The Beautiful Geometry of Soap

The Shape Japer can transform into any shape, including the whatchama-hedron you mentioned (although more complex shapes are more difficult as they require more mental calculation and energy to maintain). As much as they would like to, her three-dimensional body only has the capacity to transform into three-dimensional shapes, so she can't transform into four-dimensional shapes such as a tesseract. She also cannot properly transform into shapes with holes in them, such as tori, because homeomorphism something something. They'd probably lose an eye if they tried.

3D shapes yeee