The first pattern (the one on the bottom and top of the tablecloth), has reflective and rotational symmetry, and is called “Diamond Pattern”.
The second pattern (the middle of the carpet), has reflective and rotational symmetry.
Rosette Pattern: 4, Dihedral
The frieze pattern is going around on top of the cups / plate.
Frieze Pattern: The bulges on the headrest poles in the red rectangle in the image below is the frieze pattern.
Symmetries: Translation, Vertical Reflection, Horizontal Reflection
Rosette Pattern: The hanging light in the image below is a dihedral 8 figure. This figure can be rotated 8 times and has 8 reflection lines.
Symmetries: Rotation, Reflections