While common image object detection tasks focus on bounding boxes or segmentation masks as object representations, we consider the problem of finding objects based on four arbitrary vertices. We propose a novel model, named TetraPackNet, to tackle this problem. TetraPackNet is based on CornerNet and uses similar algorithms and ideas. It is designated for applications requiring high-accuracy detection of regularly shaped objects, which is the case in the logistics use-case of packaging structure recognition. We evaluate our model on our specific real-world dataset for this use-case. Baselined against a previous solution, consisting of a Mask R-CNN model and suitable post-processing steps, TetraPackNet achieves superior results (9% higher in accuracy) in the sub-task of four-corner based transport unit side detection.