Question: is there such thing as a 4d shape

Answer: Yes, When dimensional locations are given as ordered lists of numbers such as (t,x,y,z) they are called vectors or n-tuples. It is only when such locations are linked together into more complicated shapes that the full richness and geometric complexity of 4D and higher spaces emerges. A hint of that complexity can be seen in the accompanying animation of one of simplest possible 4D objects, the 4D cube or tesseract.