Final answer:
Marble is the metamorphic rock among the options that does not display foliation, unlike slate, schist, and gneiss, which all have a foliated texture.
Step-by-step explanation:
The metamorphic rock that does not display foliation is marble. Foliation is a texture in metamorphic rocks where mineral crystals are aligned with each other, often showing as parallel planes or bands. This is seen in rocks such as slate, schist, and gneiss. Marble, conversely, does not show this alignment of minerals; instead, its crystals grow in many directions, resulting in a non-foliated texture that appears massive and often structureless. While foliated rocks like slate form from low-grade metamorphism of shale, and gneiss forms from higher-grade metamorphism of schists or granites showing distinct banding, marble forms from the metamorphism of limestone or dolostone, and its appearance is generally uniform without a layered structure.