanical faces is costly and difficult. Instead, many robots built in recent years have faces that are rendered onto a screen. This gives great flexibility in what a robot's face can be and opens up a new design space with which to establish a robot's character and perceived properties. Despite the prevalence of robots with rendered faces, there are no systematic explorations of this design space. Our work aims to fill that gap. We conducted a survey and identified 157 robots with rendered faces and coded them in terms of 76 properties. We present statistics, common patterns, and observations about this data set of faces. Next, we conducted two surveys to understand people's perceptions of rendered robot faces and identify the impact of different face features. Survey results indicate preferences for varying levels of realism and detail in robot faces based on context, and indicate how the presence or absence of specific features affects perception of the face and the types of jobs the face would be appropriate for.