An immersed surface in 3-space is a surface with double curves and isolated triple points. In general, immersed surfaces in 3-space are not images of embedded surface in 4-space under the orthogonal projection. In this paper, we present a sufficient condition about a triple point for an immersed surface to become an unliftable surface into 4‑space. Also we construct an orientable unliftable immersed sphere.

immersion, surface, liftable immersion.